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.

scholarly journals Uncertainty-Aware Dissimilarity Measures for Interval-Valued Fuzzy Sets

2020 ◽  
Vol 28 (05) ◽  
pp. 757-768
Author(s):  
Emilio Torres-Manzanera ◽  
Pavol Král ◽  
Vladimír Janiš ◽  
Susana Montes
Keyword(s):  
Fuzzy Sets ◽  
Dissimilarity Measures ◽  
New Class ◽  
Available Information ◽  
Interval Valued

Dissimilarities are a very usual way to compare two fuzzy sets and also two interval-valued fuzzy sets. In both cases, the dissimilarity between two sets is a number. In this work, we introduce a generalization of the notion of dissimilarity for interval-valued fuzzy sets such that it assumes values on the set of subintervals instead of the set of numbers. This seems to be more realistic taking into account the available information. We also investigate its relationship with the classical notions of dissimilarity between fuzzy sets and we obtain that the new class is richer than the existing one.

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.

scholarly journals Relationship of Algebraic Theories to Powerset Theories and Fuzzy Topological Theories for Lattice-Valued Mathematics

2007 ◽  
Vol 2007 ◽  
pp. 1-71 ◽  
Author(s):  
S. E. Rodabaugh
Keyword(s):  
Sufficient Conditions ◽  
Algebraic Theory ◽  
Fuzzy Topology ◽  
New Class ◽  
Algebraic Theories ◽  
Necessary And Sufficient ◽  
Relationship Of ◽  
Topological Theories ◽  
Fixed Basis

This paper deals with a broad question—to what extent is topology algebraic—using two specific questions: (1) what are the algebraic conditions on the underlying membership lattices which insure that categories for topology and fuzzy topology are indeed topological categories; and (2) what are the algebraic conditions which insure that algebraic theories in the sense of Manes are a foundation for the powerset theories generating topological categories for topology and fuzzy topology? This paper answers the first question by generalizing the Höhle-Šostak foundations for fixed-basis lattice-valued topology and the Rodabaugh foundations for variable-basis lattice-valued topology using semi-quantales; and it answers the second question by giving necessary and sufficient conditions under which certain theories—the very ones generating powerset theories generating (fuzzy) topological theories in the sense of this paper—are algebraic theories, and these conditions use unital quantales. The algebraic conditions answering the second question are much stronger than those answering the first question. The syntactic benefits of having an algebraic theory as a foundation for the powerset theory underlying a (fuzzy) topological theory are explored; the relationship between these two specific questions is discussed; the role of pseudo-adjoints is identified in variable-basis powerset theories which are algebraically generated; the relationships between topological theories in the sense of Adámek-Herrlich-Strecker and topological theories in the sense of this paper are fully resolved; lower-image operators introduced for fixed-basis mathematics are completely described in terms of standard image operators; certain algebraic theories are given which determine powerset theories determining a new class of variable-basis categories for topology and fuzzy topology using new preimage operators; and the theories of this paper are undergirded throughout by several extensive inventories of examples.

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.

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