Robustness of the Reverse Triple I Algorithms Based on Schweizer-Sklar T-norms

doi:10.3969/j.issn.0372-2112.2016.04.029

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ACTA ELECTRONICA SINICA ›› 2016, Vol. 44 ›› Issue (4) : 959-966. DOI: 10.3969/j.issn.0372-2112.2016.04.029

Robustness of the Reverse Triple I Algorithms Based on Schweizer-Sklar T-norms

LUO Min-xia, WANG Ya-ping

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Abstract

Since the family of Schweizer-Sklar t-norm is flexible,they have good characteristics for fuzzy reasoning based on these flexible operators.In this paper,the properties of the Schweizer-Sklar operators family and the robustness of fuzzy reasoning algorithms are studied.The family of Schweizer-Sklar t-norms are decreasing for the variable m.The family of Schweizer-Sklar t-conorms are increasing for the variable m.These perturbations of Schweizer-Sklar t-conorms,Schweizer-Sklar t-norms and its residual implications are given.We proved that Schweizer-Sklar residual implication operators (include Lukasiewizc implication operator) are more suitable in fuzzy reasoning for m∈(0,∞).Moreover,we showed that the FMP reverse triple I algorithms based on the Schweizer-Sklar residual implications are robust for m∈(0,∞),and the FMT reverse triple I algorithms based on the Schweizer-Sklar residual implications are robust for m∈(0,∞).

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Schweizer-Sklar t-norms / reverse triple I algorithms / Minkowski distance / robustness

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LUO Min-xia, WANG Ya-ping. Robustness of the Reverse Triple I Algorithms Based on Schweizer-Sklar T-norms[J]. Acta Electronica Sinica, 2016, 44(4): 959-966. https://doi.org/10.3969/j.issn.0372-2112.2016.04.029

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