Multicriteria decision-making (MCDM) refers to making decisions in the presence of multiple and usually conflicting criteria. Fuzzy decision-making is used where vague and incomplete data exist for the solution. Fuzzy multicriteria decision-making is one of the most popular problems handled by the researchers in the literature. In this paper, we survey the latest status of fuzzy multicriteria decision-making methods and classify these methods dividing into two parts: fuzzy multiattribute decision-making (MADM) and fuzzy multiobjective decision-making (MODM). Most of the publications are on fuzzy MADM since there are a plenty of classical multiattribute decision-making methods in the literature. Tabular and graphical illustrations for each method are given.

Evaluation based on Distance from Average Solution (EDAS) is a new multicriteria decision making (MCDM) method, which is based on the distances of alternatives from the average scores of attributes. Classical EDAS has been already extended by using ordinary fuzzy sets in case of vague and incomplete data. In this paper, we propose an interval-valued intuitionistic fuzzy EDAS method, which is based on the data belonging to membership, nonmembership, and hesitance degrees. A sensitivity analysis is also given to show how robust decisions are obtained through the proposed intuitionistic fuzzy EDAS. The proposed intuitionistic fuzzy EDAS method is applied to the evaluation of solid waste disposal site selection alternatives. The comparative and sensitivity analyses are also included.

The extensions of ordinary fuzzy sets such as intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and neutrosophic sets (NS), whose membership functions are based on three dimensions, aim at collecting experts’ judgments more informatively and explicitly. In the literature, generalized three-dimensional spherical fuzzy sets have been developed by Kutlu Gündoğdu and Kahraman (2019), including their arithmetic operations, aggregation operators, and defuzzification operations. Spherical Fuzzy Sets (SFS) are a new extension of Intuitionistic, Pythagorean and Neutrosophic Fuzzy sets, a SFS is characterized by a membership degree, a nonmembership degree, and a hesitancy degree satisfying the condition that their squared sum is equal to or less than one. These sets provide a larger preference domain in 3D space for decision makers (DMs). In this paper, our aim is to extend classical VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method to spherical fuzzy VIKOR (SF-VIKOR) method and to show its applicability and validity through an illustrative example and to present a comparative analysis between spherical fuzzy TOPSIS (SF-TOPSIS) and SF-VIKOR. We handle a warehouse location selection problem with four alternatives and four criteria in order to demonstrate the performance of the proposed SF-VIKOR method.