On General Framework of Type-1 Membership Function Construction: Case Study in QoS Planning

Fuzzy approaches that are proposed to describe uncertain, impressive or vague concepts, are based on the construction of membership function (MF), which reflects what is known about the linguistic variables in the application domain. However, a non-trivial problem exists in how to construct the most appropriate MF that has the best-fit representation of the analysed problem. Therefore, many authors propose their own ways to construct MF using a certain technique in a particular application domain. Consequently, the need for a general approach for constructing MF led us to systematise and to generalise the analysed approaches into a general methodological framework (GMF) of constructing MF. The novelty of this paper is that the proposed GMF is general, domain independent and free of a chosen understanding of fuzziness (i.e., similarity (imprecision), preference (vagueness), and uncertainty). To verify the proposed GMF, it was applied for the enterprise business service quality (QoS EBS ) planning problem. The obtained results showed that a semi-automatic MF construction for QoS EBS planning was more sensitive, less subjective and more precise than a manual construction. Moreover, illustrative examples showed that our proposed GMF is applicable and implementable. The reliability of the results was assessed using experts and users’ experience, which is based on general guidelines of the “acceptable” response time limits for various activities.