A Framework for Triangular Fuzzy Random Multiple-Criteria Decision Making

Most real-world decisions practically occur in extremely complex environments characterized by both fuzziness and randomness. This phenomenon highlights the requirement for new evaluation methods in a fuzzy random environment and new ways to address fuzzy random multiple-criteria decision-making (MCDM) problems. This study reviews fuzzy random variable (FRV) to evaluate fuzzy random decision-making environment. Given the inaccuracy of certain precision formulas proposed in previous studies for the variance of a triangular FRV, this work presents the detailed process of calculating precision variance formulas and discusses several properties of the expectation and variance of triangular FRVs (TFRVs). The united variance of a TFRV vector is also proven to possess non-additive properties. Thus, an ordered weighted averaging (OWA) operator is extended to aggregate fuzzy random data by proposing a triangular fuzzy random OWA operator. Motivated by the idea of mean-variance analysis, an expectation-variance-based method is employed to rank TFRVs. Furthermore, a novel triangular fuzzy random MCDM method is developed, and certain numerical examples are provided to demonstrate the ability of TFRVs to comprehensively assess the performance of a specific alternative. This work also illustrates how the triangular fuzzy random MCDM framework can be extended to any fuzzy random decision-making process.