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Fuzzy Preference Modelling and Multicriteria Decision by János Fodor, Marc Roubens (auth.) PDF

Posted On April 21, 2018 at 1:55 am by / Comments Off on Fuzzy Preference Modelling and Multicriteria Decision by János Fodor, Marc Roubens (auth.) PDF

By János Fodor, Marc Roubens (auth.)

ISBN-10: 9048144663

ISBN-13: 9789048144662

ISBN-10: 940171648X

ISBN-13: 9789401716482

This booklet offers in-depth insurance of crucial effects approximately fuzzy common sense together with negations, conjunctions, disjunctions, implications and offers the interrelations among these various connectives. The paintings brings jointly a number of effects approximately valued binary family members enjoyable assorted transitivity-type stipulations.
The authors suggest the 1st sound advent to valued choice modelling throughout the systematic use of fuzzy set idea and practical equations and derive the potential foundations for multicriteria selection reduction utilizing aggregation, rating and selection methods at the foundation of axiomatic effects. The textual content offers a unified view of assorted multicriteria selection making instruments which were independently derived some time past, facing pairwise comparisons. The monograph is mathematically orientated however the effects can be of the best curiosity for engineers and economists who layout and enforce determination aid platforms in perform. it's also provided with a enough variety of examples to make it beautiful to nonspecialists.

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Extra resources for Fuzzy Preference Modelling and Multicriteria Decision Support

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X,y) = ip- 1 (min{1-

9 Let n be any strict negation. 6. 41) with n 1 = n. IJT is continuous then S is continuous. In addition, if T is Archimedean with additive genemtor f then S is Archimedean with additive genemtor g = f o n and g(1) = f(O). 42) with n 2 = n. If S is continuous then T is continuous. Moreover, if S is Archimedean with additive genemtor g then T is Archimedean with additive genemtor f = g o n and f(O) = g(1). 42) is true with n 2 = n- 1 for a continuous, Arehirneclean t-norm T ancl for a continuous, Arehirneclean t-conorm S.

Condition S4 expresses self-duality of s (compare with De Morgan laws). This condition can be extended by using any strong negation instead of 1 - x, see Dombi (1982b). Silvert has proved the following result. 36 Chapter 1. 17 Any symmetric sum has the following form g(x,y) s(xy)= g(x,y)+g(l-x,1-y)' ' where g is any continuous, nondecreasing and positive function from [0, 1]2 to [0, 1) with g(O, 0) = 0. g(x, y) and s(x, y) generate also s(x, y). The representation implies that s(x, 1- x) = 1/2 for x E (0, 1).

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Fuzzy Preference Modelling and Multicriteria Decision Support by János Fodor, Marc Roubens (auth.)

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