Academic literature on the topic 'Soft set theor'

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Journal articles on the topic "Soft set theor"

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Edi, Sutoyo, Tri Riyadi Yanto Iwan, Rohmat Saedudin Rd, and Herawan Tutut. "A Soft Set-based Co-occurrence for Clustering Web User Transactions." TELKOMNIKA Telecommunication, Computing, Electronics and Control 15, no. 3 (2017): 1344–53. https://doi.org/10.12928/TELKOMNIKA.v15i3.6382.

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Grouping web transactions into some clusters are essential to gain a better understanding the behavior of the users, which e-commerce companies widely use this grouping process. Therefore, clustering web transaction is important even though it is challenging data mining issue. The problems arise because there is uncertainty when forming clusters. Clustering web user transaction has used the rough set theory for managing uncertainty in the clustering process. However, it suffers from high computational complexity and low cluster purity. In this study, we propose a soft set-based co-occurrence for clustering web user transactions. Unlike rough set approach that uses similarity approach, the novelty of this approach uses a co-occurrence approach of soft set theory. We compare the proposed approach and rough set approaches regarding computational complexity and cluster purity. The result demonstrates better performance and is more effective so that lower computational complexity is achieved with the improvement more than 100% and cluster purity is higher as compared to two previous rough set-based approaches.
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Atiqe, Ur Rahman, Saeed Muhammad, and Zahid Saba. "Application in decision making based on fuzzy parameterized hypersoft set theory." Asia Mathematika 5, no. 1 (2021): 19–27. https://doi.org/10.5281/zenodo.4721481.

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Hypersoft set is the generalization of the soft set as it converts single attribute function to multi-attribute function. The core purpose of this study is to make the existing literature regarding fuzzy parameterized soft set in line with the need for multi-attribute function. We first conceptualize the fuzzy parameterized hypersoft set along with some of its fundamentals. Then we propose a decision-making-based algorithm with the help of this theory. Moreover, an illustrative example is presented which depicts its validity for successful application to the problems involving vagueness and uncertainties.
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Atiqe, Ur Rahman, Saeed Muhammad, Ihsan Muhammad, Arshad Muhammad, and Ayaz Sehrish. "A CONCEPTUAL FRAMEWORK OF m-CONVEX AND m-CONCAVE SETS UNDER SOFT SET ENVIRONMENT WITH PROPERTIES." Transactions in Mathematical and Computational Sciences 1, no. 1 (2021): 50–60. https://doi.org/10.5281/zenodo.4743406.

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In this paper, the classical notions of m-convex and m-concave sets are characterized under soft set environment and their important aggregation operations are discussed. Moreover, certain classical approaches (i.e. first and second senses) are employed on m-convex and m-concave soft sets to get more generalized results for uncertain scenarios.
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Saraf, Saakshi. "Survey or Review on Soft Set Theory and Development." SIJ Transactions on Computer Science Engineering & its Applications (CSEA) 01, no. 03 (2013): 01–08. http://dx.doi.org/10.9756/sijcsea/v1i3/0103510101.

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E., E. Edeghagba, I. Abubakar S., M. Umar F., and Abdullahi M. "Full Fuzzy parameterized Soft Expert Set with Application to Decision Making." International Journal of Mathematical Sciences and Optimization: Theory and Applications 10, no. 4 (2024): 12–28. https://doi.org/10.5281/zenodo.14685917.

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In this work, the authors consider a generalization of fuzzy parameterized soft expert set introducing the concept of full fuzzy parameterized soft expert set and study their properties. We define its basic operations and develop an algorithm to demonstrate its application in decision making. We also define the optimal choice object, developing and proving propositions relating to it. Finally, we use a concrete example to illustrate our algorithm.
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Anjan, Mukherjee1 and Ajoy Kanti Das2. "On Fuzzy Soft Multi Set and Its Application in Information Systems." International Journal of Computer-Aided Technologies (IJCAx) 02, Jul (2015): 01–18. https://doi.org/10.5121/ijcax.2015.2303.

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Research on information and communication technologies have been developed rapidly since it can be applied easily to several areas like computer science, medical science, economics, environments, engineering, among other. Applications of soft set theory, especially in information systems have been found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with respect to these newly defined operations. In this paper, we extend their work and study some more basic properties of their defined operations. Also, we define some basic supporting tools in information system also application of fuzzy soft multi sets in information system are presented and discussed. Here we define the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy soft multi set is a fuzzy multi valued information system.
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Anjan, Mukherjee1 and Ajoy Kanti Das2. "On Fuzzy Soft Multi Set and Its Application in Information Systems." International Journal of Computer-Aided technologies (IJCAx) 2, no. 3 (2023): 29. https://doi.org/10.5281/zenodo.8256282.

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Research on information and communication technologies have been developed rapidly since it can be applied easily to several areas like computer science, medical science, economics, environments, engineering, among other. Applications of soft set theory, especially in information systems have been found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with respect to these newly defined operations. In this paper, we extend their work and study some more basic properties of their defined operations. Also, we define some basic supporting tools in information system also application of fuzzy soft multi sets in information system are presented and discussed. Here we define the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy soft multi set is a fuzzy multi valued information system.
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Maji, P. K., R. Biswas, and A. R. Roy. "Soft set theory." Computers & Mathematics with Applications 45, no. 4-5 (2003): 555–62. http://dx.doi.org/10.1016/s0898-1221(03)00016-6.

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Muhammad, Saeed, Amad Sarwar Muhammad, Ur Rahman Atiqe, and Naz Maqbool Sana. "Representation of Fuzzy Hypersoft Set in Graphs." Palestine Journal of Mathematics 12, no. 1 (2023): 836–47. https://doi.org/10.5281/zenodo.7751699.

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In this study, a novel framework of fuzzy hypersoft graphs (FHS-graphs) is developed which is more flexible as compared to fuzzy soft graphs (FS-graphs) in the sense that it not only generalizes FS-graphs but also tackles its insufficiency for multi-argument approximate function. Some fundamentals, aggregation operations and results are investigated and elaborated with appropriate examples and their graphical depictions.
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V., Chinnadurai, Swaminathan A., and Anu B. "SOME PROPERTIES OF CUBIC SOFT SETS." International Journal of Applied and Advanced Scientific Research 1, no. 1 (2016): 145–53. https://doi.org/10.5281/zenodo.167568.

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The notion of cubic soft sets P-union, P-intersection, are introduced and their related properties are investigated. We discussed about the commutative and absorption property along with examples and also discussed the internal and external cubic soft sets.
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Dissertations / Theses on the topic "Soft set theor"

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Abbas, Mujahid. "Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications." Doctoral thesis, Universitat Politècnica de València, 2015. http://hdl.handle.net/10251/48470.

