On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators

Zhou, Lihua; Wu, Wei-Zhi; Zhang, Wenxiu

doi:10.1016/j.ins.2008.11.015

Cited by 113 publications

(35 citation statements)

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“…Xu and Yager [108] [111] proposed a general framework for the study of relation-based intuitionistic fuzzy rough approximation operators within which both constructive and axiomatic approaches are used. Zhou et al [112] presented a general framework for the study of relationbased (I, T)-intuitionistic fuzzy rough sets by using constructive and axiomatic approaches. Mursaleen and Mohiuddine [113] studied the concept of statistically convergent and statistically Cauchy double sequences in intuitionistic fuzzy normed spaces.…”

Section: Intuitionistic Fuzzy Setsmentioning

confidence: 99%

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

Kahraman¹,

Öztayşi²,

Onar³

2016

IJCIS

101

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Fuzzy sets have a great progress in every scientific research area. It found many application areas in both theoretical and practical studies from engineering area to arts and humanities, from computer science to health sciences, and from life sciences to physical sciences. In this paper, a comprehensive literature review on the fuzzy set theory is realized. In the recent years, ordinary fuzzy sets have been extended to new types and these extensions have been used in many areas such as energy, medicine, material, economics and pharmacology sciences. This literature review also analyzes the chronological development of these extensions. In the last section of the paper, we present our interpretations on the future of fuzzy sets.

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Section: Intuitionistic Fuzzy Setsmentioning

confidence: 99%

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

Kahraman¹,

Öztayşi²,

Onar³

2016

IJCIS

101

View full text Add to dashboard Cite

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“…So it is necessary to introduce the concept of intuitionistic fuzzy implications. Studies on intuitionistic fuzzy implications have obtained many results (Alcalde et al 2005;Bedregal et al 2010;Bedregal 2010;Bustince 2000;Cintula and Metcalfe 2010;Li et al 2011;Li and Li 2012;Yu and Xu 2013;Zhou et al 2009). Wang et al (2014) extended the Lukasiewicz implication operator to intuitionistic fuzzy environment, and then applied the intuitionistic fuzzy triangle product to compare the alternatives in multiple attribute decision making with intuitionistic fuzzy information, and then constructed an intuitionistic fuzzy similarity matrix to develop a direct method for intuitionistic fuzzy clustering analysis.…”

Section: Introductionmentioning

confidence: 99%

Constructive methods for intuitionistic fuzzy implication operators

2016

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In this paper, two novel constructive methods for fuzzy implication operators are proposed. And they can be used to resolve the questions about how to construct intuitionistic fuzzy implication operators to inference sentence "If x is A, then y is B," where A and B are intuitionistic fuzzy sets over X and Y , respectively. In the first method, cut sets and representation theorem of intuitionistic fuzzy sets are utilized through triple valued fuzzy implications as well as fuzzy relations to obtain seven intuitionistic fuzzy implication operators. In the second method, the Lebesgue measure of the fuzzy implications with value one and zero is used, and one intuitionistic fuzzy implication operator can be obtained. Finally, properties of those operators are discussed.

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“…The notion of rough set and its properties were applied to various areas: rings [5][6][7][8]12,14], modules [9,13,20,27], semigroups [17,31], groups [2,18], MV-algebras [28], BCKalgebras [11], graphs [30], information systems [19,22,35,36], and lattices [10,21,32]. Also, Mordeson [23] used covers of the universal set to define approximation operators on the power set of a given set.…”

Section: Introductionmentioning

confidence: 99%