By Sergei Ovchinnikov (auth.), Dr. Bernadette Bouchon-Meunier (eds.)

ISBN-10: 3662110733

ISBN-13: 9783662110737

ISBN-10: 3790818895

ISBN-13: 9783790818895

This publication offers the most instruments for aggregation of data given by means of numerous individuals of a gaggle or expressed in a number of standards, and for fusion of information supplied through a number of assets. It makes a speciality of the case the place the provision wisdom is imperfect, because of this uncertainty and/or imprecision has to be taken into consideration. The ebook includes either theoretical and utilized reports of aggregation and fusion equipment often frameworks: likelihood conception, proof idea, fuzzy set and danger concept. The latter is extra built since it permits to control either vague and unsure wisdom. functions to decision-making, picture processing, keep an eye on and type are defined. The reader can discover a cutting-edge of the most methodologies, in addition to extra complex effects and outlines of utilizations.

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Being able to relate the values of parameters defining 1i to the behavior implied by H in a decision making point of view. g. neural nets. e. being compensative, monotone and idempotent), since they are the most suitable for multicriteria decision problems. quasi-arithmetic means. the easiest way to aggregate is the simple arithmetic mean 1/n Li ai. Many other means exist, such as geometric, harmonic means, etc. In fact all these common means belong to the family of quasi-arithmetic means, defined as follows.

7. Aggregations with additive generators Associative compensatory operators combine strict t-norms and strict t-conorms in an ordinal sum-like construction. Similarly we can combine arbitrary t-norm and tconorm with continuous additive generators. However, the associativity is violated up to the case of strict t-norm and t-conorm. Let g be a continuous additive generator of the t-norm T and let h be a continuous additive generator of the tconorm S. Take an element e E ]0, 1 [and put f(x) = {-~~) h( ~ ~ :) ifx ~ e otherwise f If either T or S is not strict on the whole unit square [0, 1 we can define an aggregation operator C: [0,1 ~[0,1].

Then define G and H by G(x, y) = Ir(k, F(x, y)), H(x, y) = Js(k, F(x, y)), x, y E [0, 1]. By Lemma 1, thus defined G and Hare symmetric and nondecreasing functions. Moreover, G(x, 1) = Ir(k, F(x, 1)) = lr(k, S(k, x)) = 1, because k ::; S(k, x). Similarly, H(x,O) = Js(k,F(x,O)) = Js(k,T(k,x)) = 0, since k ~ T(k,x). We can write T(k, G(x, 0)) T(k, Ir(k, F(x, 0))) = T(k, Ir(k, T(k, x))) = min{k, T(k, x)) = T(k,x), = since Tis a continuous t-norm. Next, by continuity of S, we have S(k, H(x, 1)) = S(k, Js(k, F(x, 1))) = S(k, Js(k, S(k,x))) = max{k, S(k, x)) = S(k,x).

### Aggregation and Fusion of Imperfect Information by Sergei Ovchinnikov (auth.), Dr. Bernadette Bouchon-Meunier (eds.)

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