Equivalent bipolar fuzzy relations

Dudziak, Urszula; Pękala, Barbara

doi:10.1016/j.fss.2009.06.016

Cited by 31 publications

(14 citation statements)

References 30 publications

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“…4.-Applications. Extensions have shown to be very useful in problems of decision making [55], [85], [112], [152], [153], [154], [159], [169], [170]. In general, they work very well in problems in which we have to represent the difference between the positive and the negative representation of something [37], in particular in cognitive psychology and medicine [19].…”

Section: -Measures Yielding Pairs Each Membership Degree In Amentioning

confidence: 99%

A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince

Barrenechea

Pagola

et al. 2016

IEEE Trans. Fuzzy Syst.

407

159

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Section: -Measures Yielding Pairs Each Membership Degree In Amentioning

confidence: 99%

A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince

Barrenechea

Pagola

et al. 2016

IEEE Trans. Fuzzy Syst.

407

159

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“…Almost all properties of a classical concept lattice hold under this situation. They are in fact the general izations of the results in classical formal concept analysis (see [7,8,10,17,19,24]). …”

Section: Introductionmentioning

confidence: 66%

Axiomatic approaches of fuzzy concept operators

Song

Wang

Zhang

2012

2012 International Conference on Machine Learning and Cybernetics

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In formal concept analysis, various fuzzy generalizations of for mal concepts have been made. The fuzzy concept operators de fined under the condition that the truth values (degrees) com ing from a complete residuated lattice satisfy many interesting properties. Conversely, fuzzy concept operators can be charac terized in terms of their properties. In this paper, the axiomatic approaches in the theory of fuzzy formal concept analysis based on a complete residuated lattice are presented. In the axiomatic approach, the fuzzy conceptual knowledge system is defined, and axiom sets satisfied by the fuzzy conceptual knowledge system are stated. It is proved that axioms of the fuzzy conceptual knowledge system guarantee the existence of certain types of binary fuzzy relations producing the same fuzzy formal concepts. The indepen dence of axiom sets characterizing the fuzzy conceptual knowledge system is examined.

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“…Lee et al [24] found some properties of bases, neighborhoods, and continuities in bipolar fuzzy topological spaces. In particular, Dudziak and Pekala [25] referred to an intuitionistic fuzzy relation as a bipolar fuzzy relation and investigated some properties of equivalent bipolar fuzzy relations.…”

Section: Introductionmentioning

confidence: 99%

Bipolar Fuzzy Relations

Lee

Hur

2019

Mathematics

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We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

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Equivalent bipolar fuzzy relations

Cited by 31 publications

References 30 publications

A Historical Account of Types of Fuzzy Sets and Their Relationships

A Historical Account of Types of Fuzzy Sets and Their Relationships

Axiomatic approaches of fuzzy concept operators

Bipolar Fuzzy Relations

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