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 UPDHF-PRs 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.

A New Single-Valued Neutrosophic Rough Sets and Related Topology

“…Furthermore, from Remark 1, we know that when restricting single-valued neutrosophic sets to Pythagorean fuzzy sets, we can define a model of Pythagorean fuzzy rough sets. It is well known that Pythagorean fuzzy sets and (fuzzy) rough sets have been applied in many fields, particularly in multiple attribute decision-making [9,16,[52][53][54][55]. erefore, in the future, we will also consider the potential application of Pythagorean fuzzy rough sets.…”

A new group decision making approach based on incomplete probabilistic dual hesitant fuzzy preference relations

“…As an effective technique in decision making field, GDM based on various types of PR is widely concerned, which are summarized in Table 1. From Table 1, to date, it is rare to discuss the consistency of PDHFPRs [37].…”

“…Furthermore, probabilistic dual hesitant fuzzy environment has been widely used in GDM, which are listed in Table 2. Table 2 shows that most of the existing researches concentrated on GDM based on PDHFSs, and only Shao and Zhang [37] discussed GDM based on PDHFPRs.…”

“…To date, the research on the consistency of PR has been fruitful [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. However, only Shao and Zhang [37] have focused on the consistency of PDHFPRs. In addition, Shao and Zhang's method [37] has certain limitations, which is manifested in that the consistency index does not consider the risk attitude of DMs, and the weight of DMs is given subjectively.…”

“…However, only Shao and Zhang [37] have focused on the consistency of PDHFPRs. In addition, Shao and Zhang's method [37] has certain limitations, which is manifested in that the consistency index does not consider the risk attitude of DMs, and the weight of DMs is given subjectively. Thus, it is urgent to study the consensus of PDHFPRs and use it to solve the GDM problem.…”