By Radko Mesiar, Magda Komorníková (auth.), Chris Cornelis, Glad Deschrijver, Mike Nachtegael, Steven Schockaert, Yun Shi (eds.)
This publication is a tribute to Etienne E. Kerre at the celebration of his retirement on October 1st, 2010, after being energetic for 35 years within the box of fuzzy set conception. It gathers contributions from researchers which have been as regards to him in a single approach or one other in the course of his lengthy and fruitful occupation. in addition to a foreword by way of Lotfi A. Zadeh, it comprises thirteen chapters on either theoretical and utilized themes in fuzzy set idea, divided in 3 elements: 1) logics and connectives, 2) info research, and three) media purposes. the 1st half bargains with fuzzy logics and with operators on (extensions of) fuzzy units. half 2 offers with fuzzy equipment in tough set idea, formal proposal research, choice making and category. The final half discusses using fuzzy equipment for representing and manipulating media items, akin to pictures and textual content records. the variety of the subjects which are coated replicate the range of Etienne's examine pursuits, and certainly, the range of present learn within the sector of fuzzy set theory.
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Extra info for 35 Years of Fuzzy Set Theory: Celebratory Volume Dedicated to the Retirement of Etienne E. Kerre
Kluwer Academic Publishers, Dordrecht (2000) 33. : Fuzzy Sets, Uncertainty and Information. Prentice-Hall, Englewood Cliffs (1988) 34. : Triangular norm-based iterative compensatory operators. Fuzzy Sets and Systems 104, 109–119 (1999) 35. : k–intolerant capacities and Choquet integrals. European J. Oper. Res. 177(3), 1453–1468 (2007) 36. : On ordinal sums of triangular norms on bounded lattices. Fuzzy Sets and Systems 157(10), 1403–1416 (2006) 37. : The dominance relation in some families of continuous Archimedean t–norms and copulas.
Therefore, using this scheme, we ﬁnally obtain 23 implications. Below, we shall describe some properties of these implications and negations. Let us denote below each of these implications by I(x, y) and the negations by N (x). On the Intuitionistic Fuzzy Implications and Negations 21 In intuitionistic fuzzy logic, if x is a variable, then its truth-value is represented by the ordered pair V (x) = a, b , such that a, b, a + b ∈ [0, 1], where a and b are degrees of validity and of non-validity of x.
3 A New Argument that the Intuitionistic Fuzzy Sets Are ‘Intuitionistic’ in Nature The above assertions show that all negations, except the ﬁrst one, satisfy conditions of the intuitionistic logic, but not of the classical logic.