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Journal articles on the topic 'Fuzzy Sets Theory Concepts'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Močkoř, Jiří, and David Hýnar. "On Unification of Methods in Theories of Fuzzy Sets, Hesitant Fuzzy Set, Fuzzy Soft Sets and Intuitionistic Fuzzy Sets." Mathematics 9, no. 4 (2021): 447. http://dx.doi.org/10.3390/math9040447.

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The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. It is proven that ad hoc defined basic concepts in individual theories, such as concepts of power set structures in these theories, relations or approximation operators defined by these relations are only special examples of applications of the monad theory in categories. This makes it possible, on the one hand, to unify basic constructions in all these th

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Zhang, Zhiming. "The Parameter Reduction of Fuzzy Soft Sets Based on Soft Fuzzy Rough Sets." Advances in Fuzzy Systems 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/197435.

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Fuzzy set theory, rough set theory, and soft set theory are three effective mathematical tools for dealing with uncertainties and have many wide applications both in theory and practise. Meng et al. (2011) introduced the notion of soft fuzzy rough sets by combining fuzzy sets, rough sets, and soft sets all together. The aim of this paper is to study the parameter reduction of fuzzy soft sets based on soft fuzzy rough approximation operators. We propose some concepts and conditions for two fuzzy soft sets to generate the same lower soft fuzzy rough approximation operators and the same upper sof

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Novák, Vilém. "Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory." Mathematics 8, no. 3 (2020): 432. http://dx.doi.org/10.3390/math8030432.

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In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included in AST. Using fuzzy type theory, we generalize basic concepts of rough set theory and the topological concepts of AST to become the concepts of the fuzzy set theory. We will give mostly syntactic proofs of the main properties and relations among all the considered concepts, thus showing that they ar

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Li, Hongjie, and Yunqiang Yin. "A New Kind of Fuzzyn-ary Hypergroups in the Framework of Soft Set Theory." Scientific World Journal 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/957391.

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Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem. The aim of this paper is to apply the concept of fuzzy soft sets ton-ary hypergroup theory. The concepts of(∈γ,∈γ∨qδ)-fuzzy soft (invertible)n-ary subhypergroups over a commutativen-ary hypergroup are introduced and some related properties and characterizations are obtained. The homomorphism properties of(∈γ,∈γ∨qδ)-fuzzy soft (invertible)n-ary subhypergroups are also derived.

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Hu, Jun Hong, Guo Dong Gu, and Fu Xian Liu. "The Intuitionistic Fuzzy S-Rough Sets Model and Dynamic Transfer Degree." Applied Mechanics and Materials 513-517 (February 2014): 4352–56. http://dx.doi.org/10.4028/www.scientific.net/amm.513-517.4352.

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The Intuitionistic Fuzzy S-Rough Sets (IFS-RS) is the intuitionistic fuzzy extension of S-Rough sets theory. It has dynamic characteristic of S-Rough sets, as well as intuitionistic fuzzy characteristic of Intuitionistic Fuzzy sets. Based on S-Rough sets theory, this paper introduced the membership and non-membership concepts of Intuitionistic Fuzzy sets, builded the model of IFS-RS under general equivalence relation, put forward the rough property and transfer degree concepts of IFS-RS. By calculating the rough property and transfer degree of IFS-RS, Thus being able to describe the transforma

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Tang, Weidong, Jinzhao Wu, and Dingwei Zheng. "On Fuzzy Rough Sets and Their Topological Structures." Mathematical Problems in Engineering 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/546372.

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The core concepts of rough set theory are information systems and approximation operators of approximation spaces. Approximation operators draw close links between rough set theory and topology. This paper is devoted to the discussion of fuzzy rough sets and their topological structures. Fuzzy rough approximations are further investigated. Fuzzy relations are researched by means of topology or lower and upper sets. Topological structures of fuzzy approximation spaces are given by means of pseudoconstant fuzzy relations. Fuzzy topology satisfying (CC) axiom is investigated. The fact that there

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Quaranta, Mario. "Fuzzy Set Theory and Concepts: A Proposal for Concept Formation and Operationalization." Comparative Sociology 12, no. 6 (2013): 785–820. http://dx.doi.org/10.1163/15691330-12341283.

