A Type-2 fuzzy logic approach for multi-criteria group decision making

Multi-Criteria Group Decision Making (MCGDM) is a decision tool which is able to find a unique agreement from a group of decision makers (DMs) by evaluating various conflicting criteria. However, most multi-criteria decision making techniques utilizing a group of DMs (MCGDM) do not effectively deal with the large number of possibilities inherent in a domain with a variety of possibilities, different judgments, and ideas on opinions. In recent years, there has been a growing interest in developing MCGDM using type-2 fuzzy systems which provide a framework to handle the encountered uncertainties in decision making models. In addition, fuzzy logic is regarded as an appropriate methodology for decision making systems which are able to simultaneously handle numerical data and linguistic knowledge. In this paper, we will aim to modify the fuzzy logic theories based multi-criteria group decision making models to employ a suite of type-2 fuzzy logic systems in order to provide answers to the problems that are encountered in the real experts' decision. In the proposed framework, we will present a MCGDM method based on interval type-2 fuzzy logic combined with intuitionistic fuzzy evaluation (from intuitionistic fuzzy sets). This combination handles the linguistic uncertainties by the interval type-2 membership function and simultaneously computes the non-membership degree from the intuitionistic evaluation. However, the interval values with hesitation index cannot fully represent the uncertainty distribution associated with the decision makers. Hence, we will present a final component of our framework employing general type-2 fuzzy logic based approach for MCGDM which is more suited for higher levels of uncertainties. In order to optimally find the type-2 fuzzy sets parameters (including interval type-2 and general type-2), we have employed the Big Bang Big Crunch (BB-BC) optimisation method. In order to validate the efficiency of the proposed systems in handling various DMs' behaviour and opinion, we will present comparisons which were performed on two different real world decision making problems. As will be shown in the various experiment sections, we found that the proposed type-2 MCGDM based system better agrees with the users' decision compared to type-1 fuzzy expert system and existing type-1 fuzzy MCDMs including the Fuzzy Logic based TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution). In addition, we will show how the different type-2 fuzzy logic based MCGDM systems compare to each other when increasing the level of uncertainties where the general type-2 MCGDM will outperform the MCGDM based interval type-2 fuzzy logic combined with intuitionistic fuzzy evaluation which will outperform the MCGDM based on interval type-2 fuzzy sets. Hence, this work can be regarded as a step towards producing higher ordered fuzzy logic approach for MCGDM (HFL-MCGDM) which could be applied to complex problems with high uncertainties to produce automated decisions much closer to the group of human experts.