Fuzzy Sets and Their Operations

Abstract

Fuzzy set theory is developed for solving problems in which descriptions of activities and observations are imprecise, vague, and uncertain. The term “fuzzy” refers to the situation in which there are no well-defined boundaries of the set of activities or observations to which the descriptions apply. For example, one can easily assign a person seven feet tall to the “class of tall men”. But it would be difficult to justify the inclusion or exclusion of a six-foot tall person to that class, because the term “tall” does not constitute a well-defined boundary. This notion of fuzziness exists almost everywhere in our daily life, such as the “class of red flowers,” the “class of good kickers,” the “class of expensive cars,” or “numbers close to 10,” etc. These classes of objects cannot be well represented by classical set theory. In classical set theory, an object is either in a set or not in a set. An object cannot partially belong to a set.