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AbstractThe quantity-quality debate in social sciences also concerns concept formation and operationalization. The first approach has strong naturalist assumptions, while the second one focuses on the historical specificity of concepts. The solution to overcome this divide would be finding a path which balances the two perspectives. In this article we argue that fuzzy set theory can be a helpful tool for concept formation and operationalization. The application of fuzzy set theory to concept formation and operationalization provides, first, the opportunity of looking at concepts as complex con

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Ávila-Muñoz, Antonio M., and José María Sánchez-Sáez. "Fuzzy sets and Prototype Theory." Review of Cognitive Linguistics 12, no. 1 (2014): 133–59. http://dx.doi.org/10.1075/rcl.12.1.05avi.

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Prototype Theory offers one of the most accepted models for semantic memory organization. Lexical availability trials provide investigators with a faster and easier means of observing this cognitive organization, since lists of available lexicon are generated from associations relating some lexical elements with others. The experiments with lexical availability are able to activate one of the best-known lexical production mechanisms within experimental psychology: semantic category fluency. In this work we propose the appropriate means to reconstruct the community cognitive organization. This

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JUMARIE, GUY. "A (NEW) MEASURE OF FUZZY UNCERTAINTY VIA INTERVAL ANALYSIS, WHICH IS FULLY CONSISTENT WITH SHANNON THEORY." Tamkang Journal of Mathematics 22, no. 3 (1991): 223–41. http://dx.doi.org/10.5556/j.tkjm.22.1991.4606.

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Many authors have suggested different measures of the amount of uncertainty involved in fuzzy sets, but most of these concepts suffer from drawbacks: mainly, they are indexes of fuzziness rather than measures of uncertainty, and they are not fully consistent with Shannon theory. The question is herein once more considered by combining the information theory of deterministic functions, recently initiated by the author, with the viewpoint of interval analysis; and one so derive the new concept of "uncertainty of order c of fuzzy sets". It is shown that it satisfies the main properties which are

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Wang, Ting Zhong, and Hong Sheng Xu. "Constructing Domain Ontology Based on Fuzzy Set and Concept Lattice." Applied Mechanics and Materials 63-64 (June 2011): 715–18. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.715.

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The major content in FCA is to extract formal concepts and connections between them from data in form of formal context so as to form a lattice structure of formal concepts. Fuzzy set theory and fuzzy logic are acknowledged as an appropriate formalism for capturing imprecise and vague knowledge. The paper offers a methodology for building ontology for knowledge sharing and reusing based on fuzzy concept lattices union. This paper makes up these defects by applying formal concept analysis theory and fuzzy sets to construct concept hierarchies of ontology, and the experiments shows the CPU Time

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Zhou, Xiaoqiang, Qingguo Li, and Lankun Guo. "On Generalised Interval-Valued Fuzzy Soft Sets." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/479783.

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Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of generalised interval-valued fuzzy soft set are proposed and their basic properties are studied. The lattice structures of generalised interval-valued fuzzy soft set are also discussed. Furthermore, an application of the new approach in decision making based on generalised interval-valued fuzzy soft set is developed.

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Selvachandran, Ganeshsree, and Abdul Razak Salleh. "Possibility Intuitionistic Fuzzy Soft Expert Set Theory and Its Application in Decision Making." International Journal of Mathematics and Mathematical Sciences 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/314285.

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We propose the theory of possibility intuitionistic fuzzy soft expert theory and define some related concepts pertaining to this notion as well as the basic operations on this concept, namely, the complement, union, intersection, AND, and OR. The basic properties and relevant laws pertaining to this concept such as De Morgan’s laws are proved. Lastly, a generalized algorithm is introduced and applied to the concept of possibility intuitionistic fuzzy soft expert sets in hypothetical decision making problem.

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Luqman, Anam, Muhammad Akram, and Ahmad N. Al-Kenani. "q-Rung Orthopair Fuzzy Hypergraphs with Applications." Mathematics 7, no. 3 (2019): 260. http://dx.doi.org/10.3390/math7030260.

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The concept of q-rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the q th power of the truth-membership and the q th power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter q, q ≥ 1 . In this research study, we design a new framework for handling uncertain data by means of the comb

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Zhang, Haidong, Lan Shu, and Shilong Liao. "Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/287314.

