Formal Verification of a Fuzzy Rule-Based Classifier Using the Prototype Verification System

Abstract

This paper presents the formal specification and verification of a Type-1 (T1) Fuzzy Logic Rule-Based Classifier (FLRBC) using the Prototype Verification System (PVS). A rule-based system models a system as a set of rules, which are either collected from subject matter experts or extracted from data. Unlike many machine learning techniques, rule-based systems provide an insight into the decision making process. In this paper, we focus on a T1 FLRBC. We present the formal definition and verification of the T1 FLRBC procedure using PVS. This helps mathematically verify that the design intent is maintained in its implementation. A highly expressive language such as PVS, which is based on a strongly-typed higher-order logic, allows one to formally describe and mathematically prove that there is no contradiction or false assumption in the procedure. We show this by (1) providing the formal definition of the T1 FLRBC in PVS and then (2) formally proving or deducing rudimentary properties of the T1 FLRBC from the formal specification.