• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.321-330
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• 2006

We introduce the concept of intuitionistic fuzzy weak congruence on a semiring and obtain the relation between intuitionistic fuzzy weak congruence and intuitionistic fuzzy ideal of a semiring. Also we define and investigate intuitionistic fuzzy quotient semiring of a semiring over an intuitionistic fuzzy ideal or over an intuitionistic fuzzy weak congruence.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.2
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• pp.149-153
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• 2012

In this paper, we introduce the concept of fuzzy almost strongly (r, s)-semicontinuous mappings on intuitionistic fuzzy topological spaces in $\check{S}$ostak's sense. The relationships among fuzzy strongly (r, s)-semicontinuous, fuzzy almost (r, s)-continuous, fuzzy almost (r, s)-semicontinuous, and fuzzy almost strongly (r, s)-semicontinuous mappings are discussed. The characterization for the fuzzy almost strongly (r, s)-semicontinuous mappings is obtained.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.141-150
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• 2022

The aim of this article is to introduce hesitant fuzzy paraopen and hesitant fuzzy mean open sets in hesitant fuzzy topological spaces. Moreover we investigate and extend some properties of hesitant fuzzy mean open with hesitant fuzzy paraopen, hesitant fuzzy minmimal open and maximal open sets in hesitant fuzzy topological spaces.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.41-44
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• 2003

First, we investigate some properties of fuzzy compactness. Second, we introduce the concept of fuzzy local compactness in fuzzy topological space and study some of its properties. Finally, we investigate some relations between F-compactness in fuzzy topological spaces and one in fuzzy hyperspaces.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.265-272
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• 2023

This article presents a novel notion of hesitant fuzzy cleanly covered in hesitant fuzzy topological spaces;moreover two strong hesitant fuzzy separation axioms are investigated. Based on fuzzy maximal open sets few properties of hesitant fuzzy cleanly covered are obtained. By dint of hesitant fuzzy minimal open and fuzzy maximal closed sets two strong hesitant fuzzy separation axioms are extended.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.191-194
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• 2007

In this paper, we introduce the concepts of fuzzy (r,s)-pre-semiopen sets and fuzzy (r,s)-pre-semicontinuous mappings on intuitionistic fuzzy topological spaces in ${\v{S}}ostak's$ sense. The concepts of fuzzy (r,s)-pre-semiinterior, fuzzy (r,s)-pre-semiclosure, fuzzy (r,s)-pre-semineighborhood, and fuzzy (r,s)-quasi-pre-semineighborhood are given, and several properties of these concepts are discussed. Using these concepts, the characterizations for the fuzzy (r,s)-pre-semicontinuous mappings are obtained. Also, we introduce the notions of fuzzy (r,s)-presemiopen and fuzzy (r,s)-pre-semiclosed mappings on intuitionistic fuzzy topologica spaces in ${\v{S}}ostak's$ sense, and then we investigate some of their characteristic properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.3
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• pp.153-164
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• 2011

Equivalence relations and mappings for crisp sets are very well known. This paper attempts an investigation of equivalence relations and mappings for fuzzy sets. We list some concepts and results related to fuzzy relations. We give some examples corresponding to the concept of fuzzy equality and fuzzy mapping introduced by Demirci [1]. In addition, we introduce the notion of preimage and quotient of fuzzy equivalence relations. Finally, we investigate relations between a fuzzy equivalence relation and a fuzzy mapping.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.185-198
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• 2002

We Consider the fuzzification of sub-implicative ideals in BCI-algebras, and investigate some related properties. We give conditions for a fuzzy ideal to be a fuzzy sub-implicative ideal. we show that (1) every fuzzy sub-implicative ideal is a fuzzy ideal, but the converse is not true, (2) every fuzzy sub-implicative ideal is a fuzzy positive implicative ideal, but the converse is not true, and (3) every fuzzy p-ideal is a fuzzy sub-implicative ideal, but the converse is not true. Using a family of sub-implicative ideals of a BCI-algebra, we establish a fuzzy sub-implicative ideal, and using a level set of a fuzzy set in a BCI-algebra, we give a characterization of a fuzzy sub-implicative ideal.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.7-16
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• 2007

First, we investigate fuzzy equivalence relations on a set X in the sense of Youssef and Dib. Second, we discuss fuzzy congruences generated by a given fuzzy relation on a fuzzy groupoid. In particular, we obtain the characterizations of ${\rho}\;o\;{\sigma}{\in}$ FC(S) for any two fuzzy congruences ${\rho}\;and\;{\sigma}$ on a fuzzy groupoid ($S,{\odot}$). Finally, we study the lattice of fuzzy equivalence relations (congruences) on a fuzzy semigroup and give certain lattice theoretic properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.269-274
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• 2009

Measuring uncertainty for fuzzy sets has been carried out by calculating fuzzy entropy. Fuzzy entropy of fuzzy set is derived with the help of distance measure. The distance proportional value between the fuzzy set and the corresponding crisp set is designed as the fuzzy entropy. The usefulness is verified by proving the proposed entropy. Generally, fuzzy entropy contains the complementary characteristics that the fuzzy entropies of fuzzy set and complementary fuzzy set have the same entropies. Discrepancy that low fuzzy entropy did not guarantee the data certainty was overcome by modifying fuzzy entropy formulation. Obtained fuzzy entropy is analyzed and discussed through simple example.