An interval type-2 fuzzy LINMAP method with approximate ideal solutions for multiple criteria decision analysis

An integrated group decision-making method for the evaluation of hypertension follow-up systems using interval-valued q-rung orthopair fuzzy sets

It is imperative to comprehensively evaluate the function, cost, performance and other indices when purchasing a hypertension follow-up (HFU) system for community hospitals. To select the best software product from multiple alternatives, in this paper, we develop a novel integrated group decision-making (GDM) method for the quality evaluation of the system under the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs). The design of our evaluation indices is based on the characteristics of the HFU system, which in turn represents the evaluation requirements of typical software applications and reflects the particularity of the system. A similarity is extended to measure the IVq-ROFNs, and a new score function is devised for distinguishing IVq-ROFNs to figure out the best IVq-ROFN. The weighted fairly aggregation (WFA) operator is then extended to the interval-valued q-rung orthopair WFA weighted average operator (IVq-ROFWFAWA) for aggregating information. The attribute weights are derived using the LINMAP model based on the similarity of IVq-ROFNs. We design a new expert weight deriving strategy, which makes each alternative have its own expert weight, and use the ARAS method to select the best alternative based on these weights. With these actions, a GDM algorithm that integrates the similarity, score function, IVq-ROFWFAWA operator, attribute weights, expert weights and ARAS is proposed. The applicability of the proposed method is demonstrated through a case study. Its effectiveness and feasibility are verified by comparing it to other state-of-the-art methods and operators.

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

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.