Measures for evaluating IT2FSs constructed from data intervals

Abstract

Interval type-2 fuzzy sets (IT2FSs) are increasingly used in fuzzy systems for modeling linguistic words. Various approaches exist to construct such IT2FSs. Although the performance of a fuzzy system is significantly influenced by the quality of the utilized IT2FSs however, currently there are no objective criteria for evaluating IT2FSs. This paper introduces a novel objective measure that enables assessing IT2FSs and helps to select the most appropriate ones. The introduced measure is the aggregation of two sets of sub-measures devised to appraise the sufficiency of support and suitability of membership grades. These measures can be effective on the IT2FSs that are built using a set of data intervals collected from a group of subjects. An application with well-defined experiments is devised and implemented to assess the validity of the proposed measure. Experiments are conducted using IT2FSs constructed by the three well-known approaches, i.e., Interval Approach (IA), Enhanced Interval Approach (EIA), and Hao–Mendel Approach (HMA). It is shown that the application performance with the IT2FSs constructed by the three approaches is in accordance with the calculated measures.