By Sergei Ovchinnikov (auth.), Dr. Bernadette Bouchon-Meunier (eds.)
This booklet offers the most instruments for aggregation of knowledge given by way of a number of contributors of a gaggle or expressed in a number of standards, and for fusion of information supplied via a number of resources. It specializes in the case the place the supply wisdom is imperfect, which means uncertainty and/or imprecision has to be taken into consideration. The booklet includes either theoretical and utilized experiences of aggregation and fusion tools in most cases frameworks: chance idea, facts conception, fuzzy set and probability thought. The latter is extra built since it permits to control either vague and unsure wisdom. functions to decision-making, photograph processing, keep watch over and type are defined. The reader can discover a state of the art of the most methodologies, in addition to extra complicated effects and outlines of utilizations.
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Extra resources for Aggregation and Fusion of Imperfect Information
Academic Press, New York, 1975) pp. 227-256. 5. H. 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.
However, for practical applications the lack of associativity seldom causes difficulties, up to, possibly, computing complexity. Recall, e. , the nonassociative arithmetical mean In several types of non-associative aggregation operators, the quasi-associativity is fulfilled , allowing to reduce the computing complexity. So, e. , by the arithmetical mean, we have that x = Card Sum xi , where xi both Sum and Card are associative. The suggested aggregation operators can be applied to aggregate pointwisely the fuzzy inputs (generalizing the fuzzy intersection and/or the fuzzy union).
Fu, "An axiomatic approach to rational decision making in a fuzzy environment", in: Fuzzy Sets and Their Applications to Cognitive and Decision Processes, eds. A. Zadeh et al. (Academic Press, New York, 1975) pp. 227-256. 5. H. 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.