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Mathematical models have extensively been used in problems related to engineering, computer sciences, economics, social, natural and medical sciences etc. It has become very common to use mathematical tools to solve, study the behavior and different aspects of a system and its different subsystems. Because of various uncertainties arising in real world situations, methods of classical mathematics may not be successfully applied to solve them. Thus, new mathematical theories such as probability theory and fuzzy set theory have been introduced by mathematicians and computer scientists to handle the problems associated with the uncertainties of a model. But there are certain deficiencies pertaining to the parametrization in fuzzy set theory. Soft set theory aims to provide enough tools in the form of parameters to deal with the uncertainty in a data and to represent it in a useful way. The distinguishing attribute of soft set theory is that unlike probability theory and fuzzy set theory, it does not uphold a precise quantity. This attribute has facilitated applications in decision making, demand analysis, forecasting, information sciences, mathematics and other disciplines. In this thesis we will discuss several algebraic and topological properties of soft sets and fuzzy soft sets. Since soft sets can be considered as setvalued maps, the study of fixed point theory for multivalued maps on soft topological spaces and on other related structures will be also explored. The contributions of the study carried out in this thesis can be summarized as follows: i) Revisit of basic operations in soft set theory and proving some new results based on these modifications which would certainly set a new dimension to explore this theory further and would help to extend its limits further in different directions. Our findings can be applied to develop and modify the existing literature on soft topological spaces ii) Defining some new classes of mappings and then proving the existence and uniqueness of such mappings which can be viewed as a positive contribution towards an advancement of metric fixed point theory iii) Initiative of soft fixed point theory in framework of soft metric spaces and proving the results lying at the intersection of soft set theory and fixed point theory which would help in establishing a bridge between these two flourishing areas of research. iv) This study is also a starting point for the future research in the area of fuzzy soft fixed point theory.<br>Abbas, M. (2014). Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48470<br>TESIS
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Saeed, Mehreen. "Soft AI methods and visual speech recognition." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299270.

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Hill, Carla. "Mass assignments for inductive logic programming." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325748.

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Hoang, Xuan Ben [Verfasser]. "Soft coral (Octocorallia, Alcyonacea) diversity and distribution along a latitudinal environmental gradient and the role of their chemical defense against predatory fish in the Red Sea / Hoang Xuan Ben." Kiel : Universitätsbibliothek Kiel, 2014. http://d-nb.info/1062947932/34.

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Khaleghi, Bahador. "Distributed Random Set Theoretic Soft/Hard Data Fusion." Thesis, 2012. http://hdl.handle.net/10012/6842.

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Research on multisensor data fusion aims at providing the enabling technology to combine information from several sources in order to form a unifi ed picture. The literature work on fusion of conventional data provided by non-human (hard) sensors is vast and well-established. In comparison to conventional fusion systems where input data are generated by calibrated electronic sensor systems with well-defi ned characteristics, research on soft data fusion considers combining human-based data expressed preferably in unconstrained natural language form. Fusion of soft and hard data is even more challenging, yet necessary in some applications, and has received little attention in the past. Due to being a rather new area of research, soft/hard data fusion is still in a edging stage with even its challenging problems yet to be adequately de fined and explored. This dissertation develops a framework to enable fusion of both soft and hard data with the Random Set (RS) theory as the underlying mathematical foundation. Random set theory is an emerging theory within the data fusion community that, due to its powerful representational and computational capabilities, is gaining more and more attention among the data fusion researchers. Motivated by the unique characteristics of the random set theory and the main challenge of soft/hard data fusion systems, i.e. the need for a unifying framework capable of processing both unconventional soft data and conventional hard data, this dissertation argues in favor of a random set theoretic approach as the first step towards realizing a soft/hard data fusion framework. Several challenging problems related to soft/hard fusion systems are addressed in the proposed framework. First, an extension of the well-known Kalman lter within random set theory, called Kalman evidential filter (KEF), is adopted as a common data processing framework for both soft and hard data. Second, a novel ontology (syntax+semantics) is developed to allow for modeling soft (human-generated) data assuming target tracking as the application. Third, as soft/hard data fusion is mostly aimed at large networks of information processing, a new approach is proposed to enable distributed estimation of soft, as well as hard data, addressing the scalability requirement of such fusion systems. Fourth, a method for modeling trust in the human agents is developed, which enables the fusion system to protect itself from erroneous/misleading soft data through discounting such data on-the-fly. Fifth, leveraging the recent developments in the RS theoretic data fusion literature a novel soft data association algorithm is developed and deployed to extend the proposed target tracking framework into multi-target tracking case. Finally, the multi-target tracking framework is complemented by introducing a distributed classi fication approach applicable to target classes described with soft human-generated data. In addition, this dissertation presents a novel data-centric taxonomy of data fusion methodologies. In particular, several categories of fusion algorithms have been identifi ed and discussed based on the data-related challenging aspect(s) addressed. It is intended to provide the reader with a generic and comprehensive view of the contemporary data fusion literature, which could also serve as a reference for data fusion practitioners by providing them with conducive design guidelines, in terms of algorithm choice, regarding the specifi c data-related challenges expected in a given application.
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Hsu, Hua-Chi, and 徐華騏. "Stream flood forecasting using a soft-computing approach (neural networks and fuzzy set theory)--A case study of Wu-Tu basin." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/93037991270334908944.

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碩士<br>清雲科技大學<br>土木與防災研究所<br>96<br>The weather in Taiwan is high precipitation, and the heavy rainfall is generally in the typhoon season. Therefore, how to forecast stream flow is a worthy research subject for hydraulic engineers to avoid damages by typhoon. In this study, a flow-trend index based on the fuzzy set theory is developed for neural network models to systematically establish the relationship between the rainfall history and stream flow. The precipitation records of Wu-Tu including 18 typhoon events from 1973 to 2001 are used to train and test the stream flow forecasting model. The computing results indicate that the neural network using the flow-trend index is effective in the stream flow predictions.
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Shu, Hua-Chi, and 徐華騏. "Stream flood forecasting using a soft-computing approach (neural networks and fuzzy set theory)--A case study of Wu-Tu basin." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/08429472489760610812.

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碩士<br>清雲科技大學<br>空間資訊與防災科技研究所<br>96<br>The weather in Taiwan is high precipitation, and the heavy rainfall is generally in the typhoon season. Therefore, how to forecast stream flow is a worthy research subject for hydraulic engineers to avoid damages by typhoon. In this study, a flow-trend index based on the fuzzy set theory is developed for neural network models to systematically establish the relationship between the rainfall history and stream flow. The precipitation records of Wu-Tu including 18 typhoon events from 1973 to 2001 are used to train and test the stream flow forecasting model. The computing results indicate that the neural network using the flow-trend index is effective in the stream flow predictions.
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Chang, Kai-Ming, and 張凱銘. "Study on U.S.-China Strategic Competitions in the South China Sea: Viewed from the Perspective of Soft Balancing Theory, 2009-2014." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/eb44d6.

