Multi-Criteria Decision Making Techniques Based on Some Extensions of Fuzzy Set

Abstract

Multi-criteriadecisionmaking(MCDM)isacommonactivityineverydaylifeandtheobjectiveistoselectthe most feasible alternative from a set of given alternatives with the highest level of satisfaction in the presence of multiple, usually conflicting, criteria. Similarly, there are many real-life complex problems, where we need involve wide domain of knowledge which are beyond a single expert. Therefore, it is usually necessary to allocate more than one expert to decision process from different fields, including the education backgrounds, work experience and knowledge structure. Consequently, the multi-criteria group decision making (MCGDM) is also an important tool to deal with human activities and their problems of daily lives. In this thesis, different MCDM/MCGDM techniques are discussed based on some important extensions of fuzzy set. This thesis is comprised of three stages. In the first stage, the MCDM method called the Characteristic Objects Method (COMET) is extended to solve problems for MCGDM with hesitant fuzzy sets (HFSs) and intuitionistic fuzzy sets (IFSs). It is a completely new idea for solving problems of group decision making (GDM) under uncertainty. In this approach, we use L-R-type generalized fuzzy numbers (GFNs) and triangular intuitionistic fuzzy numbers (TIFNs) to get the degree of hesitancy in the form of hesitant fuzzy elements (HFEs) and the degree of membership and non-membership in the form of intuitionistic fuzzy numbers (IFNs) respectively for an alternative under a certain criterion. Therefore, the classical COMET methodwasadaptedtoworkwithGFNsandTIFNsinGDMproblems. Theproposedextensionsarepresented in detail, along with the necessary background information. The second stage of the thesis is comprised of three parts. In the first part, an outranking method is constructed using hesitant intuitionitic fuzzy linguistic term sets (HIFLTSs) for ranking alternatives in MCGDM problems based on intuitionistic fuzzy support function (IFSF), intuitionistic fuzzy risk function (IFRF),intuitionisticfuzzycredibilityfunction(IFCF)andthenetoutrankingflowindex(NOFI).Inthesecond part, the notion of directional Hausdorff distance between two HIFLTSs has been proposed and used it to formulate ELECTRE-based outranking method in hesitant intuitionistic fuzzy linguistic (HIFL) environment. The linguistic scale functions (LSFs) are used in two methodologies as mentioned above to conduct the transformation mechanism between qualitative information and quantitative data. In the third part, the notions of some distance measures between two HIFLTSs and weighted distance measures between two collections xiv xv of HIFLTSs are proposed and analyzed for discrete and continuous cases, and then used them to rank the alternatives in MCGDM problem. The third stage of the thesis is also comprised of two parts. In the first part, two outranking methods are developed with intuitionistic 2-tuple fuzzy linguistic (I2FL) information and a comparative discussion is conductedtodeterminetheadvantagesoftheproposedmethodovertheother. Inthesecondpart, afuzzyAHP (analytic hierarchy process) methodology for intuitionistic 2-tuple fuzzy linguistic sets (I2FLSs) is proposed and applied to solve MCDM problems. Finally, illustrative numerical examples are provided to elaborate the proposed methods with respect to the support of decision processes. This thesis closes with the conclusion along with some future research directions in this area.