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The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical examp

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15

ZHANG, ZHIMING, and JINGFENG TIAN. "ON ATTRIBUTE REDUCTION WITH INTUITIONISTIC FUZZY ROUGH SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20, no. 01 (2012): 59–76. http://dx.doi.org/10.1142/s0218488512500043.

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Intuitionistic fuzzy (IF) rough sets are the generalization of traditional rough sets obtained by combining the IF set theory and the rough set theory. The existing research on IF rough sets mainly concentrates on the establishment of lower and upper approximation operators using constructive and axiomatic approaches. Less effort has been put on the attribute reduction of databases based on IF rough sets. This paper systematically studies attribute reduction based on IF rough sets. Firstly, attribute reduction with traditional rough sets and some concepts of IF rough sets are reviewed. Then, w

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Lano, K. "Intuitionistic modal logic and set theory." Journal of Symbolic Logic 56, no. 2 (1991): 497–516. http://dx.doi.org/10.2307/2274696.

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The mathematical treatment of the concepts of vagueness and approximation is of increasing importance in artificial intelligence and related research. The theory of fuzzy sets was created by Zadeh [Z] to allow representation and mathematical manipulation of situations of partial truth, and proceeding from this a large amount of theoretical and applied development of this concept has occurred. The aim of this paper is to develop a natural logic and set theory that is a candidate for the formalisation of the theory of fuzzy sets. In these theories the underlying logic of properties and sets is i

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Paul, Ursala, and Paul Isaac. "Fuzzy Lattice Ordered G-modules." International Journal of Fuzzy System Applications 8, no. 3 (2019): 94–107. http://dx.doi.org/10.4018/ijfsa.2019070104.

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The study of mathematics emphasizes precision, accuracy, and perfection, but in many of the real-life situations, people face ambiguity, vagueness, imprecision, etc. Fuzzy set theory and rough set theory are two innovative tools in mathematics which are used for decision-making in vague and uncertain information systems. Fuzzy algebra has a significant role in the current era of mathematical research and it deals with the algebraic concepts and models of fuzzy sets. The study of various ordered algebraic structures like lattice ordered groups, Riesz spaces, etc., are of great importance in alg

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Zhang, Xing Yuan, Hai Rong Xu, Da Min Cao, and Sheng Bin Hu. "Reliability Assessment Using Fuzzy Evidence Theory." Applied Mechanics and Materials 220-223 (November 2012): 2165–68. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.2165.

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Aiming at many uncertain factors in the reliability assessment of aircraft, a new approach to reliability assessment combining D-S theory of evidence and fuzzy theory was discussed. The concepts of inclusion degree and intersection degree of fuzzy sets were redefined, and fuzzy evidence theory was extended to the circumstance when the framework of discrimination is a continuous and in finite set. Finally, the practical assessment process was given in an illustrative example of aircraft system. The results show that the method is effective and reliable.

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Yang, Yong, and Cong Cong Meng. "On Possibility Interval-Valued Fuzzy Soft Sets." Applied Mechanics and Materials 336-338 (July 2013): 2288–302. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.2288.

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Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of possibility interval-valued fuzzy soft sets are proposed. Their operations and basic properties are studied which are subset, equal, relative complement, union, intersection, restricted union, extended intersection, “AND”, “OR” and De Morgan Laws. Furthermore, an application of the new approach in decision making based on possibility interval-valued fuzzy soft set is illustrated.

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Hashmi, Masooma Raza, Syeda Tayyba Tehrim, Muhammad Riaz, Dragan Pamucar, and Goran Cirovic. "Spherical Linear Diophantine Fuzzy Soft Rough Sets with Multi-Criteria Decision Making." Axioms 10, no. 3 (2021): 185. http://dx.doi.org/10.3390/axioms10030185.

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Modeling uncertainties with spherical linear Diophantine fuzzy sets (SLDFSs) is a robust approach towards engineering, information management, medicine, multi-criteria decision-making (MCDM) applications. The existing concepts of neutrosophic sets (NSs), picture fuzzy sets (PFSs), and spherical fuzzy sets (SFSs) are strong models for MCDM. Nevertheless, these models have certain limitations for three indexes, satisfaction (membership), dissatisfaction (non-membership), refusal/abstain (indeterminacy) grades. A SLDFS with the use of reference parameters becomes an advanced approach to deal with

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Alpert, S. I. "The basic arithmetic operations on fuzzy numbers and new approaches to the theory of fuzzy numbers under the classification of space images." Mathematical machines and systems 3 (2020): 49–59. http://dx.doi.org/10.34121/1028-9763-2020-3-49-59.

