Fuzzy Convergence, Fuzzy Neighborhood Convergence and I-Tolerance Structures for Groups

We introduce a category of fuzzy convergence groups, FCONVGRP a subcategory of the category of fuzzy convergence spaces, FCONV. Viewing [Formula: see text] as a complete Heyting algebra, we prove that the category of [Formula: see text]-tolerance groups, [Formula: see text]-TOLGRP is isomorphic to a subcategory of FCONVGRP. Since FCONV is a topological universe, and thereby possesses function space structure, upon invoking this, we are able, among others, to show that FCONVGRP is topological, and more importantly, it enables us to obtain a compatible fuzzy convergence function space structure on group of homeomorphisms. It is noticeable, however, that the category of fuzzy neighborhood convergence groups, FNCONVGRP — a supercategory of the well-known category FNS, of fuzzy neighborhood spaces, as well as the category of fuzzy neighborhood groups, FNGRP — a subcategory of FNCONVGRP exhibit nice relationships with FCONVGRP. It is important to note that the objects of FCONVGRP are homogeneous, this paves the way to present two pertinent characterization theorems on fuzzy convergence groups. Finally, introducing a category PSTOPGRP, of pseudotopological groups, we reveal the embeddings of FTOPGRP and PSTOPGRP into FCONVGRP.

On a fuzzy metric space and fuzzy convergence

In this paper we introduce a new type of fuzzy metric space and obtain several properties of it. Also some topological properties and boundedness are investigated. The notion of convergence of fuzzy sequences together with the notion of fuzzy cauchy sequences in a fuzzy metric space are discussed and some basic results related to these notions are investigated.

p-Regularity and p-Regular Modification in ⊤-Convergence Spaces

Fuzzy convergence spaces are extensions of convergence spaces. ⊤-convergence spaces are important fuzzy convergence spaces. In this paper, p-regularity (a relative regularity) in ⊤-convergence spaces is discussed by two equivalent approaches. In addition, lower and upper p-regular modifications in ⊤-convergence spaces are further investigated and studied. Particularly, it is shown that lower (resp., upper) p-regular modification and final (resp., initial) structures have good compatibility.

Regularity of fuzzy convergence spaces

Abstract(Fuzzy) convergence spaces are extensions of (fuzzy) topological spaces. ⊤-convergence spaces are one of important fuzzy convergence spaces. In this paper, we present an extending dual Fischer diagonal condition, and making use of this we discuss a regularity of ⊤-convergence spaces.

SC: A NOVEL FUZZY CRITERION FOR SOLVING ENGINEERING AND CONSTRAINED OPTIMIZATION PROBLEMS

In this paper a novel fuzzy convergence system (SC) and its fundamentals are presented. The model was implemented on a monoobjetive PSO algorithm with three phases: 1) Stabilization, 2) generation and breadth-first search, and 3) generation and depth-first. The system SC-PSO-3P was tested with several benchmark engineering problems and with several CEC2006 problems. The computing experience and comparison with previously reported results is presented. In some cases the results reported in the literature are improved.

PROPERTIES OF FUZZY DITANCE ON FUZZY SET

In this paper we introduce the definition of fuzzy distance space on fuzzy set then we study and discuss several properties of this space after some illustrative examples are given . Furthermore we introduce the definition of fuzzy convergence, fuzzy Cauchy sequence of fuzzy point and fuzzy bounded fuzzy distance space .