Multiobjective Programming Approaches to Obtain the Priority Vectors under Uncertain Probabilistic Dual Hesitant Fuzzy Preference Environment

Abstract

This paper develops uncertain probabilistic dual hesitant fuzzy numbers (UPDHFN), which includes six types of dual hesitant fuzzy sets (DHFNs). Next, the UPDHFN is applied to the uncertain probabilistic dual hesitant fuzzy preference relation (UPDHFPR). Furthermore, the (acceptable) expected consistency, method of obtaining uncertain probabilistic information, and consistency-increasing iterative algorithm for flexible application of UPDHFPRs are explained respectively. Then, the UPDHFPRs and these approaches are applied to group decision-making procedure. Two operators are established to aggregate the UPDHFPRs and the integrated preference relations are also UPDHFPRs. In this model, due to the aggregated UPDHFPRs may be inconsistent. Thus an acceptable group consistency algorithm is designed. The group decision-making process is summarized under the UPDHFPR situation. Eventually, an illustrate example that selects the optimal alternative from three listed candidates is provided to verify our methods.

Keywords

• Uncertain probabilistic dual hesitant fuzzy number
• Preference relation
• Priority vector
• Group decision-making
• Multiplicative consistency