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

This publication offers the most instruments for aggregation of data given by way of numerous individuals of a bunch or expressed in a number of standards, and for fusion of knowledge supplied by means of a number of resources. It specializes in the case the place the supply wisdom is imperfect, because of this uncertainty and/or imprecision needs to be taken into consideration. The publication includes either theoretical and utilized experiences of aggregation and fusion equipment more often than not frameworks: chance conception, proof thought, fuzzy set and probability concept. The latter is extra constructed since it permits to control either obscure and unsure wisdom. functions to decision-making, picture processing, keep an eye on 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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Thus, any t-norm and any t-conorm is a T-S aggregation function. Example 2 Consider the particular case of (1) and (2) with T = T1 =min and S = 81 = max. Then, after simple calculation, we obtain that Ft (x, y) = F2(x, y) = med(x, y, k), that is, the well-known median operator characterized by Fung and Fu {1975). Example 3 Let T(x,y) = xy, S(x,y) = x+y-xy, T1 (x,y) = max(x+y1, 0), 8 1(x, y) = min(x + y, 1) and k = 1/2 in (1) and {2). Then we obtain Ft(x, y) x+y = F2(x, y) = - 2-, x, y E [0, 1].

16], Murofushi and Sugeno [27], and Mesiar [23, 24]. This paper will develop what is thought to be fundamental in a practical application of fuzzy integral to multicriteria decision problem. We will concentrate mainly on interpretation and identification issues, introducing the concept of k-order additive measure and general interaction index. As this is explained elsewhere in this book, we will not present at length the framework for multicriteria decision making, and we will restrict ourself to a quick presentation of fundamental properties for aggregation, which are necessary for the paper to be self-contained.

J. : Latent connectives in human decision making. Fuzzy Sets and Systems 4 (1980), 37- 51. 2 AGGREGATION IN DECISION MAKING AND CONTROL Aggregation Functions Defined by t-Norms and t-Conorms Janos Fodor• and Tomasa Calvo.. • Department of Mathematics University of Agricultural Sciences (GATE) Pater Karoly u. hu .. Department of Mathematics and Computer Science University of the Balearic Islands Ctra. ES Abstract We introduce a class of aggregation functions by the help of continuous t-norms and t-conorms.

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