Constructing fuzzy material implication functions derived from general grouping functions
DOI:
https://doi.org/10.5540/03.2025.011.01.0370Palabras clave:
General Grouping Functions, Fuzzy Implication Functions, System ModelingResumen
Grouping and overlap functions have been largely applied in the modeling of fuzzy systems and problems involving decision-making based on fuzzy preference relations due to their richness in the classes of aggregation functions compared to t-conorms and t-norms. Grouping functions allow one to measure the amount of evidence favoring two given alternatives in pairwise comparisons. However, as they are not associative, in the context of n-dimensional problems, some generalizations of grouping functions are required, like n-dimensional grouping functions and the more flexible class called general grouping functions (GGF). Since GGF widens the scope of applications, a novel class of fuzzy implication functions constructed from GGF and fuzzy negations is provided in this work. We study their main properties, characterizations, construction methods, and examples, paving the way for their use in modeling more flexible fuzzy systems.
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