On Fuzzy Soft Sets

By Bashir Ahmad, Athar Kharal. Advances in Fuzzy Systems, 2009

1,445 citations recorded by the source corpus.

We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. (2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition 3.3 by Maji et al., (2001). Finally we define arbitrary fuzzy soft union and fuzzy soft intersection and prove DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/71e30061b66753ff56dcdb4a9475d1904e5476ba

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Citations in the corpus

Soft matrix theory and its decision making (2010, neutral): “[22] defined the fuzzy soft sets.”
Decompositions of Some Types of Supra Soft Sets and Soft Continuity (2014, background): “In recent years, many interesting applications of soft set theory have been expanded by embedding the ideas of fuzzy sets [1, 2, 6, 12, 13, 14, 15, 16, 18, 25].”
Soft sets and soft rough sets (2011, background): “[18] initiated the study on hybrid structures involving both fuzzy sets and soft sets.”
Soft Multisets Theory (2011, background): “[3] presented the definition of fuzzy soft set and Roy and Maji [7] presented the applications of this notion to decision making problems.”
Interval-valued intuitionistic fuzzy soft sets and their properties (2010, background): “[23] initiated the study on hybrid structures involving both fuzzy sets and soft sets.”
A fuzzy soft set theoretic approach to decision making problems (2007, background): “Most of them may be found in [5].”
Products of FP-Soft Sets and their Applications (2012, background): “These and more detailed explanations related to soft sets and fuzzy sets can be found in [4, 13, 17] and [24, 25], respectively.”
Neutrosophic soft relations and some properties (2014, background): “In 1999, Molodotsov[20] introduced the theory of soft set which is free from the parameterization inadequacy syndrome of fuzzy set theory, rough set theory[24], probability theory for dealing with uncertainty.”
FUZZY SOFT SET THEORY AND ITS APPLICATIONS (2011, methodology): “[18, 20] are used in all the works mentioned above.”
On Soft Topological Spaces (2013, background): “The soft set theory has been applied to many different fields (see, for example, [ 1], [2], [4], [5], [7], [8], [11], [12], [13], [14], [15], [16], [22], [25], [27]).”
A Historical Account of Types of Fuzzy Sets and Their Relationships (2016, background): “2001 Maji, Biswas and Roy introduce the notion of FSS [88].”
Fuzzy Parameterized Interval-Valued Fuzzy Soft Set (2011, background): “[6] defined a fuzzy soft set and they gave the application of fuzzy soft set in decision making problem in [8].”
A Novel Approach towards Bipolar Soft Sets and Their Applications (2020, background): “For more studies and applications of soft sets, one may study [19–23]. notion of fuzzy soft sets was introduced by Maji et al. [24].”
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