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Classification in remote sensing is a very difficult procedure, because it involves a lot of steps and data preprocessing. Fuzzy Set Theory plays a very important role in classification problems, because the fuzzy approach can capture the structure of the image. Most concepts are fuzzy in nature. Fuzzy sets allow to deal with uncertain and imprecise data. Many classification problems are formalized by using fuzzy concepts, because crisp classes represent an oversimplification of reality, leading to wrong results of classification. Fuzzy Set Theory is an important mathematical tool to process c

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Dutta, Hemen, Adem Kilicman, and Ayhan Esi. "Fuzzy p-Absolutely Summable Difference Sequences." New Mathematics and Natural Computation 14, no. 02 (2018): 221–33. http://dx.doi.org/10.1142/s179300571850014x.

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In this work, we introduce the notion of [Formula: see text]-absolutely summability of difference sequences of fuzzy numbers and then reduce the concept of [Formula: see text]-absolutely summable sequences of fuzzy numbers. We discuss the sets of such sequences of fuzzy numbers under different fuzzy metrics. We also establish the completeness under suitable metric. Examples along with suitable explanation are incorporated to make the theory of this paper interesting and useful. Finally, the concepts of fuzzy solidity and fuzzy symmetricity are defined and the classes for these two properties a

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Onasanya, B. O., T. S. Atamewoue, and S. Hoskova-Mayerova. "Certain fuzzy hyperstructures from a fuzzy set." Journal of Intelligent & Fuzzy Systems 39, no. 3 (2020): 2775–82. http://dx.doi.org/10.3233/jifs-191054.

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Fuzzy set theory and also the hypergroups in the sense of Marty are both generalizations of some existing mathematical concepts which are used for modeling many real life situations. The main purpose of this paper is the study of the link between fuzzy sets and fuzzy hypergroups and fuzzy semihypergroups. As a matter of fact, some commutative fuzzy hypergroups and fuzzy semihypergroups have been constructed from fuzzy set and some of their properties were investigated.

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INTAN, ROLLY, and MASAO MUKAIDONO. "GENERALIZED FUZZY ROUGH SETS BY CONDITIONAL PROBABILITY RELATIONS." International Journal of Pattern Recognition and Artificial Intelligence 16, no. 07 (2002): 865–81. http://dx.doi.org/10.1142/s0218001402002039.

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In 1982, Pawlak proposed the concept of rough sets with a practical purpose of representing indiscernibility of elements or objects in the presence of information systems. Even if it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in real-world applications. Here, coverings of, or nonequivalence relations on, the universe can be considered to represent a more realistic model instead of a partition in which a generalized model of rough sets was proposed. In this paper, first a weak f

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Ullah, Rizwan, De Qun Zhou, and Peng Zhou. "Design Concept Evaluation and Selection: A Decision Making Approach." Applied Mechanics and Materials 155-156 (February 2012): 1122–26. http://dx.doi.org/10.4028/www.scientific.net/amm.155-156.1122.

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This study proposes a multi-attribute decision making based approach for product design concept evaluation and selection. The technique for order preference by similarity to ideal solution (TOPSIS) is combined with fuzzy sets and information entropy. While the fuzzy sets theory is employed to capture the associated vagueness in the expert judgment, the combination of information entropy method with multi-attribute decision making makes the approach computationally efficient. We present the results of the evaluation of design concepts which demonstrate the feasibility and practicability of the

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Oznamets, V. V. "Situational solution of the spatial location problem." Geodesy and Cartography 939, no. 9 (2018): 45–51. http://dx.doi.org/10.22389/0016-7126-2018-939-9-45-51.

