Relevant bibliographies by topics / Set-valued operation

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  2. Dissertations / Theses
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Academic literature on the topic 'Set-valued operation'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Set-valued operation"

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Khalil, Ahmed Mostafa, Dunqian Cao, Abdelfatah Azzam, Florentin Smarandache, and Wedad R. Alharbi. "Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making." Symmetry 12, no. 8 (August 14, 2020): 1361. http://dx.doi.org/10.3390/sym12081361.

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In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.
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OZAWA, MASANAO. "ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY." Review of Symbolic Logic 10, no. 4 (June 5, 2017): 782–807. http://dx.doi.org/10.1017/s1755020317000120.

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AbstractIn 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo–Fraenkel set theory with the axiom of choice (ZFC) hold in the model. In this paper, we aim at unifying Takeuti’s model with Boolean-valued models by constructing models based on general complete orthomodular lattices, and generalizing the transfer principle in Boolean-valued models, which asserts that every theorem in ZFC set theory holds in the models, to a general form holding in every orthomodular-valued model. One of the central problems in this program is the well-known arbitrariness in choosing a binary operation for implication. To clarify what properties are required to obtain the generalized transfer principle, we introduce a class of binary operations extending the implication on Boolean logic, called generalized implications, including even nonpolynomially definable operations. We study the properties of those operations in detail and show that all of them admit the generalized transfer principle. Moreover, we determine all the polynomially definable operations for which the generalized transfer principle holds. This result allows us to abandon the Sasaki arrow originally assumed for Takeuti’s model and leads to a much more flexible approach to quantum set theory.
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Ahmad, Rais, Imran Ali, Saddam Husain, A. Latif, and Ching-Feng Wen. "Generalized Implicit Set-Valued Variational Inclusion Problem with ⊕ Operation." Mathematics 7, no. 5 (May 10, 2019): 421. http://dx.doi.org/10.3390/math7050421.

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In this paper, we consider a resolvent operator which depends on the composition of two mappings with ⊕ operation. We prove some of the properties of the resolvent operator, that is, that it is single-valued as well as Lipschitz-type-continuous. An existence and convergence result is proven for a generalized implicit set-valued variational inclusion problem with ⊕ operation. Some special cases of a generalized implicit set-valued variational inclusion problem with ⊕ operation are discussed. An example is constructed to illustrate some of the concepts used in this paper.
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Iqbal, Javid, Imran Ali, Puneet Kumar Arora, and Waseem Ali Mir. "Set-valued variational inclusion problem with fuzzy mappings involving XOR-operation." AIMS Mathematics 6, no. 4 (2021): 3288–304. http://dx.doi.org/10.3934/math.2021197.

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Alhazaymeh, Khaleed, and Nasruddin Hassan. "Interval-Valued Vague Soft Sets and Its Application." Advances in Fuzzy Systems 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/208489.

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Molodtsov has introduced the concept of soft sets and the application of soft sets in decision making and medical diagnosis problems. The basic properties of vague soft sets are presented. In this paper, we introduce the concept of interval-valued vague soft sets which are an extension of the soft set and its operations such as equality, subset, intersection, union, AND operation, OR operation, complement, and null while further studying some properties. We give examples for these concepts, and we give a number of applications on interval-valued vague soft sets.
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Wang, Hong, and Ran Gao. "Knowledge Reduction of Set-Valued Decision Information Systems Based on Tolerance Relation." Applied Mechanics and Materials 462-463 (November 2013): 466–71. http://dx.doi.org/10.4028/www.scientific.net/amm.462-463.466.

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Knowledge reduction is one of the main problems in the study of rough set theory. This paper deals with knowledge reduction of set-valued decision information systems based on tolerance relation. The concepts of distribution reduct based on set-valued decision information systems is introduced. The judgement theorems and discernibility matrices associated with the tolerance relation were examined, from which we can obtain the specific operation methods to inconsistent set-valued decision information systems.
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Kon, Masamichi. "Operation and ordering of fuzzy sets, and fuzzy set-valued convex mappings." Journal of Fuzzy Set Valued Analysis 2014 (2014): 1–17. http://dx.doi.org/10.5899/2014/jfsva-00202.

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Jiang, Chao, Shenqing Jiang, and Jianlan Chen. "Interval-Valued Dual Hesitant Fuzzy Hamacher Aggregation Operators for Multiple Attribute Decision Making." Journal of Systems Science and Information 7, no. 3 (August 27, 2019): 227–56. http://dx.doi.org/10.21078/jssi-2019-227-30.

