The Place of Quasi Topological Structure in the Mathematical Theory of Categorization

Quasi Topological Structure and Soft Sets

Abstract

This work is a theoretical one bridging two mathemat- ical models namely the Quasi Topological Structure (QTS) and Soft Sets (SST) theories. We prove that theQuasi Topological Structure (QTS) can be viewed as a complexification of Soft Sets, from the point of view of its capacity of analysis. Our strategy is to compare two mathematical structures, namely the structure of Quasi Topological Structure (QTS) and the structure of Soft Sets from the point of view of their mathematical properties. These properties are expressed by means of mathematical notions that translate conceptual features. The notion of conceptual feature is taken in the com- mon sense outside of any scientific domain. However, the mathematical notions are given inside mathematics by their specific conditions. This paper is a theoretical comparison between two new mathematical structures that can become useful in many approaches of Artificial Intelligence (AI). We propose an epistemological anal- ysis in the frame of mathematical foundations and not a tool or a methodology to solving a particular problem.