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Uninorm aggregation operators. (English) Zbl 0871.04007

Summary: A generalization of the \(t\)-norm and \(t\)-conorm called the uni-norm is defined. These operators allow for an identity element lying anywhere in the unit interval rather than at one or zero as in the case of \(t\)-norms and \(t\)-conorms, respectively. Various important properties of these uni-norms are investigated. We next introduce two particular families of these uni-norms, \(R^*\) and \(R_*\), study their behavior and suggest some semantics. Finally, withdrawing the requirement of associativity, we introduce a class of operators called \(R_{Q\text{-star}}\) aggregation operators which are useful for aggregations guided by imperatives such as “if most of the scores are above the identity take the Max else use the Min”.

MSC:

03E72 Theory of fuzzy sets, etc.
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