Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems

Abstract

This paper introduces probability multi-valued neutrosophic sets (PMVNSs) based on multi-valued neutrosophic sets and probability distribution. PMVNS can serve as a reliable tool to depict uncertain, incomplete, inconsistent and hesitant decision-making information and reflect the distribution characteristics of all provided evaluation values. This paper focuses on developing an innovative method to address multi-criteria group decisionmaking (MCGDM) problems in which the weight information is completely unknown and the evaluation values taking the form of probability multi-valued neutrosophic numbers (PMVNNs). First, the definition of PMVNSs is described. Second, an extended convex combination operation of PMVNNs is defined, and the probability multi-valued neutrosophic number weighted average operator is proposed. Moreover, two cross-entropy measures for PMVNNs are presented, and a novel qualitative flexible multiple criteria method (QUALIFLEX) is developed. Subsequently, an innovative MCGDM approach is established by incorporating the proposed aggregation operator and the developed QUALIFLEX method. Finally, an illustrative example concerning logistics outsourcing is provided to demonstrate the proposed method, and its feasibility and validity are further verified by comparison with other existing methods.

Green Supplier Evaluation and Selection Using Cloud Model Theory and the QUALIFLEX Method

“…Tian et al [31] proposed a simplified neutrosophic linguistic QUALIFLEX approach for green product design selection considering risk attitudes of decision makers, and Tian et al [32] proposed an extended QUALIFLEX approach with a likelihood-based comparison method to handle MCDM problems in the context of hesitant fuzzy linguistic information. Peng et al [33] presented two cross entropy measures for probability multi-valued neutrosophic numbers and proposed a probability multi-valued neutrosophic QUALIFLEX method to address MCDM problems. Wang et al [34] developed a likelihood-based QUALIFLEX model to deal with decision-making problems under the context of interval type-2 trapezoidal fuzzy sets.…”

Picture fuzzy multi-criteria group decision-making method to hotel building energy efficiency retrofit project selection

“…Then, Wei et al [41] proposed the convex combination operation for hesitant fuzzy linguistic term sets. Afterwards, Peng et al [27] applied the convex combination operation to probability multi-valued neutrosophic environments. In addition, Cuong and Kreinovich [6] firstly defined convex combination of PFS with some simple propositions in the following.…”

“…Tian et al [33] utilized extended QUALIFLEX method to copy with green product design selection by life cycle assessment technique with simplified neutrosophic linguistic information. Peng et al [27] studied the selection problem of logistics provider through an extended QUALIFLEX method under probability multi-valued neutrosophic environment. Li et al [18] proposed an extended QUALIFLEX method for selecting green suppliers under probability hesitant fuzzy environment.…”

Dombi Aggregation Operators of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

“…The simplified forms of neutrosophic sets have been widely applied in multiple attribute decision-making (MADM) problems [9][10][11][12][13] and fault diagnosis [14]. Some extension forms of neutrosophic sets have been proposed by combining neutrosophic sets and other sets, for instance, multi-valued neutrosophic sets [15,16], intuitionistic neutrosophic soft set [17], rough neutrosophic sets [18], single-valued neutrosophic hesitant fuzzy [19], refined single-valued neutrosophic sets [20], neutrosophic soft sets [21], linguistic neutrosophic number [22,23], normal neutrosophic sets [24] and single-valued neutrosophic hesitant fuzzy set [25].…”