# An Etymological Dictionary of Astronomy and AstrophysicsEnglish-French-Persian

## فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

### M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 2 Search : fuzzy set
 fuzzy set   هنگرد ِ پرزوار   hangard-e porzvârFr.: ensemble flou   A set of → truth values in → fuzzy logic that does not have sharp boundaries. Instead, set members have degrees of membership. If the value of 1 is assigned to objects entirely within the set and a 0 is assigned to objects outside of the set, then any object partially in the set will have a value between 0 and 1. This contrast with → crisp sets in → classical logic where members assume a precise value of 1 or 0. Fuzzy sets were first introduced by Lotfi A. Zadeh (1965) and defined as follows. Let X be a space of points, with a generic element of X denoted by x. Thus X = {x}. A fuzzy set A in X is characterized by a → membership function  fA(x) which associates with each point in X a real number in the interval [0,1], with the values of fA(x) at x representing the "grade of membership" of x in A. Thus, the nearer the value of fA(x) to unity, the higher the grade of membership of x in A. Generally, the intersection operations of fuzzy sets are the expansion of that operation on → nonfuzzy sets. In other words, operations on nonfuzzy sets are a particular case of operations on fuzzy sets.→ fuzzy; → set. nonfuzzy set   هنگرد ِ ناپرزوار   hangard-e nâporzvârFr.: ensemble non flou   A set that obeys the rules of → classical logic, a → crisp set, as contrasted with a → fuzzy set.→ nonfuzzy; → set.