Some results on fuzzy topology on fuzzy sets

1993 ◽  
Vol 56 (3) ◽  
pp. 331-336 ◽  
Author(s):  
A.K. Chaudhuri ◽  
P. Das
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Topology

Suitable interval-valued intuitionistic fuzzy topological spaces

2021 ◽  
pp. 1-11
Author(s):  
O.R. Sayed ◽  
N.H. Sayed ◽  
Gui-Xiu Chen
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Set Operations ◽  
The Family ◽  
Fuzzy Topological Spaces ◽  
Interval Valued

In the present paper, a characterization of the intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy sets and their set-operations are given. By making use of these characterizations, the relationships between the interval-valued intuitionistic fuzzy topology and four fuzzy topologies associated to it are studied. For this reason, some subclasses of the family of interval-valued intuitionistic fuzzy topologies on a set which we call pre-suitable and suitable are introduced. Furthermore, the concepts of homeomorphism functions and compactness in the framework of interval-valued intuitionistic fuzzy topological spaces are introduced and studied.

scholarly journals Weak fuzzy topology on vector spaces

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 501-514
Author(s):  
Bayaz Daraby ◽  
Nasibeh Khosravi ◽  
Asghar Rahimi
Keyword(s):  
Vector Space ◽  
Fuzzy Sets ◽  
Topological Vector Space ◽  
Weak Topology ◽  
Vector Spaces ◽  
Fuzzy Topology ◽  
Lower Semi

In this paper, we study the concept of weak linear fuzzy topology on a fuzzy topological vector space as a generalization of usual weak topology. We prove that this fuzzy topology consists of all weakly lower semi-continuous fuzzy sets on a given vector space when K (R or C) endowed with its usual fuzzy topology. In the case that the fuzzy topology of K is different from the usual fuzzy topology, we show that the weak fuzzy topology is not equivalent with the fuzzy topology of weakly lower semi-continuous fuzzy sets.

On Multi-Fuzzy Rough Sets, Relations, and Topology

2019 ◽  
Vol 8 (1) ◽  
pp. 101-119
Author(s):  
Gayathri Varma ◽  
Sunil Jacob John
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Primitive Concept ◽  
Closed Sets ◽  
Fuzzy Topological Spaces

This article describes how rough set theory has an innate topological structure characterized by the partitions. The approximation operators in rough set theory can be viewed as the topological operators namely interior and closure operators. Thus, topology plays a role in the theory of rough sets. This article makes an effort towards considering closed sets a primitive concept in defining multi-fuzzy topological spaces. It discusses the characterization of multi-fuzzy topology using closed multi-fuzzy sets. A set of axioms is proposed that characterizes the closure and interior of multi-fuzzy sets. It is proved that the set of all lower approximation of multi-fuzzy sets under a reflexive and transitive multi-fuzzy relation forms a multi-fuzzy topology.

scholarly journals A New Representation of Semiopenness of L-fuzzy Sets in RL-fuzzy Bitopological Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 611
Author(s):  
Ibtesam Alshammari ◽  
Omar H. Khalil ◽  
A. Ghareeb
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Topology ◽  
Bitopological Spaces

In this paper, we introduce a new representation of semiopenness of L-fuzzy sets in RL-fuzzy bitopological spaces based on the concept of pseudo-complement. The concepts of pairwise RL-fuzzy semicontinuous and pairwise RL-fuzzy irresolute functions are extended and discussed based on the (i,j)-RL-semiopen gradation. Further, pairwise RL-fuzzy semi-compactness of an L-fuzzy set in RL-fuzzy bitopological spaces are given and characterized. As RL-fuzzy bitopology is a generalization of L-bitopology, RL-bitopology, L-fuzzy bitopology, and RL-fuzzy topology, the results of our paper are more general.

scholarly journals On (L,M)-fuzzy convex structures

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4151-4163 ◽  
Author(s):  
Osama Sayed ◽  
El-Sayed El-Sanousy ◽  
Yaser Sayed
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Topology ◽  
Convexity Space ◽  
New Class

This paper defines a new class of L-fuzzy sets called r-L-fuzzy biconvex sets in (L,M)-fuzzy convex structures (X,C), where C is an (L,M)-fuzzy convexity on X, and some of their properties were studied. In addition, weintroduce (L,M)-fuzzy topological convexity space and study some of its properties. Finally, we introduce locally (L,M)-fuzzy topology (L,M)-fuzzy convexity space and study some of its properties.

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