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The rational allocation of resources is the basis for sustainable development of the territories. In reality, spatial planning often does not have clear information for decision- making. This factor puts the task of allocating resources under fuzzy information. The author suggests such a placement method. The basis for the solution and analysis is a well-known model of the informational situation. The author develops this concept and introduces a new one, of the informational spatial situation. Fuzzy spatial information makes grounds to introduce a new concept of fuzzy information situation. A

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Boricic, Branislav, and Snezana Konjikusic. "Logika preferencija na grubim i rasplinutim skupovima." Ekonomski anali 44, no. 160 (2004): 131–46. http://dx.doi.org/10.2298/eka0460131b.

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Theories of fuzzy sets and rough sets, as alternatives to the usual set theory founded on the two valued classical logic, present an appropriate context for developing the basic notions of the logic of preference and consequently, of the social choice theory. In this paper we present an introductory survey of two non-classical concepts of set: fuzzy set and rough set, as originally introduced by L. A. Zadeh and Z. Pawlak respectively, and then we prove that a preference relation defined by means of rough sets has the same basic properties as the classical or the fuzzy one. Moreover, we prove t

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Zihni, Onur, Yıldıray Çelik, and Güven Kara. "Interval-Valued Fuzzy Soft Graphs." Topological Algebra and its Applications 5, no. 1 (2017): 19–27. http://dx.doi.org/10.1515/taa-2017-0004.

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Abstract In this paper, we combine concepts of interval-valued fuzzy soft sets and graph theory. Then we introduce notations of interval-valued fuzzy soft graphs and complete interval-valued fuzzy soft graphs. We also present several different types operations including cartesian product, strong product and composition on interval-valued fuzzy soft graphs and investigate some properties of them.

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Çelik, Yildiray. "On bipolar fuzzy soft graphs." Creative Mathematics and Informatics 27, no. 2 (2018): 123–32. http://dx.doi.org/10.37193/cmi.2018.02.04.

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In this paper, we combine the concepts of bipolar fuzzy soft sets and graph theory. Then we introduce notations of bipolar fuzzy soft graph and strong bipolar fuzzy soft graph. We also present several different types of operations including cartesian product, strong product and composition on bipolar fuzzy soft graphs and investigate some properties of them.

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Ali, Ghous, G. Muhiuddin, Arooj Adeel, and Muhammad Zain Ul Abidin. "Ranking Effectiveness of COVID-19 Tests Using Fuzzy Bipolar Soft Expert Sets." Mathematical Problems in Engineering 2021 (July 24, 2021): 1–19. http://dx.doi.org/10.1155/2021/5874216.

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The theory of fuzzy bipolar soft sets is an efficient extension of soft sets for depicting the bipolarity of uncertain fuzzy soft information; however, it is limited to a single expert. The present research article introduces the theory of an innovative hybrid model called the fuzzy bipolar soft expert sets, as a natural extension of two existing models (including fuzzy soft expert sets and fuzzy bipolar soft sets). The proposed model is highly suitable for describing the bipolarity of fuzzy soft information having multiple expert opinions. Some fundamental properties of the developed hybrid m

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Keikha, Abazar. "Introducing a new type of HFSs and its application in solving MAGDM problems." Journal of Intelligent & Fuzzy Systems 40, no. 5 (2021): 9333–44. http://dx.doi.org/10.3233/jifs-201808.

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Uncertainty has long been explored as an objective and inalienable reality, and then modeled via different theories such as probability theory, fuzzy sets (FSs) theory, vague sets, etc. Hesitant fuzzy sets (HFSs) as a generalization of FSs, because of their flexibility and capability, extended and applied in many practical problems very soon. However, the above theories cannot meet all the scientific needs of researchers. For example, in some decision-making problems we encounter predetermined definite data, which have inductive uncertainties. In other words, the numbers themselves are crisp i

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Lemaire, Jean. "Fuzzy Insurance." ASTIN Bulletin 20, no. 1 (1990): 33–55. http://dx.doi.org/10.2143/ast.20.1.2005482.

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AbstractFuzzy set theory is a recently developed field of mathematics, that introduces sets of objects whose boundaries are not sharply defined. Whereas in ordinary Boolean algebra an element is either contained or not contained in a given set, in fuzzy set theory the transition between membership and non-membership is gradual. The theory aims at modelizing situations described in vague or imprecise terms, or situations that are too complex or ill-defined to be analysed by conventional methods. This paper aims at presenting the basic concepts of the theory in an insurance framework. First the

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Bhattacharya (Halder), Sharmistha, and Bijan Davvaz. "Some More Results on IF Soft Rough Approximation Space." International Journal of Combinatorics 2011 (December 21, 2011): 1–10. http://dx.doi.org/10.1155/2011/893061.