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博士<br>國立中興大學<br>國際政治研究所<br>102<br>South China Sea sovereignty disputes are one of the most important security issues in the Asia Pacific region. Due to the complex relationships between the states involved, however, an effective solution has been impossible since a long time ago. The return of the United States to the Asia Pacific region and its reinforced involvement in local disputes over the past few years have gradually led to its increased interaction and confrontation with China, one of the parties to the disputes. To explore the competitions between the US and China in the South China Sea disputes, this thesis follows the theoretical model of realism and "balancing" theory. The “soft balancing” theory is adopted as the research approach in this study to analyze the motivations for striking a balance between the two states in current South China Sea disputes and examine the various kinds of "soft balancing" actions taken by the two states against each other. This thesis firstly explores the significance of “soft balancing” theory, and clarify the motives and manipulation patterns when states apply “soft balancing” in international politics. Secondly, the interactions between the US and China in the South China Sea will be explored at the strategic level, followed by the descriptions of their motivations and disputes. Finally, the various "soft balancing" actions taken by the US and China are examined and evaluated according to their utilities and traits. This research reveals that the South China Sea and local sovereignty disputes are highly valuable in the strategic planning of both the US and China. Nevertheless, the contradictory positions of the two states have remained. In light of their extensive common and conflicting interests, along with the potential perceptions of threats, nevertheless, both the US and China tend to apply relatively "mild" or "indirect" practices to restrict each other’s behaviors. At the implementation level, although the “soft balancing” strategies adopted by the US and China vary due to their respective conditions and abilities, both sides' limited strategic interactions consistently cover in such fields as diplomacy, military, multilateral mechanisms, so as to to deter or weaken the other's previleges while avoiding head on confrontations simultaneously.
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Hadrava, Lukáš. "Strategické partnerství USA a Indie jako způsob vyvažování Číny." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-322438.

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The master thesis called US-India Strategic Partnership as a Balance for China's Increasing Power examines development of relationship between USA and India in the years 2000-2011. American foreign policy toward India has been transformed in this period; it has evolved from open hostility during Cold War and mistrust in the nineties to the position when it is helping India to gain status of global importance. Improvement of US-India ties are explained by the need of the United States to contain increasing Chinese power. Main arguments of the analysis are based on the realistic balance of power theory, which is further enhanced by the by Joseph Nye's three dimensional concept of power. The thesis therefore distinguishes three different sources of threat to American dominant position caused by China. These sources are following: expanding China's sphere of influence into Indian Ocean and South China Sea; US-China bilateral trade deficit and high amount of American bonds owned by China, challenge to the legitimacy of American power by soft power of China. American efforts to establish cooperation with India in order to balance Chinese influence can be founded in all of these issues. The thesis concludes that motivation of the United States to enter into a strategic partnership with India can be...
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Books on the topic "Soft set theor"

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International Conference on Rough Sets, Fuzzy Sets and Soft Computing (2009 Dept. of Mathematics, Tripura University). Proceedings, International Conference on Rough Sets, Fuzzy Sets, and Soft Computing, November 5-7, 2009. Serials Publications, 2011.

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Huang, Chongfu. Towards efficient fuzzy information processing: Using the principle of information diffusion. Physica-Verlag, 2002.

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Coss, Lauren. Let's sort shapes. Cherry Lake Publishing, 2014.

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Cooke, Andy. Bear's playschool sorting: Sort it out. Barron's Educational Series, 1997.

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NATO Advanced Research Workshop on Systematic Organisation of Information in Fuzzy Systems (2001 Vila Real, Portugal). Systematic organisation of information in fuzzy systems. IOS Press, 2003.

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Yao, JingTao. Rough Sets and Knowledge Technology: 6th International Conference, RSKT 2011, Banff, Canada, October 9-12, 2011. Proceedings. Springer-Verlag GmbH Berlin Heidelberg, 2011.

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North American Fuzzy Information Processing Society. Conference. 18th International Conference of the North American Fuzzy Information Processing Society--NAFIPS: June 10-12, 199 [sic], New York, New York, U.S.A. Institute of Electrical and Electronics Engineers, 1999.

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2006), Dortmunder Fuzzy-Tage (9th. Computational intelligence: Theory and applications : international conference, 9th Fuzzy Days in Dortmund, Germany, Sept. 18-20, 2006 : proceedings. Springer, 2006.

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2006), Dortmunder Fuzzy-Tage (9th. Computational intelligence: Theory and applications : international conference, 9th Fuzzy Days in Dortmund, Germany, Sept. 18-20, 2006 : proceedings. Springer, 2006.

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Sifeng, Liu, and Lin Yi 1959-, eds. Hybrid rough sets and applications in uncertain decision-making. Auerbach Publications, 2010.

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Book chapters on the topic "Soft set theor"

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Shanahan, James G. "Fuzzy Set Theory." In Soft Computing for Knowledge Discovery. Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4335-0_3.

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Niskanen, Vesa A. "Brief Introduction to Fuzzy Set Theory." In Soft Computing Methods in Human Sciences. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-36421-4_2.

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Pérez, Rafael Bello, and Maria M. Garcia. "Probabilistic Approaches to the Rough Set Theory and Their Applications in Decision-Making." In Soft Computing for Business Intelligence. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-53737-0_4.

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Rakus-Andersson, Elisabeth. "Rough Set Theory in the Classification of Diagnoses." In Advances in Soft Computing. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04462-5_5.

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Miyamoto, Sadaaki. "A Short Course for Fuzzy Set Theory." In Soft Computing and Human-Centered Machines. Springer Japan, 2000. http://dx.doi.org/10.1007/978-4-431-67907-3_12.

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Suresh, G. Vijay, E. Venkateswara Reddy, and E. Srinivasa Reddy. "Uncertain Data Classification Using Rough Set Theory." In Advances in Intelligent and Soft Computing. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-27443-5_100.

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Hakim, R. B. Fajriya, Eka Novita Sari, and Tutut Herawan. "Soft Solution of Soft Set Theory for Recommendation in Decision Making." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07692-8_30.

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Handaga, Bana, and Mustafa Mat Deris. "Text Categorization Based on Fuzzy Soft Set Theory." In Computational Science and Its Applications – ICCSA 2012. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31128-4_25.

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Becher, Thomas, Alessandro Broggio, and Andrea Ferroglia. "Scalar SCET." In Introduction to Soft-Collinear Effective Theory. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14848-9_3.

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De Baets, Bernard. "Quasi-copulas: A Bridge between Fuzzy Set Theory and Probability Theory." In Advances in Intelligent and Soft Computing. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11960-6_6.

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Conference papers on the topic "Soft set theor"

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Dumont, Marie-No�lle, Marc Philippart de Foy, and Gr�goire L�onard. "Integrated Project in the Master of Chemical Engineering and Materials Science at the University of Li�ge." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.132784.