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AbstractAs an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given, and an numerical example is provided to demonstrate that the developed approach is both valid and practical.
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Lu, Lin, and Xiaochun Luo. "Emergency Transportation Problem Based on Single-Valued Neutrosophic Set." Discrete Dynamics in Nature and Society 2020 (April 21, 2020): 1–8. http://dx.doi.org/10.1155/2020/4813497.

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Emergency events are full of large number of uncertain information. The existence of these uncertain information leads to less research on emergency logistics involving transshipment scenarios. In this paper, a new emergency transport model is proposed, which simulates the scenario of emergency transport from the logistics center to each disaster site and between each disaster site. The single-valued neutrosophic set (SVNS) is applied to transform the emergency transshipment problem into a multiattribute decision-making problem in ambiguous and uncertain environments. Technology for order preference by similarity to ideal solution (TOPSIS) is extended to the single-valued neutrosophic environment to rank and optimize the alternative transshipment routes. Firstly, the attribute weight is determined by using the entropy weight method; secondly, the scoring function of the single-valued neutrosophic fuzzy number is defined; thirdly, the TOPSIS method is used to rank the decision-making; finally, the feasibility and rationality of the proposed method are verified by an emergency operation example.
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Wang, Jin-Ying, Yan-Ping Wang, and Lei Liu. "Hesitant Bipolar-Valued Fuzzy Soft Sets and Their Application in Decision Making." Complexity 2020 (August 17, 2020): 1–12. http://dx.doi.org/10.1155/2020/6496030.

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As an extension of fuzzy sets, hesitant bipolar-valued fuzzy set is a new mathematical tool for dealing with fuzzy problems, but it still has the problem with the inadequacy of the parametric tools. In order to further improve the accuracy of decision making, a new mixed mathematical model, named hesitant bipolar-valued fuzzy soft set, is constructed by combining hesitant bipolar-valued fuzzy sets with soft sets. Firstly, some related theories of hesitant bipolar-valued fuzzy sets are discussed. Secondly, the concept of hesitant bipolar-valued fuzzy soft set is given, and the algorithms of complement, union, intersection, “AND,” and “OR” are defined. Based on the above algorithms, the corresponding results of operation are analyzed and the relevant properties are discussed. Finally, a multiattribute decision-making method of hesitant bipolar-valued fuzzy soft sets is proposed by using the idea of score function and level soft sets. The effectiveness of the proposed method is illustrated by an example.
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Dissertations / Theses on the topic "Set-valued operation"

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Eryuzlu, Menevse. "Two Generalizations of the Filippov Operation." TopSCHOLAR®, 2016. http://digitalcommons.wku.edu/theses/1593.

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The purpose of this thesis is to generalize Filippov's operation, and to get more useful results. It includes two main parts: The C-Filippov operation for the finite and countable cases and the Filippov operation with different measures. In the first chapter, we give brief information about the importance of Filippov's operation, our goal and the ideas behind our generalizations. In the second chapter, we give some sufficient background notes. In the third chapter, we introduce the Filippov operation, explain how to calculate the Filippov of a function and give some sufficient properties of it. In the fourth chapter, we introduce a generalization of the Filippov operation, the C-Filippov, and give some of its properties which we need for the next chapter. In the fifth chapter, in the first main part, we discuss some properties of the C-Filippov for special cases and observe the differences and common properties between the Filippov and C-Filippov operations. Finally, in the sixth chapter, we present the other generalization of the Filippov operation which is Filippov with different measures. We observe the properties of the corresponding Filippovs when we know the relationship between the measures. We finish the thesis by summarizing our work and discussing future work.
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Schaich, Rainer Manuel. "Robust model predictive control." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:94e75a62-a801-47e1-8cb8-668e8309d477.

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This thesis deals with the topic of min-max formulations of robust model predictive control problems. The sets involved in guaranteeing robust feasibility of the min-max program in the presence of state constraints are of particular interest, and expanding the applicability of well understood solvers of linearly constrained quadratic min-max programs is the main focus. To this end, a generalisation for the set of uncertainty is considered: instead of fixed bounds on the uncertainty, state- and input-dependent bounds are used. To deal with state- and input dependent constraint sets a framework for a particular class of set-valued maps is utilised, namely parametrically convex set-valued maps. Relevant properties and operations are developed to accommodate parametrically convex set-valued maps in the context of robust model predictive control. A quintessential part of this work is the study of fundamental properties of piecewise polyhedral set-valued maps which are parametrically convex, we show that one particular property is that their combinatorial structure is constant. The study of polytopic maps with a rigid combinatorial structure allows the use of an optimisation based approach of robustifying constrained control problems with probabilistic constraints. Auxiliary polytopic constraint sets, used to replace probabilistic constraints by deterministic ones, can be optimised to minimise the conservatism introduced while guaranteeing constraint satisfaction of the original probabilistic constraint. We furthermore study the behaviour of the maximal robust positive invariant set for the case of scaled uncertainty and show that this set is continuously polytopic up to a critical scaling factor, which we can approximate a-priori with an arbitrary degree of accuracy. Relevant theoretical statements are developed, discussed and illustrated with examples.
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Bauwe, Anne, and Wilfried Grecksch. "A parabolic stochastic differential inclusion." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501221.