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Fuzzy sets, rough sets, and later on IF sets became useful mathematical tools for solving various decision making problems and data mining problems. Molodtsov introduced another concept soft set theory as a general frame work for reasoning about vague concepts. Since most of the data collected are either linguistic variable or consist of vague concepts so IF set and soft set help a lot in data mining problem. The aim of this paper is to introduce the concept of IF soft lower rough approximation and IF upper rough set approximation. Also, some properties of this set are studied, and also some p

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GAO, XIAOYU, Q. S. GAO, Y. HU, and L. LI. "A PROBABILITY-LIKE NEW FUZZY SET THEORY." International Journal of Pattern Recognition and Artificial Intelligence 20, no. 03 (2006): 441–62. http://dx.doi.org/10.1142/s0218001406004697.

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In this paper, the reasons for the shortcoming of Zadeh's fuzzy set theory — it cannot correctly reflect different kinds of fuzzy phenomenon in the natural world — are discussed. In addition, the proof of the error of Zadeh's fuzzy set theory — it incorrectly defined the set complement that cannot exist in Zadeh's fuzzy set theory — is proposed. This error of Zadeh's fuzzy set theory causes confusion in thinking, logic and conception. It causes the seriously mistaken belief that logics of fuzzy sets necessarily go against classical and normal thinking, logic and conception. Two new fuzzy set t

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Zakaria, Rozaimi, Abd Fatah Wahab, and R. U. Gobithaasan. "Fuzzy B-Spline Surface Modeling." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/285045.

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This paper discusses the construction of a fuzzy B-spline surface model. The construction of this model is based on fuzzy set theory which is based on fuzzy number and fuzzy relation concepts. The proposed theories and concepts define the uncertainty data sets which represent fuzzy data/control points allowing the uncertainties data points modeling which can be visualized and analyzed. The fuzzification and defuzzification processes were also defined in detail in order to obtain the fuzzy B-spline surface crisp model. Final section shows an application of fuzzy B-spline surface modeling for te

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Huang, Han-Chen, and Xiaojun Yang. "A Comparative Investigation of Type-2 Fuzzy Sets, Nonstationary Fuzzy Sets and Cloud Models." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 24, no. 02 (2016): 213–27. http://dx.doi.org/10.1142/s0218488516500112.

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Since Zadeh introduced fuzzy sets, a lot of extensions of this concept have been proposed, such as type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models, to represent higher levels of uncertainty. This paper provides a comparative investigation of type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models. Type-2 fuzzy sets study the fuzziness of the membership function (MF) using primary MF and secondary MF based on analytic mathematical methods; nonstationary fuzzy sets study the randomness of the MF using primary MF and variation function based on type-1 fuzzy sets theory; cloud

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Alkouri, Abd Ulazeez M., and Abdul Razak Salleh. "Complex Atanassov's Intuitionistic Fuzzy Relation." Abstract and Applied Analysis 2013 (2013): 1–18. http://dx.doi.org/10.1155/2013/287382.

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This paper presents distance measure between two complex Atanassov's intuitionistic fuzzy sets (CAIFSs). This distance measure is used to illustrate an application of CAIFSs in solving one of the most core application areas of fuzzy set theory, which is multiattributes decision-making (MADM) problems, in complex Atanassov's intuitionistic fuzzy realm. A new structure of relation between two CAIFSs, called complex Atanassov's intuitionistic fuzzy relation (CAIFR), is obtained. This relation is formally generalised from a conventional Atanassov's intuitionistic fuzzy relation, based on complex A

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Feng, Feng, Hamido Fujita, Young Bae Jun, and Madad Khan. "Decomposition of Fuzzy Soft Sets with Finite Value Spaces." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/902687.

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The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Usingt-level soft sets, we define level equivalent relations and show that

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WEI, LI-LI, and WEN-XIU ZHANG. "PROBABILISTIC ROUGH SETS CHARACTERIZED BY FUZZY SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, no. 01 (2004): 47–60. http://dx.doi.org/10.1142/s0218488504002643.