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The Integrated Project in the Master of Chemical Engineering and Materials Science at the University of Li�ge (ULi�ge) aims to consolidate technical knowledge and promote the acquisition of soft skills by integrating various chemical engineering disciplines. The project focus on the design of an industrial process and is divided into five parts: individual work on mass balances and literature reviews, detailed modeling of thermodynamics and key unit operations, sensitivity studies, process integration, and report to a general audience. Key learning outcomes include developing critical thinking, addressing complex multidisciplinary topics, and understanding the role of science and technology in society. Students enhance their soft skills in project management, teamwork, and effective communication in English. Regular interactions with industry and academic experts, along with support from the ULi�ge Soft Skills Team, ensure comprehensive development. Evaluation includes both technical and soft skills assessments, with individual and group performance contributing to final grades. This project, running for several years, is highly regarded by students for its rigorous and instructive nature, preparing them well for their future careers.
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S�nchez, Luis F., Eva C. Coelho, Francesco Negri, et al. "Machine Learning-Based Soft Sensor for Hydrogen Sulfide Monitoring in the Gas Treatment Section of an Industrial-Scale Oil Regeneration Plant." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.181239.

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Monitoring chemical composition is key in several industrial-scale chemical processes. However, traditional composition sensors usually convey drawbacks, including high costs, short lifetimes, and frequent calibration requirements. As an alternative, software (soft) sensors have gained attention in recent years due to their accuracy, ease of training, and potential of integrating widely known machine learning techniques. This study presents the methodology followed to train a soft sensor for hydrogen sulfide monitoring in the gas treatment section of an industrial facility in Italy. In particular, this methodology includes a novel approach for steady-state determination from historical plant data in the presence of several steady states and noise. Unfortunately, only four steady states were found in the plant data, which was insufficient for accurate soft sensor training. As an alternative, these steady states were used to develop and validate a rigorous Aspen HYSYS process simulation. The relative error of the simulation compared to the steady states found was around 1%. This simulation was used to extract additional steady state data, which was sufficient for soft sensor training. The soft sensor, trained following a Kriging Gaussian Process regression, showed a relative error with respect to the rigorous simulation of around 0.7%. The high accuracy of the sensor suggests it is a quick, low-cost, and accurate alternative to estimate the hydrogen sulfide composition and identify potential operating conditions that may lead to off-specification conditions. Future work will focus on field implementation and evaluation of the trained sensor.
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F�ber, Rastislav, Marco Vaccari, Riccardo Bacci di Capaci, Karol Lubu�k�, Gabriele Pannocchia, and Radoslav Paulen. "Soft-Sensor-Enhanced Monitoring of an Alkylation Unit via Multi-Fidelity Model Correction." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.125527.

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Industrial process monitoring can benefit from utilizing historical data, providing insights for decision-making and operational efficiency. This study develops a soft-sensor-based approach leveraging multi-fidelity modeling to correct discrepancies between online sensors and laboratory analyses. A Gaussian process-based strategy is used to predict deviations between high-frequency low-fidelity sensor data and less frequent high-fidelity laboratory measurements. By exploring static and dynamic modeling frameworks, we assess their suitability for capturing process dynamics and addressing time-dependent variability. The multi-fidelity soft sensor noticeably improves predictive accuracy, outperforming high-fidelity and low-fidelity methods. This approach demonstrates applicability across various industrial settings where integrating diverse data sources enhances real-time process control and monitoring, reducing reliance on costly laboratory sampling.
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Leenhouts, Roel, Sebastien Jankelevitch, Roel Raike, Simon M�ller, and Florence Vermeire. "Thermodynamics-informed Graph Neural Networks for Phase Transition Enthalpies." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.140638.

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Phase transition enthalpies, such as those for fusion, vaporization, and sublimation, are vital for understanding thermodynamic properties and aiding early-stage process design. However, measuring these properties is often time-consuming and costly, leading to increased interest in computational methods for fast and accurate predictions. Graph neural networks (GNNs), known for their ability to learn complex molecular representations, have emerged as state-of-the-art tools for predicting various thermophysical properties. Despite their success, GNNs do not inherently obey thermodynamic laws. In this study, we present a multitask GNN designed to predict vaporization, fusion, and sublimation enthalpies of organic compounds. We modified the loss function of the GNN, accounting for the thermodynamic cycle of the three phase transition enthalpies. To train the model, we digitized the extensive Chickos and Acree compendium, which encompasses 32,023 experimental measurements. Two approaches were explored: soft constraints, which guide the model toward thermodynamic consistency, and hard constraints, which enforce fully consistent predictions. The GNN achieved root mean squared errors (RMSEs) of 19.9 kJ/mol for sublimation, 11.0 kJ/mol for fusion, and 16.5 kJ/mol for vaporization enthalpies on the test set. Soft constraints were found to provide a good balance between accuracy and thermodynamic consistency, whereas hard constraints prioritized fidelity at the expense of predictive performance. When compared to the conventional Joback group contribution method the GNN demonstrated an improved accuracy and applicability range. This work underscores the potential of thermodynamics-informed GNNs for predicting thermodynamic properties accurately while maintaining consistency, paving the way for more reliable and efficient computational approaches.
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Sun, Wei, James G. Brigman, Cheng Ji, Pratap Nair, Fangyuan Ma, and Jingde Wang. "Data-Driven Soft Sensors for Process Industries: Case Study on a Delayed Coker Unit." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.185205.

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This research addresses the challenges associated with data-driven soft sensors in industrial applications, where successful implementations remain limited. The scarcity of practical applications can be attributed to variable operating conditions and frequent disturbances in real-time processes. Industrial data are often nonlinear, dynamic, and highly unbalanced, complicating efforts to capture the essential characteristics of underlying processes. To tackle these issues, we propose a comprehensive solution for industrial application, that encompasses feature selection, feature extraction, and model updating. Feature selection aims to pinpoint the independent variables that have a substantial impact on key performance indicators, including quality, safety, efficiency, reliability, and sustainability. By doing so, it simplifies the model and boosts its predictive accuracy. The process begins with screening variables based on process knowledge, followed by a thorough analysis of correlation and redundancy to eliminate redundant information, which can burden computational resources and degrade prediction accuracy. We propose a mutual information-based algorithm for feature selection that assesses the relevance and redundancy among process variables through a comprehensive correlation function. This algorithm ranks variables by their importance using a Greedy search method to identify the optimal set of variables. After selecting the optimal variables, feature extraction is carried out to derive internal features from this set and establish a relationship between these latent features and the output variables. Given the intricate nature of industrial processes, we employ deep learning techniques, specifically Long Short-Term Memory (LSTM) networks, which are a type of Recurrent Neural Network (RNN) well-suited for capturing long-term dependencies in sequential data. LSTMs excel at modeling temporal correlations due to their ability to maintain memory states that allow for learning from sequential data over extended periods. To address short-term nonstationary features resulting from process disturbances, we incorporate a differential unit into the latent layer of the LSTM network. Once trained, the model is updated during online applications to incorporate gradual changes in equipment and reaction agents. Quality-related data, although typically available only post-measurement, can be leveraged to fine-tune model parameters, ensuring sustained predictive accuracy over time. To validate our approach, we present a case study on a delayed coker unit, yielding promising long-term predictions for tube metal temperature and showcasing the potential of our methodology for industrial applications.
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Salasi, Mobin, Taghi Shahrabi, and Emad Roayaei. "Influence of Silicate-Phosphonate Mixture on Corrosion Inhibition of Mild Steel in Simulated Soft Water Solution." In CORROSION 2007. NACE International, 2007. https://doi.org/10.5006/c2007-07072.

