الفهرس 
Some basic conceptsof fuzzy sets
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Abstract
The notion of a fuzzy set, introduced by Lotfi A. Zadeh [37] in 1965, has caused great interest among both pure and applied mathematicians. It has also raised enthusiasm among some engineers, biologists, phychologists, economists, and experts in other areas, who use (or at least try to use) mathematical ideas and methods in their research. By this notion of fuzzy set it possible to obtain a more distinctive description of some phenomena than the one which is offered by systems based on classical two-valued logic and classical set theory. In the classical set theory, an element either belong to a set or dose not belong to a set. In many real life applications, there exists a ’ gray area’, can be determined by a function on a scale of centimeters with value in the closed real unit interval [0,1]. The usefulness of fuzzy theory appeared and is applicable in fuzzy control system. Moreover, fuzzy control is used in fuzzy air conditioner, fuzzy vacuum clear and cameras, and so on.
General topology was one of the first branches of pure mathematics to which fuzzy sets have been applied. It was in 1968, that is, three years after Zadeh’s paper bad appeared, that Change [8] introduced the notion of fuzzy topology. Several authors continued the investigation of such spaces. In Goguen paper’s [25] the considered as values of the fuzzy sets not only elements of the closed unit interval but elements of some more general lattice L. The notion stratified fuzzy topology has been introduced by Lowen [30]. By a fuzzy topology to be stratified is meant that all constant fuzzy sets are open.