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Theories of fuzzy sets and rough sets have emerged as two major mathematical approaches for managing uncertainty that arises from inexact, noisy, or incomplete information. They are generalizations of classical set theory for modelling vagueness and uncertainty. Some integrations of them are expected to develop a model of uncertainty stronger than either. The present work may be considered as an attempt in this line, where we would like to study fuzziness in probabilistic rough set model, to portray probabilistic rough sets by fuzzy sets. First, we show how the concept of variable precision lo

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Varma, Gayathri, and Sunil Jacob John. "On Multi-Fuzzy Rough Sets, Relations, and Topology." International Journal of Fuzzy System Applications 8, no. 1 (2019): 101–19. http://dx.doi.org/10.4018/ijfsa.2019010106.

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This article describes how rough set theory has an innate topological structure characterized by the partitions. The approximation operators in rough set theory can be viewed as the topological operators namely interior and closure operators. Thus, topology plays a role in the theory of rough sets. This article makes an effort towards considering closed sets a primitive concept in defining multi-fuzzy topological spaces. It discusses the characterization of multi-fuzzy topology using closed multi-fuzzy sets. A set of axioms is proposed that characterizes the closure and interior of multi-fuzzy

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Khan, Sami Ullah, Naeem Jan, Kifayat Ullah, and Lazim Abdullah. "Graphical Structures of Cubic Intuitionistic Fuzzy Information." Journal of Mathematics 2021 (May 11, 2021): 1–21. http://dx.doi.org/10.1155/2021/9994977.

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The theory developed in this article is based on graphs of cubic intuitionistic fuzzy sets (CIFS) called cubic intuitionistic fuzzy graphs (CIFGs). This graph generalizes the structures of fuzzy graph (FG), intuitionistic fuzzy graph (IFG), and interval-valued fuzzy graph (IVFG). Moreover, several associated concepts are established for CIFG, such as the idea subgraphs, degree of CIFG, order of CIFG, complement of CIFG, path in CIFG, strong CIFG, and the concept of bridges for CIFGs. Furthermore, the generalization of CIFG is proved with the help of some remarks. In addition, the comparison am

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Dixit, Sonal, and Kirti Verma. "COMPARATIVE STUDY OF FUZZY MATHEMATICS AS FUZZY SETS AND FUZZY LOGICS." Journal of Mathematical Sciences & Computational Mathematics 2, no. 4 (2021): 500–510. http://dx.doi.org/10.15864/jmscm.2404.

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Fuzzy mathematics is considered to be an important aspect in the field of mathematics that interprets the uncertainties and deals with the unreliable information and vagueness of data. In this chapter we shall discuss the concept of fuzzy mathematics as fuzzy set and fuzzy logics and the beginning of fuzzy set theory and the fuzzy logics with their applications in the real life. As fuzzy mathematics and fuzzy logics are becoming increasingly significant as it is applied in almost every field of developments, engineering design and models and in new technologies also. We also discuss some recen

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JOSLYN, CLIFF. "AGGREGATION AND COMPLETION OF RANDOM SETS WITH DISTRIBUTIONAL FUZZY MEASURES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 04, no. 04 (1996): 307–29. http://dx.doi.org/10.1142/s0218488596000184.

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The two known information theories, probability and possibility theory, are based on t-conorm decomposable fuzzy measures, so that bijective mappings exist between their set-valued measures and their point-valued distributions. Further, their random set (Dempster-Shafer evidence theoretical) interpretations have simple topological structures, with bijective mappings between the subset focal elements and the point singletons. We introduce the concepts of distributional and aggregable random sets and random set completion, and first use them as a model in which to cast probability and possibilit

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Shahzadi, Sundas, Musavarah Sarwar, and Muhammad Akram. "Decision-Making Approach with Fuzzy Type-2 Soft Graphs." Journal of Mathematics 2020 (November 17, 2020): 1–25. http://dx.doi.org/10.1155/2020/8872446.