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Abstract Synergistic effects of environment friendly compounds of sodium silicate and 1-hydroxyethylidene 1,1 diphosphonic acid (HEDP) on mild steel corrosion control in neutral and aerated soft water solutions have been investigated using electrochemical impedance spectroscopy and Tafel polarization techniques. The impedance and polarization results revealed that inhibitors mixtures have shown synergistic effects at lower value of HEDP. At 15ppm silicate and 10ppm HEDP showed optimum enhanced inhibition compared to their individual effects. The co-addition of 15ppm HEDP and 15ppm silicate have shown antagonistic behaviour. These observations have been supported by scanning electron microscopy (SEM) images, illustrating that the surface homogeneity increases in case of inhibitors mixture application and this provides good protection to mild steel against corrosion in soft water solution.
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Hassan, Nasruddin, and Khaleed Alhazaymeh. "Vague soft expert set theory." In PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP, 2013. http://dx.doi.org/10.1063/1.4801233.

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Csajbok, Zoltan. "Partial approximative set theory: A generalization of the rough set theory." In 2010 International Conference of Soft Computing and Pattern Recognition (SoCPaR). IEEE, 2010. http://dx.doi.org/10.1109/socpar.2010.5686424.

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Alhazaymeh, Khaleed, and Nasruddin Hassan. "Generalized vague soft expert set theory." In THE 2013 UKM FST POSTGRADUATE COLLOQUIUM: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2013 Postgraduate Colloquium. AIP Publishing LLC, 2013. http://dx.doi.org/10.1063/1.4858779.

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Gobithaasan, R. U., Nurfarhana Hassan, Kenjiro T. Miura, and Hiromasa Suzuki. "Product design with soft set theory." In ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23). Author(s), 2016. http://dx.doi.org/10.1063/1.4954565.

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Reports on the topic "Soft set theor"

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Martínez Jorge, Angel, and Javier Martínez Santos. Heterogeneous response and spillover effects of SSB taxes. Esade EcPol, 2023. http://dx.doi.org/10.56269/20230327/amj.

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In this paper we evaluate the taxation of sugar-sweetened and edulcorated beverages by using the natural quasi-experiment in Spain: in 2021 an increase in Value Added Tax was introduced in all regions of Spain except for some of them, which do not have VAT. These regions serve as a control group offering a unique opportunity in the literature for two reasons, the guarantee of avoiding cross-border consumer movements due to their geographical location and the opportunity to have a household consumption database with a rich set of characteristics. We find a pass-through of the tax to prices of over 95\% and a fall in soft drink consumption of 15\% among the poorest tertile of households, especially among those with children aged 5-16. In addition, we find a significant reduction in spending on unhealthy complementary goods among the same households in the first tertile. However, the remaining households did not react to the tax by reducing either their consumption of soft drinks or their consumption of complementary goods. Our results show the importance of considering the structure and economic capacity of the household, as well as the response of the consumption of complementary goods, when assessing the effect of this type of tax on consumption.
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Chioda, Laura, Paul Gertler, and Nicole Perales. Empowering Women: Teaching Leadership Skills to Youth in Uganda. Centre for Excellence and Development Impact and Learning (CEDIL), 2023. http://dx.doi.org/10.51744/crpp10.

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Empowering adolescent girls through education has become a priority among numerous stakeholder. However, recent evidence suggests that education alone may not be suffcient if women remain in a low-empowerment equilibrium and face internal constraints as they relate to aspirations, self-efficacy, leadership, and other life (soft) skills. We study the long-term impacts of a school-based upper-secondary intervention, the Educate! Experience, designed to enhance adolescents’ leadership and social entrepreneurship skills in Uganda. The program was implemented as a cluster randomized controlled trial (RCT) in 48 schools. Four years post-intervention, we document lasting impacts on a wide array of leadership and soft skills. Overall, Educate! graduates developed skills that are traditionally associated with greater focus on long-term goals; they reported being more in control of aspects of their lives (self-efficacy and grit) and more empowered to implement actions towards their plans. Young women in the treatment group are also more likely to complete secondary education, delay family formation, enroll in tertiary education, and pursue STEM and Business majors relative to their counterparts in the control group. The program yielded socially desirable and gender relevant spillovers, including expansions in women’s agency. Both male and female Educate! graduates embraced more progressive views concerning women’s standing in the society and women’s ability to exercise their agency to engage in the labor market and refuse sex. The incidence of intimate partner violence (IPV) also improved among Educate! graduates, as did their attitudes toward IPV social acceptability.
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Marsden, Nick, and Niranjan Singh. Preparing Vocational Students for Future Workplaces: Towards a course evaluation of the Unitec Bachelor of Applied Engineering. Unitec ePress, 2017. http://dx.doi.org/10.34074/ocds.42017.

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This exploratory study set out to evaluate how well a particular course in automotive engineering is set up to enable students to develop skills necessary to enter the workplace. The research set out to identify trends in student expectations and in the needs of employers at a time when this field of work is characterised by disruptive technological developments such as computerisation and automation. The intended outcome of the research is that the findings will assist the critical thinking of course designers as they reflect on modifications that might be necessary for Unitec Bachelor of Applied Technology (BAT) graduate attributes to fully meet future workplace demands. It is also an aim that this exploratory evaluation of a small cohort of students can, despite its limitations, identify trends for future pedagogical research in the ITP (Institutes of Technology and Polytechnics) sector. Although not a full course evaluation, this study invited feedback from students and recent graduates in relevant employment regarding the alignment of the Unitec Bachelor of Applied Technology (BAT) course design with their perceptions of skills necessary in the workplace. Another intention was to highlight any misalignments between the realities of the automotive engineering sector and student expectations of the course: To what degree are work capability expectations in agreement between the student stakeholders and the institution? Are the course goals realistic and in line with actual industry needs? How is the definition of work readiness changing? The paper also samples current speculative thinking about skills that are becoming progressively more important in the workplace, namely the so-called ‘soft skills’ in communication, problem solving, management and collaboration, and in dialogic and creative attributes relevant to increasingly automated and globalised workplaces.
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Mazzoni, Silvia, Nicholas Gregor, Linda Al Atik, Yousef Bozorgnia, David Welch, and Gregory Deierlein. Probabilistic Seismic Hazard Analysis and Selecting and Scaling of Ground-Motion Records (PEER-CEA Project). Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, 2020. http://dx.doi.org/10.55461/zjdn7385.

