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In 1982, Trillas introduced the notion of indistinguishability operator with the main aim of fuzzifying the crisp notion of equivalence relation. In the study of such a class of operators, an outstanding property must be stressed. Concretely, there exists a duality relationship between indistinguishability operators and metrics. The aforesaid relationship was deeply studied by several authors that...
We propose a new type of weighted averaging functions given implicitly as a solution to an algebraic equation. The main ingredient is incorporation of weights performed by using a function different to the product. Strict triangular norms are one example of such functions. We show that the weights should be normalized in this case differently to the usual sum to one condition. We establish the conditions...
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