By Radko Mesiar, Magda Komorníková (auth.), Chris Cornelis, Glad Deschrijver, Mike Nachtegael, Steven Schockaert, Yun Shi (eds.)
This e-book is a tribute to Etienne E. Kerre at the get together of his retirement on October 1st, 2010, after being energetic for 35 years within the box of fuzzy set idea. It gathers contributions from researchers which have been just about him in a single method or one other in the course of his lengthy and fruitful occupation. along with a foreword through Lotfi A. Zadeh, it includes thirteen chapters on either theoretical and utilized subject matters in fuzzy set conception, divided in 3 components: 1) logics and connectives, 2) information research, and three) media purposes. the 1st half offers with fuzzy logics and with operators on (extensions of) fuzzy units. half 2 bargains with fuzzy equipment in tough set conception, formal inspiration research, determination making and category. The final half discusses using fuzzy equipment for representing and manipulating media items, reminiscent of photographs and textual content files. the variety of the subjects which are coated replicate the range of Etienne's study pursuits, and certainly, the range of present learn within the quarter of fuzzy set theory.
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Extra resources for 35 Years of Fuzzy Set Theory: Celebratory Volume Dedicated to the Retirement of Etienne E. Kerre
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. A part of these negations were generated by implications, that were generated by fuzzy implications.
There are good means in FTT using which notions of context, horizon, and many other general characteristics of the meaning of evaluative expressions can be modeled. The result is a formal logical theory of evaluative linguistic expressions T Ev which is determined by 11 special axioms. Interpretation of extensions of evaluative expressions in a model is depicted in Fig. 1. The context is determined a by the triple vL , vS , vR of points (left bound, middle point, and right bound). The LH, MH and RH are fuzzy sets interpreting left, medium and right horizon, respectively which are determined by a special fuzzy equality ≈w constructed for each context w from one universal one.
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.
35 Years of Fuzzy Set Theory: Celebratory Volume Dedicated to the Retirement of Etienne E. Kerre by Radko Mesiar, Magda Komorníková (auth.), Chris Cornelis, Glad Deschrijver, Mike Nachtegael, Steven Schockaert, Yun Shi (eds.)