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Stochastic differential inclusions can be considered as a generalisation of stochastic differential equations. In particular a multivalued mapping describes the set of equations, in which a solution has to be found. This paper presents an existence result for a special parabolic stochastic inclusion. The proof is based on the method of upper and lower solutions. In the deterministic case this method was effectively introduced by S. Carl.
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Bauwe, Anne, and Wilfried Grecksch. "Finite dimensional stochastic differential inclusions." Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800515.

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This paper offers an existence result for finite dimensional stochastic differential inclusions with maximal monotone drift and diffusion terms. Kravets studied only set-valued drifts in [5], whereas Motyl [4] additionally observed set-valued diffusions in an infinite dimensional context. In the proof we make use of the Yosida approximation of maximal monotone operators to achieve stochastic differential equations which are solvable by a theorem of Krylov and Rozovskij [7]. The selection property is verified with certain properties of the considered set-valued maps. Concerning Lipschitz continuous set-valued diffusion terms, uniqueness holds. At last two examples for application are given.
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Books on the topic "Set-valued operation"

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Burachik, Regina S., and Alfredo N. Iusem. Set-Valued Mappings and Enlargements of Monotone Operators. Springer, 2010.

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Set-Valued Mappings and Enlargements of Monotone Operators (Springer Optimization and Its Applications). Springer, 2007.

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Vector Optimization: Set-valued and Variational Analysis (Lecture Notes in Economics and Mathematical Systems). Springer, 2005.

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Topological Fixed Point Theory of Multivalued Mappings (Topological Fixed Point Theory and Its Applications). 2nd ed. Springer, 2006.

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Book chapters on the topic "Set-valued operation"

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Martynyuk, Anatoly A. "Dynamics of Systems with Causal Operator." In Qualitative Analysis of Set-Valued Differential Equations, 151–71. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-07644-3_7.

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Küçük, Mahide, Mustafa Soyertem, and Yalçin Küçük. "On the Scalarization of Set-Valued Optimization Problems with Respect to Total Ordering Cones." In Operations Research Proceedings, 347–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20009-0_55.

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Cho, Yeol Je, Themistocles M. Rassias, and Reza Saadati. "Coincidence Points for Set-Valued Mappings in Fuzzy Metric Spaces." In Fuzzy Operator Theory in Mathematical Analysis, 383–99. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93501-0_13.

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Ma, Sheng-quan, and Sheng-gang Li. "Complex Fuzzy Set-Valued Complex Fuzzy Integral and Its Convergence Theorem." In Fuzzy Systems & Operations Research and Management, 143–55. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19105-8_14.

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Száz, Árpád. "The Hyers–Ulam and Hahn–Banach Theorems and Some Elementary Operations on Relations Motivated by Their Set-Valued Generalizations." In Springer Optimization and Its Applications, 631–705. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3498-6_39.

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Lan, Heng-you, Xiao Wang, Tingjian Xiong, and Yumin Xiang. "An Over-Relaxed (A,η,m)-Proximal Point Algorithm for System of Nonlinear Fuzzy-Set Valued Operator Equation Frameworks and Fixed Point Problems." In Lecture Notes in Computer Science, 133–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-24918-1_16.

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"20. The superposition set-valued operator." In Convex and Set-Valued Analysis, 129–34. De Gruyter, 2016. http://dx.doi.org/10.1515/9783110460308-021.

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Gayen, Sudipta, Florentin Smarandache, Sripati Jha, and Ranjan Kumar. "Interval-Valued Neutrosophic Subgroup Based on Interval-Valued Triple T-Norm." In Neutrosophic Sets in Decision Analysis and Operations Research, 215–43. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-2555-5.ch010.

