# zbMATH — the first resource for mathematics

Aggregation operators based on indistinguishability operators. (English) Zbl 1112.68122
Summary: This article gives a new approach to aggregation assuming that there is an indistinguishability operator or similarity defined on the universe of discourse. The very simple idea is that when we want to aggregate two values $$a$$ and $$b$$ we are looking for a value $$\lambda$$ with which $$a$$ and $$b$$ must be equivalent. Interesting aggregation operators on the unit interval are obtained from natural indistinguishability operators associated to t-norms that are ordinal sums.

##### MSC:
 68T37 Reasoning under uncertainty in the context of artificial intelligence 03E72 Theory of fuzzy sets, etc.
Full Text:
##### References:
 [1] , . Triangular norms. Dordrecht: Kluwer; 2000. [2] Ling, Publ Math Debrecen 12 pp 189– (1965) [3] . Probabilistic metric spaces. Amsterdam: North-Holland; 1983. [4] Boixader, Mathware Soft Comput 5 pp 5– (1998) [5] , . Fuzzy equivalence relations: Advanced material. In: , editors. Fundamentals of fuzzy sets. Dordrecht: Kluwer; 2000. pp 261–290. [6] Metamathematics of fuzzy logic. Dordrecht: Kluwer; 1998. [7] , , . Aggregation operators: Properties, classes and construction methods. In: , , editors. Aggregation operators: New trends and applications. Studies in fuzziness and soft computing. Berlin: Springer; 2002. pp 3–104. [8] Lectures on functional equations and their applications. New York/London: Academic Press; 1966. · Zbl 0139.09301 [9] De Soto, Fuzzy Set Syst 121 pp 427– (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.