Fuzzy Approach to Reasoning and Decision-Making: Selected by Didier Dubois, Henri Prade (auth.), Vilém Novák, Jaroslav PDF

By Didier Dubois, Henri Prade (auth.), Vilém Novák, Jaroslav Ramík, Milan Mareš, Martin Černý, Jiří Nekola (eds.)

ISBN-10: 9401052220

ISBN-13: 9789401052221

ISBN-10: 9401127530

ISBN-13: 9789401127530

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Additional resources for Fuzzy Approach to Reasoning and Decision-Making: Selected Papers of the International Symposium held at Bechyně, Czechoslovakia, 25-29 June 1990

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The extensions E(Ai(Xi' y)), E(B(y)) are abstract fuzzy sets (fuzzy relations) and the formula (16) then becomes the formula for composition of fuzzy relations. n The level of extensions is very important as we do not always know the resulting syntagm 8, and even the formula B(y) = sling (8). It is the level we work on in the practice and which is, in fact, concerned in the theory of approximate reasoning presented in the literature. The last task is the estimation of 8. We may stem from an abstract fuzzy set C C '.

For further deliberation, we may thus consider the degrees at in (11) to be equal to the corresponding degrees of provability in (12). 21 ViJem Novak We may summarize the situation in approximate reasoning as follows. First, we must define fuzzy sets of closed formulae siuzz(siorm(A)) for some primary syntagms A}, ... g. ) where si uzz is a certain estimation of (12). These fuzzy sets are, in fact, fuzzy sets of special axioms and they represent starting portion of our knowledge. Due to Lemma 1, approximate reasoning can be understood to be a derivation of fuzzy sets (12) of various formulae in a fuzzy theory T = {siuzz(siorm(At}), ...

Lfj(x). e. Lfj(x) E {O, I}, then we end up with the conventional case. L fj( x) 's will be interpreted here in terms of degrees of membership in fuzzy sets theory which is convenient for our purposes. e. to find an "(sub)optimal" R* in the sense that (18) is satisfied (is true) to the highest possible extent. Lfj(x) where JIQ+ (R) is the degree of completeness and JIQ- (R) is the degree of consistency. Evidently, "A" may be replaced by, say, at-norm. JIQ-(R) To proceed to the description of the algorithm, we introduce now the concept of a typoid.

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Fuzzy Approach to Reasoning and Decision-Making: Selected Papers of the International Symposium held at Bechyně, Czechoslovakia, 25-29 June 1990 by Didier Dubois, Henri Prade (auth.), Vilém Novák, Jaroslav Ramík, Milan Mareš, Martin Černý, Jiří Nekola (eds.)


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