Abstract

Traditional set theory, or crisp set theory, is built on the concept of crisp sets. These are sets for which the membership of an element within a set is defined as either true or false; in or out; 1 or 0. This construction is extremely useful, as mathematics has shown, but it struggles to model concepts of our world that possess vagueness or uncertainty. Therefore, we explore an expansion of set theory to allow an element to be partially within a set, thus constituting what is known as a fuzzy set. This paper introduces the basic concept of fuzzy sets, which includes fuzzy sets and crisp sets, as well as the operations of a fuzzy set and fuzzy classification systems. Fuzzy logic has been utilized to solve numerous textile-related difficulties, one of which was determining the proper clothing size. In this study, we examined fuzzy logic applications in textiles, such as the construction of fuzzy expert systems and fuzzy logic for predicting clothing size. This research demonstrates that when determining the correct size of clothing, the outcome is heavily reliant on fuzzy logic.

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