Behavioural three-way decision making with Fermatean fuzzy Mahalanobis distance: Application to the supply chain management problems

Abstract

Behavioural three-way decision making has superseded conventional two-way decision making as a result of a surge in risk and complexity of decision making. Additionally, uncertainty management is necessary for decision making issues. Thus, the goal of this study is to set up new three-way multi-attribute decision making (MADM) model, particularly targeting the following: (i) to properly deal with issues regarding ambiguity and interrelationship in MADM problems, (ii) to incorporate mindsets of decision maker in all possible aspects, (iii) to depict outcomes in terms of acceptance, suspension and rejection rather than just ranking when there are numerous elements present Firstly, the presence of ambiguity in assessment information is reflected by Fermatean fuzzy set. An advanced distance measure, the Fermatean fuzzy Mahalanobis distance, is devised in order to address the connectivity of attributes. Therefore, regret theory-based gain and loss scores are calculated to define the dominant and dominated relations. The conditional probability is then estimated using a new method based on the two relations discussed before. After that, the value functions associated to each object are derived based on closeness coefficient and prospect theory. Finally, prospect theory-based three-way decision rules are forwarded to classify and rank the objects. The application of the developed model is demonstrated through two case studies of supply chain management. Several experimental analyses are conducted under two substantial datasets taken from the KEEL database. The Spearman correlation coefficient (greater than 0.648) and hypothesis testing (p-value is less than 0.01) are employed to establish the validity and rationality of the proposed model. What is more, the error rate and modified error rate under two datasets are 6.71%, 16.85% and 6.35%, 20.65%, respectively, indicate that the proposed model is superior to other available models.