Indistinguishability operators and generalized distances: the transformation problem revisited

Gonzalez-Hedstrom, Juan De Dios; Miñana, Juan-José; Valero, Oscar

doi:10.22111/ijfs.2025.51414.9084

Document Type : Research Paper

Authors

¹ Department of Mathematics and Computer Science, Universitat de les Illes Balears

² Instituto de Investigación para la Gestión Integrada de Zonas Costeras, Universitat Politécnica de Valencia

https://doi.org/10.22111/ijfs.2025.51414.9084

Abstract

In this paper we characterize those functions that induce a fuzzy preorder from a quasi-pseudo-metric even when the considered t-norm is not continuous. On the one hand, we prove that they must be decreasing and fulfill a special property of dominance with respect to the ordinary addition and the t-norm T under consideration. On the other hand, we have shown that they must transform asymmetric triangular triplets into asymmetric T-triangular triplets. Moreover, we also study the case in which fuzzy preorders are exactly indistinguishability operators. Concretely, we show that the monotonicity of the function and the previously mentioned dominance are sufficient but not necessary conditions. In addition, we prove that such functions must transform triangular triplets into T-triangular triplets. The developed theory is illustrated by means of appropriate examples. Furthermore, we prove that the well-known technique based on the use of the pseudo-inverses of the additive generators of continuous and Archimedean t-norms is recovered as a particular case of the new one presented here.

Keywords

Main Subjects

Fuzzy Math

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Iranian Journal of Fuzzy Systems

Indistinguishability operators and generalized distances: the transformation problem revisited

References

References

Volume 22, Issue 5
September and October 2025
Pages 97-109

Indistinguishability operators and generalized distances: the transformation problem revisited

References

References

Volume 22, Issue 5September and October 2025Pages 97-109

Volume 22, Issue 5
September and October 2025
Pages 97-109