A dynamic fuzzification approach for interval type-2 membership function development: case study for QoS planning

Abstract

Nowadays, there is a great interest in expressing uncertain concepts by means of fuzzy set theory proposed by L.A. Zadeh. The application of the fuzzy sets theory includes a fuzzification process that expresses an uncertain concept by a membership function (MF). However, due to a lack of a general systematic approach for the fuzzification process, its effectiveness and applicability in different domains is still insufficient and difficult to evaluate. The aim of this paper is to propose a general dynamic fuzzification approach for interval type-2 fuzzy sets (DFSIT2), which in general manner identifies and describes the main steps of the fuzzification process. We propose four basic requirements of the fuzzification approach and on their basis developed DFSIT2. Its novelty and relevance is triple. First, it systematizes the fuzzification process independently of understanding of fuzziness, application domain, and techniques for interval type-2 membership function (IT2MF) development. Second, it consists of an extended implementation component, which provides IT2MF development rules, and a refined evaluation component, which allows us to verify and validate the obtained result. Third, DFSIT2 architecture is proposed and implemented into a prototype in a service-oriented enterprise system for an Invoice Submission service. A case study of IT2MF development from the WS-DREAM dataset#1 was carried out using this prototype. The obtained results correspond to the needs of fuzzification process, as well as possibilities for dynamic and flexible IT2MF development. We expect that our results inspire researchers and practitioners for further work aiming at bringing forward fuzzification problem modelling and implementation.