Optimal solutions to granular fuzzy relation equations with fuzzy logic operations

Abstract

Fuzzy relation equations are commonly utilized to describe the fuzzy relationship between the antecedent and the consequent parts of complex data environment, and play a vital role in fuzzy system modeling. An interesting topic is to determine fuzzy relation equations based on existing fuzzy logic operations, including the t-norms and t-conorms (s-norms). However, fuzzy rule-based models developed in form of numeric values still face significant challenges in accuracy and interpretability. This study aims to introduce the idea of granular computing to formulate granular fuzzy relation equations based on the fuzzy logic operations and evaluate the performance of granular fuzzy relation equations using the general principle of justifiable granularity. A two-phase development of granular fuzzy relation equations is designed: In the first phase, fuzzy relation equations are constructed based on t-norms and t-conorms; in the second phase, granular augmentation of fuzzy relation equations is realized by allocating a certain level of information granularity as the granular parameters of fuzzy relations. The capability of granular outputs is evaluated with the aid of two conflicting criteria—coverage (cov) and specificity (sp). The optimal solutions to granular fuzzy relation equations are explored using combinations of optimization algorithms. The originality of this study lies on the development of granular fuzzy relation equations with fuzzy logic operations, which provides a human-centric platform of fuzzy system modeling to enhance accuracy and interpretability. Experimental studies are carried out based on the UCI and KEEL machine learning datasets to report on the feasibility and performance of the proposed model.