Intuitionistic Fuzzy Sets: Theory and ApplicationsIn the beginning of 1983, I came across A. Kaufmann's book "Introduction to the theory of fuzzy sets" (Academic Press, New York, 1975). This was my first acquaintance with the fuzzy set theory. Then I tried to introduce a new component (which determines the degree of non-membership) in the definition of these sets and to study the properties of the new objects so defined. I defined ordinary operations as "n", "U", "+" and "." over the new sets, but I had began to look more seriously at them since April 1983, when I defined operators analogous to the modal operators of "necessity" and "possibility". The late George Gargov (7 April 1947 - 9 November 1996) is the "god father" of the sets I introduced - in fact, he has invented the name "intu itionistic fuzzy", motivated by the fact that the law of the excluded middle does not hold for them. Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. In this sense, it has also a referential character. |
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analogous applications Artificial Intelligence Atanassov Atanassov K Based Expert Systems basic BUSEFAL Cartesian product Conference on Intuitionistic define the following degrees of membership elements example Expert Systems Fa,ß fA(x following definition following theorem function Fuzzy Based Expert fuzzy set theory Fuzzy Systems Ga,ß Geometric interpretation given GN models IFGN2 IFS2 IFSs inf MA(x interval valued intuitionistic fuzzy logic Intuitionistic Fuzzy Modal Intuitionistic Fuzzy Sets ISBN IVIFS IVIFSS Ja,ß Kacprzyk Lakov Mathematical max(a max(b max(VA(x min(a min(b min(µ(p min(µA(x modal logic modal type NA(x nets non-membership norms Notes on Intuitionistic ordinary fuzzy sets Petri nets Proof properties propositional calculus propositional form real numbers respect Sets and Systems shown in Figure Sofia ẞE sup MA(x topological universe VA(x valid VB(x VC(X Vi,k Workshop on Fuzzy µA(x µB(X