## 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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### Contents

Intuitionistic Fuzzy Sets | 1 |

Interval Valued Intuitionistic Fuzzy Sets | 139 |

Other Extensions of Intuitionistic Fuzzy Sets | 179 |

Copyright | |

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analogous applications Artificial Intelligence Atanassov Based Expert Systems basic BUSEFAL Bustince H Cartesian product components concept Conference on Intuitionistic construct Da(A define the following degrees of membership example expert estimations expert systems fi(x fiA(x fiB(x following definition following operators following theorem function Fuzzy Based Expert fuzzy model fuzzy set theory fuzzy systems G E2 given GN models GN theory HA(x hold IFGN2 IFS2 IFSs intuitionistic fuzzy logic intuitionistic fuzzy relation Intuitionistic Fuzzy Sets ISBN IVIFS IVIFSs Kacprzyk Lakov MA(x max(a max(l MB(x min(a min(l modal logic modal operators modal type nets neuron norms Notes on Intuitionistic Obviously ordinary fuzzy sets Petri nets predicates Preprint Proc Proof properties propositional form real numbers respect Section Sets and Systems sg(fiB(x shown in Figure Sofia supMA(x time-moment tokens topological topological spaces universe vA(x valid vB(x vc(x Workshop on Fuzzy x,fiA(x