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Presently, interval-valued neutrosophic set theory has become an important research topic. It is widely used in various pure as well as applied fields. This chapter will provide some essential scopes to study interval-valued neutrosophic subgroup. Here the notion of interval-valued triple T-norm has been introduced, and based on that, interval-valued neutrosophic subgroup has been defined. Furthermore, some homomorphic characteristics of this notion have been studied. Additionally, based on interval-valued triple T-norm, interval-valued neutrosophic normal subgroup has been introduced and some of its homomorphic characteristics have been analyzed.
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Broumi, Said, Selçuk Topal, Assia Bakali, Mohamed Talea, and Florentin Smarandache. "A Novel Python Toolbox for Single and Interval-Valued Neutrosophic Matrices." In Neutrosophic Sets in Decision Analysis and Operations Research, 281–330. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-2555-5.ch013.

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Recently, single valued neutrosophic sets and interval valued neutrosophic sets have received great attention among the scholars and have been applied in many applications. These two concepts handle the indeterminacy and consistent information existing in real-life problems. In this chapter, a new Python toolbox is proposed under neutrosophic environment, which consists of some Python code for single valued neutrosophic matrices and interval valued neutrosophic matrices. Some definitions of interval neutrosophic vague set such as union, complement, and intersection are presented. Furthermore, the related examples are included.
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Deli, Irfan, and Emel Kırmızı Öztürk. "Two Centroid Point for SVTN-Numbers and SVTrN-Numbers." In Advances in Data Mining and Database Management, 279–307. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-1313-2.ch010.

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In this chapter, some basic definitions and operations on the concepts of fuzzy set, fuzzy number, intuitionistic fuzzy set, single-valued neutrosophic set, single-valued neutrosophic number (SVN-number) are presented. Secondly, two centroid point are called 1. and 2. centroid point for single-valued trapezoidal neutrosophic number (SVTN-number) and single-valued triangular neutrosophic number (SVTrN-number) are presented. Then, some desired properties of 1. and 2. centroid point of SVTN-numbers and SVTrN-numbers studied. Also, based on concept of 1. and 2. centroid point of SVTrN-numbers, a new single-valued neutrosophic multiple-attribute decision-making method is proposed. Moreover, a numerical example is introduced to illustrate the availability and practicability of the proposed method. Finally, since centroid points of normalized SNTN-numbers or SNTrN-numbers are fuzzy values, all definitions and properties of fuzzy graph theory can applied to SNTN-numbers or SNTrN-numbers. For example, definition of fuzzy graph theory based on centroid points of normalized SVTN-numbers and SVTrN-numbers is given.
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Conference papers on the topic "Set-valued operation"

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Vladova, A. "Identification Method of Oil Pipelines Technical Condition Based Upon Multigraph Models." In 2014 10th International Pipeline Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/ipc2014-33429.

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The problem of technical condition identification of aging oil pipelines in Russian Federation and in the world is relevant, since a significant number of them have been in service for over 30 years. More and more of them are getting closer to running out of normative resources. Within a method for reducing the size of task of identifying the technical condition of oil pipelines there were created special types of multigraph models (MGM) with interval-valued states of geometric characteristic of metallic shell defects. Depending on oil pipelines operation time, the behavior of proposed models has been examined and operating performance with due account for technical condition identification has been determined, also the possibility of diminishing scope of inspections and repair works was shown. Multigraph models proposed here contain a set of states, which were singled out for the first time according to the analogue variable and are connected with multidirectional arcs with intensities of damage calculated on the relative amount of defects in the states.
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Zhang, Xuezheng, Qian Zhu, and Zheng Pei. "Linguistic set-valued decision making based on LWA operator." In EM). IEEE, 2010. http://dx.doi.org/10.1109/ieem.2010.5674338.

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GUO, RENKUAN, and ERNIE LOVE. "FUZZY SET-VALUED STATISTICAL INFERENCES ON A SYSTEM OPERATING DATA." In Proceedings of the 2004 Asian International Workshop (AIWARM 2004). WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702685_0022.

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Verhaeghe, Hélène, Christophe Lecoutre, and Pierre Schaus. "Compact-MDD: Efficiently Filtering (s)MDD Constraints with Reversible Sparse Bit-sets." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/192.

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Multi-Valued Decision Diagrams (MDDs) are instrumental in modeling combinatorial problems with Constraint Programming.In this paper, we propose a related data structure called sMDD (semi-MDD) where the central layer of the diagrams is non-deterministic.We show that it is easy and efficient to transform any table (set of tuples) into an sMDD.We also introduce a new filtering algorithm, called Compact-MDD, which is based on bitwise operations, and can be applied to both MDDs and sMDDs.Our experimental results show the practical interest of our approach, both in terms of compression and filtering speed.
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