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This report is one of a series of reports documenting the methods and findings of a multi-year, multi-disciplinary project coordinated by the Pacific Earthquake Engineering Research Center (PEER) and funded by the California Earthquake Authority (CEA). The overall project is titled “Quantifying the Performance of Retrofit of Cripple Walls and Sill Anchorage in Single-Family Wood-Frame Buildings,” henceforth referred to as the “PEER–CEA Project.” The overall objective of the PEER–CEA Project is to provide scientifically based information (e.g., testing, analysis, and resulting loss models) that measure and assess the effectiveness of seismic retrofit to reduce the risk of damage and associated losses (repair costs) of wood-frame houses with cripple wall and sill anchorage deficiencies as well as retrofitted conditions that address those deficiencies. Tasks that support and inform the loss-modeling effort are: (1) collecting and summarizing existing information and results of previous research on the performance of wood-frame houses; (2) identifying construction features to characterize alternative variants of wood-frame houses; (3) characterizing earthquake hazard and ground motions at representative sites in California; (4) developing cyclic loading protocols and conducting laboratory tests of cripple wall panels, wood-frame wall subassemblies, and sill anchorages to measure and document their response (strength and stiffness) under cyclic loading; and (5) the computer modeling, simulations, and the development of loss models as informed by a workshop with claims adjustors. This report is a product of Working Group 3 (WG3), Task 3.1: Selecting and Scaling Ground-motion records. The objective of Task 3.1 is to provide suites of ground motions to be used by other working groups (WGs), especially Working Group 5: Analytical Modeling (WG5) for Simulation Studies. The ground motions used in the numerical simulations are intended to represent seismic hazard at the building site. The seismic hazard is dependent on the location of the site relative to seismic sources, the characteristics of the seismic sources in the region and the local soil conditions at the site. To achieve a proper representation of hazard across the State of California, ten sites were selected, and a site-specific probabilistic seismic hazard analysis (PSHA) was performed at each of these sites for both a soft soil (Vs30 = 270 m/sec) and a stiff soil (Vs30=760 m/sec). The PSHA used the UCERF3 seismic source model, which represents the latest seismic source model adopted by the USGS [2013] and NGA-West2 ground-motion models. The PSHA was carried out for structural periods ranging from 0.01 to 10 sec. At each site and soil class, the results from the PSHA—hazard curves, hazard deaggregation, and uniform-hazard spectra (UHS)—were extracted for a series of ten return periods, prescribed by WG5 and WG6, ranging from 15.5–2500 years. For each case (site, soil class, and return period), the UHS was used as the target spectrum for selection and modification of a suite of ground motions. Additionally, another set of target spectra based on “Conditional Spectra” (CS), which are more realistic than UHS, was developed [Baker and Lee 2018]. The Conditional Spectra are defined by the median (Conditional Mean Spectrum) and a period-dependent variance. A suite of at least 40 record pairs (horizontal) were selected and modified for each return period and target-spectrum type. Thus, for each ground-motion suite, 40 or more record pairs were selected using the deaggregation of the hazard, resulting in more than 200 record pairs per target-spectrum type at each site. The suites contained more than 40 records in case some were rejected by the modelers due to secondary characteristics; however, none were rejected, and the complete set was used. For the case of UHS as the target spectrum, the selected motions were modified (scaled) such that the average of the median spectrum (RotD50) [Boore 2010] of the ground-motion pairs follow the target spectrum closely within the period range of interest to the analysts. In communications with WG5 researchers, for ground-motion (time histories, or time series) selection and modification, a period range between 0.01–2.0 sec was selected for this specific application for the project. The duration metrics and pulse characteristics of the records were also used in the final selection of ground motions. The damping ratio for the PSHA and ground-motion target spectra was set to 5%, which is standard practice in engineering applications. For the cases where the CS was used as the target spectrum, the ground-motion suites were selected and scaled using a modified version of the conditional spectrum ground-motion selection tool (CS-GMS tool) developed by Baker and Lee [2018]. This tool selects and scales a suite of ground motions to meet both the median and the user-defined variability. This variability is defined by the relationship developed by Baker and Jayaram [2008]. The computation of CS requires a structural period for the conditional model. In collaboration with WG5 researchers, a conditioning period of 0.25 sec was selected as a representative of the fundamental mode of vibration of the buildings of interest in this study. Working Group 5 carried out a sensitivity analysis of using other conditioning periods, and the results and discussion of selection of conditioning period are reported in Section 4 of the WG5 PEER report entitled Technical Background Report for Structural Analysis and Performance Assessment. The WG3.1 report presents a summary of the selected sites, the seismic-source characterization model, and the ground-motion characterization model used in the PSHA, followed by selection and modification of suites of ground motions. The Record Sequence Number (RSN) and the associated scale factors are tabulated in the Appendices of this report, and the actual time-series files can be downloaded from the PEER Ground-motion database Portal (https://ngawest2.berkeley.edu/)(link is external).
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Levy, Brian. How Political Contexts Influence Education Systems: Patterns, Constraints, Entry Points. Research on Improving Systems of Education (RISE), 2022. http://dx.doi.org/10.35489/bsg-rise-2022/pe04.

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This paper synthesises the findings of a set of country studies commissioned by the RISE Programme to explore the influence of politics and power on education sector policymaking and implementation. The synthesis groups the countries into three political-institutional contexts: Dominant contexts, where power is centred around a political leader and a hierarchical governance structure. As the Vietnam case details, top-down leadership potentially can provide a robust platform for improving learning outcomes. However, as the case studies of Ethiopia, Indonesia, Nigeria, and Tanzania illustrate, all-too-often dominant leaders’ goals vis-à-vis the education sector can veer in other directions. In impersonal competitive contexts, a combination of strong formal institutions and effective processes of resolving disagreements can, on occasion, result in a shared commitment among powerful interests to improve learning outcomes—but in none of the case studies is this outcome evident. In Peru, substantial learning gains have been achieved despite messy top-level politics. But the Chilean, Indian, and South African case studies suggest that the all-too-common result of rule-boundedness plus unresolved political contestation over the education sector’s goals is some combination of exaggerated rule compliance and/or performative isomorphic mimicry. Personalised competitive contexts (Bangladesh, Ghana, and Kenya for example) lack the seeming strengths of either their dominant or their impersonal competitive contexts; there are multiple politically-influential groups and multiple, competing goals—but no credible framework of rules to bring coherence either to political competition or to the education bureaucracy. The case studies show that political and institutional constraints can render ineffective many specialised sectoral interventions intended to improve learning outcomes. But they also point to the possibility that ‘soft governance’ entry points might open up some context-aligned opportunities for improving learning outcomes. In dominant contexts, the focus might usefully be on trying to influence the goals and strategies of top-level leadership. In impersonal competitive contexts, it might be on strengthening alliances between mission-oriented public officials and other developmentally-oriented stakeholders. In personalised competitive contexts, gains are more likely to come from the bottom-up—via a combination of local-level initiatives plus a broader effort to inculcate a shared sense among a country’s citizenry of ‘all for education’.
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Levy, Brian. How Political Contexts Influence Education Systems: Patterns, Constraints, Entry Points. Research on Improving Systems of Education (RISE), 2022. http://dx.doi.org/10.35489/bsg-rise-wp_2022/122.

