• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.463-468
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• 2020

The purpose of this article is to study the concepts of fuzzy mean open and fuzzy mean closed sets in fuzzy topological spaces. Further, in what way they are similar to those of other. Also we discuss some properties of fuzzy mean open and fuzzy mean closed with fuzzy paraopen and fuzzy paraclosed sets in fuzzy topology.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.3
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• pp.184-189
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• 2011

Generalized intuitionistic fuzzy soft set theory, proposed by Park et al. [Journal of Korean Institute of Intelligent Systems 21(3) (2011) 389-394], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we prove that certain De Margan's law hold in generalized intuitionistic fuzzy soft set theory with respect to union and intersection operations on generalized intuitionistic fuzzy soft sets. We discuss the basic properties of operations on generalized intuitionistic fuzzy soft sets such as necessity and possibility. Moreover, we illustrate their interconnections between each other.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.34-37
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• 2001

Park et al. [Proc. KFIS Fall Conf. 10(2) (2000), 59-62] defined fuzzy ${\gamma}$-open sets by using an operation ${\gamma}$ on a fts (X, $\tau$) and investigated the related fuzzy topological properties of the associated fuzzy topology $\tau$/seb ${\gamma}$/ and $\tau$. As generalizations of the notion of fuzzy ${\gamma}$-closed sets, we define gf. ${\gamma}$-closed sets and g*f. ${\gamma}$-closed sets and study basic properties of these sets relative to union and intersection. Also, we introduce and study two classes of ftss called fuzzy ${\gamma}$-T* and fuzzy ${\gamma}$-T$_{1}$2/ spaces by using the notions of gf. ${\gamma}$-closed and g*f. ${\gamma}$-closed sets.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.200-202
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• 2010

In this paper, we introduce the concept of fuzzy ${\gamma}$-quasi open sets which are generalizations of fuzzy ${\gamma}$-open sets, and obtain some basic properties of such fuzzy sets. Also we introduce and study the concepts of fuzzy ${\gamma}$-quasi continuous mapping and fuzzy ${\gamma}$-quasi open(closed) mapping.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.3
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• pp.237-241
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• 2002

In this paper, we describe how to represent hand witten decimal digits by a sequence of one to five fuzzy sets. Each fuzzy set represents an arc segment of the digit and is a Cartesian product of four fuzzy sets; the first is fur the arc length of the segment, the second is for the arc direction, the third is fur the arc shape, and the fourth is a crisp number indicating whether it has a junction point and if it has an end point of a stroke. We show that an arbitrary pair of these sequences representing two different digits is mutually disjoint. We also show that various forms of a digit written in different styles can be represented by the same sequence of fuzzy sets and hence the deviations due to different writers can be modeled by using these fuzzy sets.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.459-476
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• 2017

Interval valued intuitionistic fuzzy sets (IVIFSs) is widely used to model uncertainty, imprecise, incomplete and vague information. In this paper, newly defined modal operators over an extensional generalized interval valued intuitionistic fuzzy sets ($GIVIFS_Bs$) are proposed. Some of the basic properties of the new operators are discussed and few theorems were proved. The actual contribution in this paper is to discuss ten operators on $GIVIFS_Bs$.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.2
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• pp.201-208
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• 2014

Park et al. introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, we introduce new operations such as restricted union and restricted intersection and study their basic properties, and deal with the algebraic structure of generalized intuitionistic fuzzy soft sets. The lattice structures of generalized intuitionistic fuzzy soft sets are constructed.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.59-63
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• 2005

In this paper, we introduce the concept of fuzzy m-sets induced by a given fuzzy supratopology and investigate general properties of the new class consisted of fuzzy m-sets. We also introduce notions of fuzzy m-continuity, fuzzy m-open(closed) maps and study some properties of them.

• 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.

• 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.