On robustness of the full implication triple I inference method with respect to finer measurements

Authors:
Guojun Wang;Jingyao Duan
Affiliations:
Department of Mathematics and Information Sciences, Shaanxi Normal University, Xi'an 710062, PR China;Department of Mathematics and Information Sciences, Shaanxi Normal University, Xi'an 710062, PR China and Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, PR China
Venue:
International Journal of Approximate Reasoning
Year:
2014

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Abstract

This paper mainly discusses three points. First of all, different types of equalities and similarity degrees between two fuzzy sets on a given universe of discourse are compared and analyzed. In particular, the concept of (T,@d) equality is revised as a measure to evaluate robustness of fuzzy reasoning. Besides, several induced metrics with respect to left-continuous T-norms are investigated, and properties of the related metric spaces are discussed. Finally, based on discussions above, the continuity of the triple I method with respect to the revised measures is proved, which reflects the good behavior of robustness of the triple I method.