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Molodtsov’s theory of soft sets is free from the parameterizations insufficiency of fuzzy set theory. Type-2 soft set as an extension of a soft set has an essential mathematical structure to deal with parametrizations and their primary relationship. Fuzzy type-2 soft models play a key role to study the partial membership and uncertainty of objects along with underlying and primary set of parameters. In this research article, we introduce the concept of fuzzy type-2 soft set by integrating fuzzy set theory and type-2 soft set theory. We also introduce the notions of fuzzy type-2 soft graphs, re

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Thirunavukarasu, Ashok Kumar, Suresh, and Lilly Merline. "EXTENDED THEORETICAL CONCEPT OF COMPLEX FUZZY SETS BY COMPLEX FUZZY SOFT HYPERGROUP, COMPLEX FUZZY SOFT HYPERRING." International Journal of Research -GRANTHAALAYAH 4, no. 7(SE) (2016): 62–69. http://dx.doi.org/10.29121/granthaalayah.v4.i7(se).2016.2629.

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In this paper, we develop the initial theory of complex fuzzy soft hypergroup by introducing the novel concept of complex fuzzy soft hypergroup, complex fuzzy soft hyperring. Consequently, a major part of this work is dedicated to extend the theory of complex fuzzy soft set, complex fuzzy hypergroup. Complex fuzzy soft quasihypergroup, complex fuzzy soft semihypergroup and complex fuzzy soft subhypergroup also discussed in this paper.

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Alshehri, Noura, and Muhammad Akram. "Intuitionistic Fuzzy Planar Graphs." Discrete Dynamics in Nature and Society 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/397823.

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Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomor

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Kukkurainen, Paavo. "Level Sets as a Topological Base Applied to Subgroups of a Group of Moebius Transformations." Journal of Advanced Computational Intelligence and Intelligent Informatics 9, no. 5 (2005): 511–13. http://dx.doi.org/10.20965/jaciii.2005.p0511.

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We applied the theory of Moebius transformations, known in complex analysis, to fuzzy subgroups. We start using the two results presented by B. Seselja and A. Tepavcevic [4,5], taking a topological view point not in these papers. This leads to topological subgroups of a group of Moebius transformations. Although this is known in complex analysis, we approach it through of fuzzy concepts.

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Lee, Hai-Wu. "A study of the use of fuzzy control theory to stabilize the gait of biped robots." Robotica 34, no. 4 (2014): 777–90. http://dx.doi.org/10.1017/s0263574714001854.

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SUMMARYThis paper designs a biped robot to perform appropriate walking exercises according to the terrain, which then walks stably on a flat environment. The concept of fuzzy logic is combined with the Linear Quadratic Regulator (LQR) controller theory to design the best method to allow the biped robot system to have a balanced and stable gait. Traditional controllers are designed using mathematical models of physical systems, but a fuzzy controller is a physical system that uses an inexact mathematical model, which involves sets and membership functions. Fuzzy controllers use fuzzification, f

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Zhang, Zhiming, and Shouhua Zhang. "Type-2 Fuzzy Soft Sets and Their Applications in Decision Making." Journal of Applied Mathematics 2012 (2012): 1–35. http://dx.doi.org/10.1155/2012/608681.

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Molodtsov introduced the theory of soft sets, which can be used as a general mathematical tool for dealing with uncertainty. This paper aims to introduce the concept of the type-2 fuzzy soft set by integrating the type-2 fuzzy set theory and the soft set theory. Some operations on the type-2 fuzzy soft sets are given. Furthermore, we investigate the decision making based on type-2 fuzzy soft sets. By means of level soft sets, we propose an adjustable approach to type-2 fuzzy-soft-set based decision making and give some illustrative examples. Moreover, we also introduce the weighted type-2 fuzz

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Garg, Harish, R. Sujatha, D. Nagarajan, J. Kavikumar, and Jeonghwan Gwak. "Evidence Theory in Picture Fuzzy Set Environment." Journal of Mathematics 2021 (May 18, 2021): 1–8. http://dx.doi.org/10.1155/2021/9996281.

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Picture fuzzy set is the most widely used tool to handle the uncertainty with the account of three membership degrees, namely, positive, negative, and neutral such that their sum is bound up to 1. It is the generalization of the existing intuitionistic fuzzy and fuzzy sets. This paper studies the interval probability problems of the picture fuzzy sets and their belief structure. The belief function is a vital tool to represent the uncertain information in a more effective manner. On the other hand, the Dempster–Shafer theory (DST) is used to combine the independent sources of evidence with the

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