Design of fuzzy rule-based classifiers with semantic cointension

Abstract

In computing with words (CWW), knowledge is linguistically represented and has an explicit semantics defined through fuzzy information granules. The linguistic representation, in turn, naturally bears an implicit semantics that belongs to users reading the knowledge base; hence a necessary condition for achieving interpretability requires that implicit and explicit semantics are cointensive. Interpretability is definitely stringent when knowledge must be acquired from data through inductive learning. Therefore, in this paper we propose a methodology for designing interpretable fuzzy models through semantic cointension. We focus our analysis on fuzzy rule-based classifiers (FRBCs), where we observe that rules resemble logical propositions, thus semantic cointension can be partially regarded as the fulfillment of the “logical view”, i.e. the set of basic logical laws that are required in any logical system. The proposed approach is grounded on the employment of a couple of tools: DC f, which extracts interpretable classification rules from data, and Espresso, that is capable of fast minimization of Boolean propositions. Our research demonstrates that it is possible to design models that exhibit good classification accuracy combined with high interpretability in the sense of semantic cointension. Also, structural parameters that quantify model complexity show that the derived models are also simple enough to be read and understood.