Multilevel AHP approach with interval type-2 fuzzy sets to portfolio selection problem

Abstract

Decision making (DM) is an important process encountered in every moment of life. Since it is difficult to interpret life depending on a single criterion, Multi-Criteria Decision Making (MCDM) enables to make decisions easier by creating appropriate choice in situations of uncertainty, complexity, and conflicting objectives. Therefore, we have studied the Analytic Hierarchy Process (AHP) which is one of the MCDM methods based on binary comparison logic. When uncertainties concerning the nature of life are considered, the solution procedure of AHP has been addressed by using Interval Type-2 Fuzzy Numbers (IT2FN)s to obtain more realistic results. The usability of AHP with IT2FN is increased by amplifying hierarchy with sub-levels. Since sub-criterion may also need to be evaluated on sub-criteria in some cases of real multi-criteria problems, it is explicitly essential that each of sub-sub-criterion is included in the hierarchy at the own level in the real sense. In this paper, a new multilevel type-2 fuzzy AHP method is expanded by adding sub-criteria to the Interval Type-2 Fuzzy AHP (IT2FAHP) method developed by Kahraman et al. [C. Kahraman, B. Öztayşi, İ. Sarı and B. Turanoğlu, Fuzzy analytic hierarchy process with interval type-2 fuzzy sets, Knowledge-Based Systems 59 (2014), 48–57.]. Thanks to the extended method, another aim is to ensure that even complex situations that have multiple levels can be solved simply. Also, the proposed method is illustrated with a portfolio selection problem. Thus, the AHP method with type-2 fuzzy sets is carried out to the portfolio selection problem, which is in the scope of finance theory, for the first time in the literature.