Axiomatic theory of intuitionistic fuzzy sets

doi:10.1016/S0165-0114(98)00010-4

Fuzzy Sets and Systems

Volume 110, Issue 2, 1 March 2000, Pages 253-266

https://doi.org/10.1016/S0165-0114(98)00010-4 Get rights and content

Abstract

A Bernays-like axiomatic theory of intuitionistic fuzzy sets involving five primitives and seven axioms is presented.

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On generalized intuitionistic fuzzy rough approximation operators
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In rough set theory, the lower and upper approximation operators defined by binary relations satisfy many interesting properties. Various generalizations of Pawlak’s rough approximations have been made in the literature over the years. This paper proposes a general framework for the study of relation-based intuitionistic fuzzy rough approximation operators within which both constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper intuitionistic fuzzy rough approximation operators induced from an arbitrary intuitionistic fuzzy relation are defined. Basic properties of the intuitionistic fuzzy rough approximation operators are then examined. By introducing cut sets of intuitionistic fuzzy sets, classical representations of intuitionistic fuzzy rough approximation operators are presented. The connections between special intuitionistic fuzzy relations and intuitionistic fuzzy rough approximation operators are further established. Finally, an operator-oriented characterization of intuitionistic fuzzy rough sets is proposed, that is, intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of lower and upper intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of intuitionistic fuzzy relations which produce the same operators.
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Axiomatic theory of intuitionistic fuzzy sets

Abstract

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Inform. Sci.