Interval-valued intuitionistic fuzzy stochastic multi-criteria decision-making method based on Prospect theory

The purpose of this paper is to provide a new approach to solving the interval-valued intuitionistic fuzzy stochastic multi-criteria decision-making (MCDM) problems.

To transform the interval-valued intuitionistic fuzzy number (IVIFN) into a computational numerical value, a new precision score (P-score) function is developed based on the degrees of membership, non-membership and hesitation. The prospect decision-making matrix is derived by applying P-score function and Prospect theory. A new criteria weighting model is put forward based on the least square method, the maximizing deviation method and Prospect theory. Consequently, combined criteria weighting model with the prospect decision-making matrix, the integrated prospect value is derived which presents a measurement scale for ranking the order of alternatives.

As a result, the method of the interval-valued intuitionistic fuzzy stochastic MCDM is suggested. In this method, the new P-score function responses the comprehensive information of the criteria. The prospect decision-making matrix can reflect the risk attitude of the decision maker. The new criteria weighting model can express both the subjective considerations of the decision maker and the objective information meaning.

The research results may lack generalizability for other fuzzy decision making because of the chosen research approach for IVIFN decision making. Therefore, researchers are encouraged to test the proposed propositions further.

The developed approach can be applied in many decision-making fields such as selection of renewable energy alternatives, assessment of flexible manufacturing system alternatives and human resource alternatives performance evaluation, etc. where the evaluation values are IVIFNs.

This paper succeeds in studying the interval-valued intuitionistic fuzzy MCDM based on Prospect theory, which has not been reported in the existing academic literature.