Novel Subsethood Measures for Totally Dependent-Neutrosophic Sets and Their Usage in Multiple Attribute Decision-Making

Abstract

Multiple attribute decision-making (MADM) models are accepted as powerful tools for evaluating alternatives when the decision-analysts should consider more than one attribute while reaching a decision. The decision-makers who are consulted need a scale for expressing their judgments, experiences, or opinions. The fuzzy logic and its contemporary versions can supply different kinds of scales to allow the decision-makers to state their ideas. A recent version is totally dependent-neutrosophic (picture fuzzy) sets which include independently assignable elements: positive, neutral, negative, and refusal membership degrees. In this study, we aim to contribute to the literature of the totally dependent-neutrosophic sets by (i) proposing three new subsethood measures dedicatedly developed for totally dependent-neutrosophic sets for the first time in the literature and (ii) showing their applicability in a decision-making case study including a novel totally dependent-neutrosophic version of EDAS (Evaluation Based on Distance from Average Solution) method which is extended differently from the existing ones. To validate the proposed method, a comparative analysis with the existing totally dependent-neutrosophic MADM methods is provided. As a result, the proposed Subsethood Measure-based Totally Dependent-Neutrosophic Version of EDAS (SM-TDN-EDAS) method involving fewer steps than others gave similar rankings.

Keywords

• totally dependent-neutrosophic sets
• subsethood measure
• multiple criteria evaluation
• fuzzy numbers