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

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

This ebook provides the most instruments for aggregation of knowledge given by means of a number of contributors of a gaggle or expressed in a number of standards, and for fusion of knowledge supplied by means of a number of resources. 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 under consideration. The e-book comprises either theoretical and utilized stories of aggregation and fusion tools ordinarily frameworks: chance thought, facts concept, fuzzy set and probability conception. The latter is extra built since it permits to control either vague and unsure wisdom. functions to decision-making, photograph processing, regulate and class are defined. The reader can discover a state of the art of the most methodologies, in addition to extra complex effects and outlines of utilizations.

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The argument which was put ahead at this time was that fuzzy measure is more flexible than probability, which is stuck into its additivity property: the importance of two criteria in the probability framework can be nothing else than the sum of the individual importances, while with fuzzy measures, it can be greater or lower, allowing the modelling of interaction phenomena between criteria. Many applications in Japan were conducted along this line, during the eighties [19, 31, 41, 18, 43] (see also a summary in [14], and a short description in [11]), showing that the method was effectively successfull and could bring new insights into the problem of aggregation.

N-1TI Xj + i=1 Recall that C(1) = L1 p f1 (1-xi) i=1 was introduced already in the previous section, i. , that c< 1> is a convex non-linear compensatory operator, too. 8 26 Example 6. 5. 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.

Ling, Representation of associative functions, Publ. Math. Debrecen 12 (1965) 182-212. 48 6. G. Mayor, On a family of quasi-arithmetic means, Aeq. Math. 48 (1994) 137-142. 7. G. Mayor and E. 'frillas, On the representation of some aggregation functions, Proc. ISMVL (1986) 110-114. 8. R. Yager and A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems 80 (1996) 111-120. 9. -J. Zimmermann and P. Zysno, Latent connectives in human decision making, Fuzzy Sets and Systems 4 (1980) 37-51. Fuzzy Integral as a Flexible and Interpretable Tool of Aggregation Michel GRABISCH Thomson-CSF, Central Research Laboratory Domaine de Corbeville, 91404 Orsay Cedex, France Abstract The fuzzy integral with respect to a fuzzy measure has been used in many applications of multicriteria evaluation.

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