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This paper synthesises the findings of a set of country studies commissioned by the RISE Programme to explore the influence of politics and power on education sector policymaking and implementation. The synthesis groups the countries into three political-institutional contexts: Dominant contexts, where power is centred around a political leader and a hierarchical governance structure. As the Vietnam case details, top-down leadership potentially can provide a robust platform for improving learning outcomes. However, as the case studies of Ethiopia, Indonesia, Nigeria, and Tanzania illustrate, all-too-often dominant leaders’ goals vis-à-vis the education sector can veer in other directions. In impersonal competitive contexts, a combination of strong formal institutions and effective processes of resolving disagreements can, on occasion, result in a shared commitment among powerful interests to improve learning outcomes—but in none of the case studies is this outcome evident. In Peru, substantial learning gains have been achieved despite messy top-level politics. But the Chilean, Indian, and South African case studies suggest that the all-too-common result of rule-boundedness plus unresolved political contestation over the education sector’s goals is some combination of exaggerated rule compliance and/or performative isomorphic mimicry. Personalised competitive contexts (Bangladesh, Ghana, and Kenya for example) lack the seeming strengths of either their dominant or their impersonal competitive contexts; there are multiple politically-influential groups and multiple, competing goals—but no credible framework of rules to bring coherence either to political competition or to the education bureaucracy. The case studies show that political and institutional constraints can render ineffective many specialised sectoral interventions intended to improve learning outcomes. But they also point to the possibility that ‘soft governance’ entry points might open up some context-aligned opportunities for improving learning outcomes. In dominant contexts, the focus might usefully be on trying to influence the goals and strategies of top-level leadership. In impersonal competitive contexts, it might be on strengthening alliances between mission-oriented public officials and other developmentally-oriented stakeholders. In personalised competitive contexts, gains are more likely to come from the bottom-up—via a combination of local-level initiatives plus a broader effort to inculcate a shared sense among a country’s citizenry of ‘all for education’.
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Jameel, Yusuf, Paul West, and Daniel Jasper. Reducing Black Carbon: A Triple Win for Climate, Health, and Well-Being. Project Drawdown, 2023. http://dx.doi.org/10.55789/y2c0k2p3.

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Black carbon – also referred to as soot – is a particulate matter that results from the incomplete combustion of fossil fuels and biomass. As a major air and climate pollutant, black carbon (BC) emissions have widespread adverse effects on human health and climate change. Globally, exposure to unhealthy levels of particulate matter, including BC, is estimated to cause between three and six million excess deaths every year. These health impacts – and the related economic losses – are felt disproportionately by those living in low- and middle-income countries. Furthermore, BC is a potent greenhouse gas with a short-term global warming potential well beyond carbon dioxide and methane. Worse still, it is often deposited on sea ice and glaciers, reducing reflectivity and accelerating melting, particularly in the Arctic and Himalayas. Therefore, reducing BC emissions results in a triple win, mitigating climate change, improving the lives of more than two billion people currently exposed to unclean air, and saving trillions of dollars in economic losses. Today, the majority of BC emissions stem from just a handful of sectors and countries. Over 70% of BC comes from the residential and transportation sectors, with the latter being the dominant source in high-income countries and the former driving emissions in low- and middle-income nations. On a country-level, China and India are the biggest emitters accounting for one-third of global BC emissions. When combined with Brazil, Indonesia, and Nigeria, these five countries alone emit 50% of all BC. While BC emissions trends over the past 20 years have been inconsistent globally, there has been a notable decline in Europe, North America, and China. Conversely, emissions have been rising in regions like Africa, South Asia, and Central Asia. The Intergovernmental Panel on Climate Change recommends deep reductions in BC emissions by 2030 to achieve the Paris Climate Agreement goal of limiting warming to below 1.5°C, yet very few countries have addressed BC in their climate plans. Fortunately, solutions that can rapidly reduce BC emissions by the end of this decade are readily available. By implementing the right policies, deploying targeted interventions in hotspots, and redirecting climate finance, policymakers and funders can mitigate the climate effects of BC while saving millions of lives and trillions of dollars. Below are key recommendations to achieve these aims based on the findings of this report: Urgently implement clean cooking solutions Providing clean cooking fuels and technologies in sub-Saharan Africa and South Asia, especially in the hotspots of the Indo-Gangetic Plains, Nigeria, and Uganda, can significantly reduce BC emissions. Countries with low penetration of clean cooking fuel must urgently develop policies that make clean cooking a priority for health and climate. Target transportation to reduce current – and prevent future – emissions Retrofitting older diesel engines with diesel particulate filters can remove up to 95% of BC. Countries around the world must implement policies to phase out polluting vehicles, set emission standards, and accelerate the uptake of EVs and hybrids, especially in urban regions where transportation demand is growing rapidly. A successful shift to EVs demands national investments complemented with international financing and private capital. Multilateral development banks need to play a pivotal role in this transition, with strategies like concessional finance to fast-track key projects and stimulate private sector investment. Reduce BC from the shipping industry BC emissions from the shipping industry must be urgently reduced to protect the Arctic ecosystem. Shifting shipping away from heavy fuel oil and equipping ships with diesel particulate filters is a cost-effective approach that would quickly and significantly reduce emissions. Regulate air quality Stringent emissions standards, clean air laws, baselines, and mandatory monitoring programs can effectively reduce BC emissions. Such policies have already resulted in large reductions in Europe, North America, and, more recently, China. However, several low- and middle-income countries have no legal protection for ambient air quality and lack legislatively-mandated standards. Implementing strong and legally binding policies can result in a large decrease in BC emissions, particularly across the transportation and industry sectors. Include BC in nationally determined contributions and the UNFCCC Only 12 countries have explicitly addressed BC in their nationally determined contributions (NDCs). This limited focus on BC is partly due to its omission from the United Nations Framework Convention on Climate Change’s (UNFCCC) list of climate pollutants, an oversight that should be reconsidered given that reducing BC would save countless lives and slow global warming. As nations review their NDCs by 2025, they must incorporate BC reduction efforts to meet climate and well-being targets. Improve BC measurements and estimates BC estimates are plagued by uncertainties. Therefore, there is an urgent need for more accurate inventories in order to develop better emission reduction plans. Stakeholders must collaborate to develop a consistent BC measurement protocol, prioritize the collection of high-quality data, and use state of the art models to enhance estimates and reduce uncertainties.
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Galili, Naftali, Roger P. Rohrbach, Itzhak Shmulevich, Yoram Fuchs, and Giora Zauberman. Non-Destructive Quality Sensing of High-Value Agricultural Commodities Through Response Analysis. United States Department of Agriculture, 1994. http://dx.doi.org/10.32747/1994.7570549.bard.

