Fuzzy Set Theory

Fuzzy set theory has been developed to solve problems where the descriptions of activities and observations are imprecise, vague, or uncertain. The term “fuzzy” refers to a situation in where 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 180cm tall to the “class of tall men”. But it would be difficult to justify the inclusion or exclusion of a 173cm 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 a “class of red flowers,” a “class of good shooters,” a “class of comfortable speeds for traveling, a “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.