The 10th International Conference on Fuzzy Systems and Data Mining (FSDM 2024)

Abstract: The idea of tolerance relation attributed to Zeeman is based on two fundamental concepts: reflexivity and symmetric relation. Although tolerance relations are used to study indiscernibility or indistinguishability phenomena, it has wide range of applications; recent trend has witnessed its application in the field of information system and image analysis. We have recently identified tolerance spaces in the context of quantale-valued convergence spaces, showing that the category of quantale-valued tolerance spaces is isomorphic to the category of quantale-valued convergence spaces. In this talk, we look at function spaces of tolerance spaces and convergence spaces, the role of the degree of transitivity in relation to quantale-valued convergence groups, and their related categorical aspects. Furthermore, we investigate monad and its Eilenberg-Moore category from the perspective of quantale-valued tolerance groups, and convergence groups.
Keywords: Tolerance space, convergence space, probabilistic convergence space, transitive relation, grade of trasitivity, closure operator, function space, group, category theory, monad, Eilenberg-Moore category.

Biography: Dr. T.M.G Ahsanullah obtained Ph. D degree from VUB (Vrije Universiteit Brussel, Belgium) in June, 1984 in an area of Mathematical Analysis, specializing in Fuzzy Topological Algebraic Structures, giving particular emphasis on semigroups and groups structures. Presently, he is engaged in studying categorical aspects of various convergence theories, such as, probabilistic convergence groups and rings; probabilistic convergence transformation groups; many-valued topological convergence groups and rings; approach convergence groups, approach convergence transformation groups; classical biconvergence groups and their quasi-uniformizations. He spent quite some time in studying categorical aspects of quatale-valued convergence structures on algebraic structures, specifically investigated characterization of transitivity in quantale-valued tolerance spaces by convergence and closure. Recently, he did some work on rough uniformity of topological rough groups and lattice-valued fuzzy approximation groups. He is interested to study various lattice-valued approximation theories and their categorical aspects. Professor Ahsanullah supervised several Ph. D students while teaching presently at King Saud University in Riyadh, Saudi Arabia, and M.Sc. and M. Phil students while at Dhaka University, Bangladesh until 2001. He is in the editorial board of New Mathematics and Computation, and serving as reviewer of various journals.