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The objectives of this project were to develop nondestructive methods for detection of internal properties and firmness of fruits and vegetables. One method was based on a soft piezoelectric film transducer developed in the Technion, for analysis of fruit response to low-energy excitation. The second method was a dot-matrix piezoelectric transducer of North Carolina State University, developed for contact-pressure analysis of fruit during impact. Two research teams, one in Israel and the other in North Carolina, coordinated their research effort according to the specific objectives of the project, to develop and apply the two complementary methods for quality control of agricultural commodities. In Israel: An improved firmness testing system was developed and tested with tropical fruits. The new system included an instrumented fruit-bed of three flexible piezoelectric sensors and miniature electromagnetic hammers, which served as fruit support and low-energy excitation device, respectively. Resonant frequencies were detected for determination of firmness index. Two new acoustic parameters were developed for evaluation of fruit firmness and maturity: a dumping-ratio and a centeroid of the frequency response. Experiments were performed with avocado and mango fruits. The internal damping ratio, which may indicate fruit ripeness, increased monotonically with time, while resonant frequencies and firmness indices decreased with time. Fruit samples were tested daily by destructive penetration test. A fairy high correlation was found in tropical fruits between the penetration force and the new acoustic parameters; a lower correlation was found between this parameter and the conventional firmness index. Improved table-top firmness testing units, Firmalon, with data-logging system and on-line data analysis capacity have been built. The new device was used for the full-scale experiments in the next two years, ahead of the original program and BARD timetable. Close cooperation was initiated with local industry for development of both off-line and on-line sorting and quality control of more agricultural commodities. Firmalon units were produced and operated in major packaging houses in Israel, Belgium and Washington State, on mango and avocado, apples, pears, tomatoes, melons and some other fruits, to gain field experience with the new method. The accumulated experimental data from all these activities is still analyzed, to improve firmness sorting criteria and shelf-life predicting curves for the different fruits. The test program in commercial CA storage facilities in Washington State included seven apple varieties: Fuji, Braeburn, Gala, Granny Smith, Jonagold, Red Delicious, Golden Delicious, and D'Anjou pear variety. FI master-curves could be developed for the Braeburn, Gala, Granny Smith and Jonagold apples. These fruits showed a steady ripening process during the test period. Yet, more work should be conducted to reduce scattering of the data and to determine the confidence limits of the method. Nearly constant FI in Red Delicious and the fluctuations of FI in the Fuji apples should be re-examined. Three sets of experiment were performed with Flandria tomatoes. Despite the complex structure of the tomatoes, the acoustic method could be used for firmness evaluation and to follow the ripening evolution with time. Close agreement was achieved between the auction expert evaluation and that of the nondestructive acoustic test, where firmness index of 4.0 and more indicated grade-A tomatoes. More work is performed to refine the sorting algorithm and to develop a general ripening scale for automatic grading of tomatoes for the fresh fruit market. Galia melons were tested in Israel, in simulated export conditions. It was concluded that the Firmalon is capable of detecting the ripening of melons nondestructively, and sorted out the defective fruits from the export shipment. The cooperation with local industry resulted in development of automatic on-line prototype of the acoustic sensor, that may be incorporated with the export quality control system for melons. More interesting is the development of the remote firmness sensing method for sealed CA cool-rooms, where most of the full-year fruit yield in stored for off-season consumption. Hundreds of ripening monitor systems have been installed in major fruit storage facilities, and being evaluated now by the consumers. If successful, the new method may cause a major change in long-term fruit storage technology. More uses of the acoustic test method have been considered, for monitoring fruit maturity and harvest time, testing fruit samples or each individual fruit when entering the storage facilities, packaging house and auction, and in the supermarket. This approach may result in a full line of equipment for nondestructive quality control of fruits and vegetables, from the orchard or the greenhouse, through the entire sorting, grading and storage process, up to the consumer table. The developed technology offers a tool to determine the maturity of the fruits nondestructively by monitoring their acoustic response to mechanical impulse on the tree. A special device was built and preliminary tested in mango fruit. More development is needed to develop a portable, hand operated sensing method for this purpose. In North Carolina: Analysis method based on an Auto-Regressive (AR) model was developed for detecting the first resonance of fruit from their response to mechanical impulse. The algorithm included a routine that detects the first resonant frequency from as many sensors as possible. Experiments on Red Delicious apples were performed and their firmness was determined. The AR method allowed the detection of the first resonance. The method could be fast enough to be utilized in a real time sorting machine. Yet, further study is needed to look for improvement of the search algorithm of the methods. An impact contact-pressure measurement system and Neural Network (NN) identification method were developed to investigate the relationships between surface pressure distributions on selected fruits and their respective internal textural qualities. A piezoelectric dot-matrix pressure transducer was developed for the purpose of acquiring time-sampled pressure profiles during impact. The acquired data was transferred into a personal computer and accurate visualization of animated data were presented. Preliminary test with 10 apples has been performed. Measurement were made by the contact-pressure transducer in two different positions. Complementary measurements were made on the same apples by using the Firmalon and Magness Taylor (MT) testers. Three-layer neural network was designed. 2/3 of the contact-pressure data were used as training input data and corresponding MT data as training target data. The remaining data were used as NN checking data. Six samples randomly chosen from the ten measured samples and their corresponding Firmalon values were used as the NN training and target data, respectively. The remaining four samples' data were input to the NN. The NN results consistent with the Firmness Tester values. So, if more training data would be obtained, the output should be more accurate. In addition, the Firmness Tester values do not consistent with MT firmness tester values. The NN method developed in this study appears to be a useful tool to emulate the MT Firmness test results without destroying the apple samples. To get more accurate estimation of MT firmness a much larger training data set is required. When the larger sensitive area of the pressure sensor being developed in this project becomes available, the entire contact 'shape' will provide additional information and the neural network results would be more accurate. It has been shown that the impact information can be utilized in the determination of internal quality factors of fruit. Until now,
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