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T M G Ahsanullah

Professor

Professor

كلية العلوم
Department of Mathematics, Building 4, Room No. 2B 80
المنشورات
مقال فى مجلة
2021

Fuzzy Convergence, Fuzzy Neighborhood Convergence and I-Tolerance Structures for Groups by T. M. G. Ahsanullah

Ahsanullah, T. M. G. . 2021

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.

نوع عمل المنشور
Original Research Article
رقم المجلد
17
رقم الانشاء
4
مجلة/صحيفة
New Math. and Natural Computation
الصفحات
1-26
مزيد من المنشورات
publications

Introducing the notion of probabilistic convergence ring, and probabilistic limit ring, our motivations among others are, to focus at two vital issues, such as, (a) to provide characterization…

بواسطة T. M. G. Ahsanullah and Gunther Jaeger
2024
publications

Starting with an approximation space as the underlying structure, we
look at the rough uniformity of a topological rough group. Next, taking L as a
complete residuated lattice, we…

بواسطة T M G Ahsanullah
2022
تم النشر فى:
Journal of Intelligent and Fuzzy Systems