The concept of closure operator is key in several branches mathematics. In this paper, operators are extended to relational structures, more specifically fuzzy relations the framework complete lattices. core work search for a suitable definition (strong) relation, that is, relation whose with systems one-to-one. study properties and helps narrow down exploration until an appropriate settled.

This paper introduces a new class of fuzzy closure operators called implicative closure operators, which generalize some notions of fuzzy closure operators already introduced by different authors. We show that implicative closure operators capture some usual consequence relations used in Approximate Reasoning, like Chakraborty s graded consequence relation, Castro et al. s fuzzy consequence rel...

The starting point of this paper is the classical well-known theorem due to G. BIRKHOFF, P. HALL, and J. SCHMIDT which establishes a one-to-one correspondence between compact closure operators, inductive closure operators, inductive closure systems, and closure operators generated in universal algebras (and generated in deductive systems, respectively). In the paper presented we make first step...

In this paper we introduce various notions of continuous fuzzy proper functions by using the existing notions of fuzzy closure and fuzzy interior operators like Rτ -closure, Rτ -interior, etc., and present all possible relations among these types of continuities. Next, we introduce the concepts of α-quasi-coincidence, qα r -pre-neighborhood, qα r -pre-closure and qα r pre-continuous function in...

In this paper we highlight the specific meaning of images of fuzzy sets under fuzzy relations in the context of fuzzy topology. More precisely we show that fuzzy modifiers taking direct and superdirect images of fuzzy sets under fuzzy pre-orderings are respectively closure and interior operators, inducing fuzzy topologies. Furthermore we investigate under which conditions the same applies to th...

In this paper, we characterize the intuitionistic fuzzy δ-continuous, intuitionistic fuzzy weakly δ-continuous, intuitionistic fuzzy almost continuous, and intuitionistic fuzzy almost strongly θ-continuous functions in terms of intuitionistic fuzzy δ-closure and interior or θ-closure and interior.

in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

This paper presents the applications of hierarchical clustering to the generators in a power system. A useful application of fuzzy mathematics is that the correction of clustering results and determination of whether it can obtain correct transitive closure. Thus, the fuzzy transitive closure plays an important role in hierarchical clustering. Based on the fuzzy relation matrix, the hierarchica...