ON THE RELATIONSHIP OF ASSOCIATIVE COMPENSATORY OPERATORS TO TRIANGULAR NORMS AND CONORMS
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- ERICH PETER KLEMENT
- Department of Mathematics, Johannes Kepler University, A-4040 Linz, Austria
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- RADKO MESIAR
- Department of Mathematics, Faculty of Civil Engineering, Slovak Technical University, SK-81368 Bratislava, Slovakia
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- ENDRE PAP
- Institute of Mathematics, University of Novi Sad, YU-21000 Novi Sad, Yugoslavia
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説明
<jats:p> When using a t-norm for combining fuzzy sets, no compensation between small and large degrees of membership takes place. On the other hand, a t-conorm provides full compensation. Since many real situations do not fall into either one category, so-called compensatory operators have been proposed in the literature [H.-J. Zimmermann and P. Zysno, Fuzzy Sets and Systems4 (1980) 37–51] which are non-associative in nature. In this paper, associative compensatory operators (whose domain is the unit square with the exception of the two points (0, 1) and (1, 0) and whose only associative extensions to the whole unit square are the aggregative operators suggested in [J. Dombi, Europ. J. Oper. Res.10 (1982) 282–293]) are studied and their representation in terms of multiplicative generators is given. It is shown that these operators are constructed with the help of strict t-norms and t-conorms, in a way which is similar to ordinal sums. Finally, the duals of such operators are shown to be again associative compensatory operators, and a characterization of self-dual operators is given. </jats:p>
収録刊行物
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- International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
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International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 04 (02), 129-144, 1996-04
World Scientific Pub Co Pte Lt
