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

Journal Article
Ahsanullah, T. M. G. . 2021
Publication Work Type: 
Original Research Article
Magazine \ Newspaper: 
New Math. and Natural Computation
Issue Number: 
4
Volume Number: 
17
Pages: 
1-26
Publication Abstract: 

We introduce a category of fuzzy convergence groups, FCONVGRP a subcategory of the category of fuzzy convergence spaces, FCONV. Viewing I as a complete Heyting algebra, we prove that the category of I-tolerance groups, I-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.