الفهرس 
from The Fuzzy Set To Its ExtensionsOnly 14 pages are availabe for public view
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Abstract
This chapter is devoted to review the basics in this thesis and to show the grand shift from crisp set due to Cantorian to fuzzy set due to Lofti Zadeh and its motivations. This chapter includes two parts: The first part is a brief introduction on the set theory and displays crisp set and displays the fuzzy set and the grand shift to it because it represents modern method for handling uncertainty. The second part introduces new definition over the Intuitionistic Fuzzy set in its intersection and union operations. The third part talks about the picture set and display some of its operations. By developing intelligent systems, we can operate with the real life and the engineering problems. A large part of mathematics is based on the notions of a set,Set theory. On the other hand, was developed by George Cantor’s single paper ”on a property of the collection of all real algebraic numbers” in 1874 [1]. In classical set theory, an element either belongs to a set or does not belong to a set. Fuzziness plays an essential role in human life because most of the classes encountered in the real physical world are fuzzy. In 1965, Zabeh [2] introduced the idea of a fuzzy set as an extension of the classical set theory. The idea of ”intuitionistic fuzzy set” was first published by krassimir T. Atanassov [3] and many works by the same author and his colleagues appeared in the literature [4], [5], [6]. Established by Florentin smarandache in 1980, neurosophy was presented as well as the research of origins, nature, and neutrality’s scope, in addition to their experiences with various ideational spectra.