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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”.

03E72 Theory of fuzzy sets, etc.
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