The Novel Integrated Model of Plithogenic Sets and MAIRCA Method for MCDM Problems

Abstract

The most of the decision making processes contain uncertainty due to the real world problems. In order to deal with this uncertainty, different set theories have been introduced in the literature. Plithonegic set is the relatively newest one among them. The concept of plithogeny which was developed by Smarandache [4] is the generalizations of neutrosophic sets, logic, probability, and statistics. Two main elements, contradiction and appurtenance degrees, of plithogenic set help to improve the accuracy of the results under the uncertain environment. In this study, it is aimed to propose a model based on plithogenic sets and the MAIRCA (Multi-Attributive Ideal-Real Comparative Analysis) method. To the best of our knowledge plithonegic sets are integrated for the first time in this study with the MAIRCA method which aims to minimize the gap between ideal and empirical values. A case study about green supplier selection problem in the automotive industry adapted from Gupta et al. [18] is handled to show the applicability of the proposed model. The plithogenic aggregation operations are performed to aggregate different decision makers’ opinions on criteria performance values with respect to each green supplier. Results have showed that the MAIRCA method could be integrated with plithonegic sets efficiently. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.