By Radko Mesiar, Magda Komorníková (auth.), Chris Cornelis, Glad Deschrijver, Mike Nachtegael, Steven Schockaert, Yun Shi (eds.)
This ebook is a tribute to Etienne E. Kerre at the social gathering of his retirement on October 1st, 2010, after being lively for 35 years within the box of fuzzy set conception. It gathers contributions from researchers which were with regards to him in a single means or one other in the course of his lengthy and fruitful profession. in addition to a foreword via Lotfi A. Zadeh, it comprises thirteen chapters on either theoretical and utilized issues in fuzzy set thought, divided in 3 elements: 1) logics and connectives, 2) info research, and three) media functions. the 1st half bargains with fuzzy logics and with operators on (extensions of) fuzzy units. half 2 bargains with fuzzy tools in tough set concept, formal inspiration research, determination making and type. The final half discusses using fuzzy tools for representing and manipulating media items, akin to pictures and textual content records. the range of the themes which are lined mirror the variety of Etienne's learn pursuits, and certainly, the variety of present examine within the sector of fuzzy set theory.
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Additional info for 35 Years of Fuzzy Set Theory: Celebratory Volume Dedicated to the Retirement of Etienne E. Kerre
Library of Bulg. Acad. ) 2. : Two variants of intuitonistc fuzzy propositional calculus. Preprint IM-MFAIS-5-88, Soﬁa (1988) 3. : Intuitionistic Fuzzy Sets. Springer Physica-Verlag, Berlin (1999) On the Intuitionistic Fuzzy Implications and Negations 37 4. : Intuitionistic fuzzy implications and Modus Ponens. Notes on Intuitionistic Fuzzy Sets 11(1), 1–5 (2005) 5. : On some types of intuitionistic fuzzy negations. Notes on Intuitionistic Fuzzy Sets 11(4), 170–172 (2005) 6. : On some intuitionistic fuzzy negations.
1 = 1 + 1 − (1 − max(a, d)) − max(a, d) = 1. T. 0 = 1 − 1 + min(b, c) + 1 − 1 + max(a, d) = min(b, c) + max(a, d) ≤ 1. 1 = 1 − 1 + min(b, c) + 1 − 1 + max(a, d) = min(b, c) + max(a, d) ≤ 1. 0 = 1 − 1 + min(b, c)) − min(b, c) + 1 = 1. Therefore, implication →15 is valid. Theorem 1. If I is any of the 23 implications, then I( 0, 1 , 0, 1 ) = 1, 0 , I( 0, 1 , 1, 0 ) = 1, 0 , I( 1, 0 , 1, 0 ) = 1, 0 , I( 1, 0 , 0, 1 ) = 0, 1 . Therefore, the restriction of each of these implications coincides over the constants false and true with the implication from the ordinary propositional calculus.
Given a linguistic description LD R1 := IF X is small THEN Y is very big, R2 := IF X is very big THEN Y is small. Each rule provides us with a certain knowledge (related to the concrete application). We are able to distinguish between the rules despite the fact that their meaning is vague. Let us now consider specific linguistic contexts: w ∈ W for values of X, say, w = 150, 330, 600 (for example, temperature in some oven) and w ∈ W for values of Y , w = 0, 36, 90 (for example, a turncock position in degrees).