The concept of a fuzzifying topology was given in [1] under the name L-fuzzy topology. Ying studied in [9, 10, 11] the fuzzifying topologies in the case of L = [0,1]. A classical topology is a special case of a fuzzifying topology. In a fuzzifying topology τ on a set X , every subset A of X has a degree τ(A) of belonging to τ, 0 ≤ τ(A) ≤ 1. In [4], we defined the degrees of compactness, of loca...

We proposed the theory of multi-fuzzy sets [Sabu and Ramakrishnan (2010a), (2011a)] as an extension of theories of fuzzy sets, L-fuzzy sets [Goguen (1967)] and intuitionistic fuzzy sets [Atanassov (1986)]. Theory of multi-fuzzy sets deals with multi-level fuzziness and multi-dimensional fuzziness. Our previous papers discussed the basic notions of multi-fuzzy sets, multi-fuzzy topology, and mul...

Topology is an important and major area of mathematics and it can give many relationships between other scientific areas and mathematical models.The aim of this paper is to construct intuitionistic fuzzy soft multi topological space and it is shown that an intuitionistic fuzzy soft multi topological space gives a family of parameterized topological spaces and some basic properties regarding wit...

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy α-I-open and r-fuzzy β-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy α-I-openness (r-fuzzy pre-I-openn...

In this paper, we further study properties of fuzzy almost continuous functions in Singal’s and Hussain’s sense and establish a condition for their equivalence which is an improvement of Theorem 5.5 of [2]. Some divergences from straightforward fuzzification of General Topology have also been noted in Example 1 and Theorem 4. We also define fuzzy almost weakly continuous and fuzzy nearly almost...

Considering the increasing interest in fuzzy theory and possible applications, the concept of fuzzy metric space concept has been introduced by several authors from different perspectives. This paper interprets the theory in terms of metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology. We study interrelationships between this theory and other fuzzy theories such as intuit...

In this paper a new class of fuzzy sets, namely r-(τi, τj)-θ-generalized fuzzy closed sets is introduced for smooth bitopological spaces. This class falls strictly in between the class of r-(τj, τi)fuzzy θ-closed sets and the class of r-(τi, τj)generalized fuzzy closed sets. Furthermore, by using the class of r-(τi, τj)-θgeneralized fuzzy closed sets we establish a new fuzzy closure operator wh...

Intelligent Universal Transformer (IUT) is a power electronic base transformer introducing for Advanced Distribution Automation (ADA) in future. ADA is the state of art employing the new architecture based on both the flexible electrical network and open communication construction comprise the Future Distribution System. Fuzzy control is a method based on fuzzy logic concept emphasizes on fuzzy...

the purpose of the present work is to establish a one-to-one correspondence between the family of interval type-2 fuzzy reflexive/tolerance approximation spaces and the family of interval type-2 fuzzy closure spaces.

Ever since the introduction of fuzzy sets by L. A. Zadeh [14], the fuzzy concept has invaded almost all branches of Mathematics. The concept of fuzzy topological space was introduced and developed by C.L. Chang [3] and since then many fuzzy topologists [1,6-13] have extended various notions in classical topology to fuzzy topological spaces. The concept of somewhat continuous functions was intro...