On Soft Sets and Formal Concept Analysis (FCA) as mathematical categorization systems - An Engineering Application

Abstract

This paper deals with an analysis of the reasoning for the cognitive problem of categorization in systems. Such reasoning requires the construction of a formal model of the system that is performed in 3 steps: cognitive description of the system, extraction of system’s meaningful concepts, and design of the mathematical model based on the concepts. Our goal is to explore the cognitive features and their predominance in some old models of categorization well known in literature. We highlight the relation between Formal Concept Analysis (FCA) model and soft sets and we analyze the notion of "parameter" from the cognitive point of view. Based on this analysis, we propose the notion of double soft sets as a mathematical notion more adequate in the engineering applications. All our study is conducted in the framework of material selection in mechanical engineering.