• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.2
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• pp.125-129
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• 2004

There are several kinds of fuzzy set extensions in the fuzzy set theory. Among them, this paper is concerned with interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets. In interval-valued fuzzy sets, membership degrees are represented by an interval value that reflects the uncertainty in assigning membership degrees. In intuitionistic fuzzy sets, membership degrees are described with a pair of a membership degree and a nonmembership degree. In bipolar-valued fuzzy sets, membership degrees are specified by the satisfaction degrees to a constraint and its counter-constraint. This paper investigates the similarities and differences among these fuzzy set representations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.12-15
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• 2001

There are several kinds of fuzzy set extensions in the fuzzy set theory. Among them, this paper is concerned with interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets. In interval-valued fuzzy sets, membership degrees are represented by an interval value that reflects the uncertainty in assigning membership degrees. In intuitionistic sets, membership degrees are described with a pair of a membership degree and a nonmembership degree. In bipolar-valued fuzzy sets, membership degrees are specified by the satisfaction degrees to a constraint and its counter-constraint. This paper investigates the similarities and differences among these fuzzy set representations.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.3
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• pp.316-322
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• 2008

We introduce the concept of interval-valued intuitionistic fuzzy soft sets, which is an extension of the interval-valued fuzzy soft set. We also introduce the concepts of operations for the interval-valued intuitionistic fuzzy soft sets and study basic some properties.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.413-437
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• 2023

In this paper, we introduce the concepts of (inf, sup)-hesitant fuzzy subsemigroups and (inf, sup)-hesitant fuzzy (generalized) bi-ideals of semigroups, and investigate their properties. The concepts are established in terms of sets, fuzzy sets, negative fuzzy sets, interval-valued fuzzy sets, Pythagorean fuzzy sets, hesitant fuzzy sets, and bipolar fuzzy sets. Moreover, some characterizations of bi-ideals, fuzzy bi-ideals, anti-fuzzy bi-ideals, negative fuzzy bi-ideals, Pythagorean fuzzy bi-ideals, and bipolar fuzzy bi-ideals of semigroups are given in terms of the (inf, sup)-type of hesitant fuzzy sets. Also, we characterize a semigroup which is completely regular, a group and a semilattice of groups by (inf, sup)-hesitant fuzzy bi-ideals.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.253-266
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• 2011

We would like to generalize about trapezoidal fuzzy set and to calculate four operations based on the Zadeh's extension principle for two generalized trapezoidal fuzzy sets. And we roll up triangular fuzzy numbers and generalized triangular fuzzy sets into it. Since triangular fuzzy numbers and generalized triangular fuzzy sets are generalized trapezoidal fuzzy sets, we need no more the separate painstaking calculations of addition, subtraction, multiplication and division for two such kinds once the operations are done for generalized trapezoidal fuzzy sets.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.79-84
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• 2022

We have observed that there exist certain fuzzy topological spaces with no fuzzy minimal open sets. This observation motivates us to investigate fuzzy topological spaces with neither fuzzy minimal open sets nor fuzzy maximal open sets. We have observed if such fuzzy topological spaces exist and if it is connected are not fuzzy cut-point spaces. We also study and characterize certain properties of fuzzy mean open sets in fuzzy T₁-connected fuzzy topological spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.864-874
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• 2010

We introduce the notion of intuitionistic interval-valued fuzzy sets as the another generalization of interval-valued fuzzy sets and intuitionistic fuzzy sets and hence fuzzy sets. Also we introduce some operations over intuitionistic interval-valued fuzzy sets. And we study some fundamental properties of intuitionistic interval-valued fuzzy sets and operations.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.317-331
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• 2018

This paper aims to extend the notion of hesitant fuzzy sets on UP-algebras to hesitant fuzzy soft sets over UP-algebras by merging the notions of hesitant fuzzy sets and soft sets. Further, we discuss the notions of hesitant fuzzy soft strongly UP-ideals, hesitant fuzzy soft UP-ideals, hesitant fuzzy soft UP-filters, and hesitant fuzzy soft UP-subalgebras of UP-algebras, and provide some properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.4
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• pp.284-287
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• 2008

In this paper, we introduce multi-intuitionistic fuzzy sets and intuitionistic fuzzy hybrid sets. The basic operations between such structures are defined. The use of these structures in the definition of intuition is tic fuzzy variants of P systems and their properties are presented.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.251-257
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• 2021

This article is devoted to introduce the notion of fuzzy cleanly covered fuzzy topological spaces; in addition two strong fuzzy separation axioms are studied. By means of fuzzy maximal open sets some properties of fuzzy cleanly covered fuzzy topological spaces are obtained and also by means of fuzzy maximal closed sets few identical results of a fuzzy topological spaces are investigated. Through fuzzy minimal open and fuzzy maximal closed sets, two strong fuzzy separation axioms are discussed.