n-Dimensional Fuzzy Implications: Analytical, Algebraic and Applicational Approaches

Abstract

The study of n-dimensional fuzzy logic contributes to overcome the insufficiency of traditional FL in modeling imperfect and imprecise information coming from different experts. Based on representability, we extend results from fuzzy connectives to n-dimensional approach. This research on n-dimensional fuzzy implications (n-DI) pass through the next steps: (i) analytical studies; (ii) algebraic aspects; (iii) n-dimensional approach of fuzzy implication classes represented by fuzzy connectives as (S, N)-implications and QL-implications; (iv) studies of n-dimensional R-implications (n-DRI); (v) constructive method obtaining n-DRI based on n-dimensional aggregation operators and (vi) an introductory study considering an n-DI in modeling approximate reasoning.