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...

There have been many research developments on the conceptual description of topological relations between spatial objects. In order to practically implement these conceptual topological relations in a computer environment, we need to calculate the values of the topological relations. One of the theoretical bases for doing this is a computational fuzzy topology, which is the research focus of th...

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...

Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.

We study properties of classes of closure operators and closure systems parameterized by systems of isotone Galois connections. The parameterizations express stronger requirements on idempotency and monotony conditions of closure operators. The present approach extends previous approaches to fuzzy closure operators which appeared in analysis of objectattribute data with graded attributes and re...

This chapter tries to answer the fundamental question of what main contributions of fuzzy clustering to the theory of cluster analysis from theoretical viewpoints. While fuzzy clustering is thought to be clearly useful by users of this technique, others think that the concept of fuzziness is not needed in clustering. Thus the usefulness of fuzzy clustering is not trivial. The discussion here is...

On the process of power system black start after an accident, it can help to optimize the resources allocation and accelerate the recovery process that decomposing the power system into several independent partitions for parallel recovery. On the basis of adequate consideration of fuzziness of black-start zone partitioning, a new algorithm based on fuzzy clustering analysis is presented. Charac...

Closure (interior) operators and closure systems are important tools in many mathematical environments. Considering the logical sense of a complete residuated lattice L, this paper aims to present concepts L-closure (L-interior) by means infimums (supremums) L-families L-subsets show their equivalence categorical sense. Also, two types fuzzy relations between corresponding L-interior proposed, ...