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Towards a General Class of Operators for Fuzzy Systems

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1 Author(s)
Dombi, J. ; Univ. of Szeged, Szeged

Our starting point is the multiplicative utility function which is extensively used in the theory of multicriteria decision making. Its associativity is shown and as its generalization a class of operators is introduced with fine and useful properties. As in special cases, it reduces to well-known operators of fuzzy set theory: min/max, product, Einstein, Hamacher, Dombi, and drastic. As a consequence, we generalize the addition of velocities in Einstein's special relativity theory to multiple moving objects. Also, a new form of the Hamacher operator is given, which makes multiargument calculations easier. We examine the De Morgan identity which connects the conjunctive and disjunctive operators by a negation. It is shown that in some special cases (min/max, drastic, and Dombi) the operator class forms a De Morgan triple with any involutive negation.

Published in:

Fuzzy Systems, IEEE Transactions on  (Volume:16 ,  Issue: 2 )