On generalized intuitionistic fuzzy rough approximation operators

Zhou, Lihua; Wu, Wei-Zhi

doi:10.1016/j.ins.2008.01.012

Cited by 80 publications

(94 citation statements)

References 60 publications

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“…Li [107] worked on intuitionistic fuzzy multiattribute decision making and constructed several linear programming models to generate optimal weights for attributes. 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.…”

Section: Intuitionistic Fuzzy Setsmentioning

confidence: 99%

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

Kahraman¹,

Öztayşi²,

Onar³

2016

IJCIS

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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

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“…Obviously, DHFRS is a "deep" extension of rough set while classical fuzzy rough set [10], intuitionistic fuzzy rough sets [11] and HFRS [5] are all special cases of DHFRS. Therefore, it is fundamentally worthwhile to study on DHFRS.…”

Section: Introductionmentioning

confidence: 99%

A Dual Hesitant Fuzzy Rough Pattern Recognition Approach Based on Deviation Theories and Its Application in Urban Traffic Modes Recognition

et al. 2017

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Abstract:In this paper, the dual hesitant fuzzy rough set (DHFRS) is studied from the viewpoint of assessment deviations. Firstly, according to the relationship between intuitionistic fuzzy set and vague set, the DHFRS is transferred into a fuzzy set, where the membership of any given element to it has multi-grouped values. By the idea of bootstrap sampling, a group of four sets are generated to describe the membership degree on DHFRS, where the elements of the aforementioned sets are all considered as assessment values. Secondly, the generated sets are dealt with by assessment deviation theories, and specifically, two variables are proposed to describe the systematic and random deviations of the sets. Thirdly, the true-value of the membership degree of any elements to the set is estimated by a deviation-based dual hesitant fuzzy rough weighted aggregating operator. Fourthly, a dual hesitant fuzzy rough pattern recognition approach based on assessment deviation theories is proposed. Finally, an urban traffic modes recognition example is given to illustrate the validity of the proposed theories on DHFRSs.

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“…Recently, the approximation operators of rough set theory were introduced into vague sets and intuitionistic fuzzy sets [31][32][33][34]. Due to their different motivations and background material, so the definitions are given in different ways, for example, Samamta and Mondal [32] define a rough intuitionistic fuzzy set which does not correspond to the theory of approximate spaces.…”

Section: Introductionmentioning

confidence: 99%

“…Due to their different motivations and background material, so the definitions are given in different ways, for example, Samamta and Mondal [32] define a rough intuitionistic fuzzy set which does not correspond to the theory of approximate spaces. Wang et al [33] define rough vague sets based on equivalence relations; and Zhou and Wu [34] define rough intuitionistic fuzzy sets based on intuitionistic fuzzy relations, mainly discussing cut-sets of intuitionistic fuzzy rough sets, and classical representations of intuitionistic fuzzy rough approximation operators.…”

Section: Introductionmentioning

confidence: 99%

Approximation operators based on vague relations and roughness measures of vague sets

2011

Front. Comput. Sci. China

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Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy set model based on fuzzy relations to vague sets. We mainly focus on the lower and upper approximation operators of vague sets based on vague relations, and investigate the basic properties of approximation operators on vague sets. Specially, we give some essential characterizations of the lower and upper approximation operators generated by reflexive, symmetric, and transitive vague relations. Finally, we structure a parameterized roughness measure of vague sets and similarity measure methods between two rough vague sets, and obtain some properties of the roughness measure and similarity measures. We also give some valuable counterexamples and point out some false properties of the roughness measure in the paper of Wang et al.

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On generalized intuitionistic fuzzy rough approximation operators

Cited by 80 publications

References 60 publications

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

A Dual Hesitant Fuzzy Rough Pattern Recognition Approach Based on Deviation Theories and Its Application in Urban Traffic Modes Recognition

Approximation operators based on vague relations and roughness measures of vague sets

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