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An Extended Multi-criteria Group Decision-Making PROMETHEE Method Based on Probability Multi-valued Neutrosophic Sets

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Abstract

The PROMETHEE method, one of the most widely used and best known methods, takes advantage of the outranking principle to rank potential alternatives. The probability multi-valued neutrosophic sets (PMVNSs) have the power to describe complex uncertain information more comprehensively. Thus, in order to integrate the merits of PROMETHEE method and PMVNSs, this paper extends the PROMETHEE method to PMVNSs environment. Firstly, some basic preliminaries are reviewed, such as multi-valued neutrosophic sets (MVNSs), PMVNSs and classical PROMETHEE method. Then, we propose the operational laws of PMVNSs based on the operational rules of the MVNSs and probability distribution. Meanwhile, the score function and accuracy function of PMVNSs are given to simplify the comparison of any two probability multi-valued neutrosophic numbers (PMVNNs). Further, we develop a new distance measure for PMVNNs with unequal length, and then based on the distance measure and deviation maximization method, the attribute weights are determined; an extended PROMETHEE method for multi-criteria group decision-making with the information of PMVNSs is established to achieve the process for optimal alternative selection. In the end, a practical example concerning third party logistics providers is used to highlight the feasibility and superiority of the proposed approach.

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Abbreviations

DMs:

Decision makers

ELECTRE:

Elimination and choice translating reality

FF:

Falsity-membership function

FSs:

Fuzzy sets

HFSs:

Hesitant fuzzy sets

IF:

Indeterminacy-membership function

IFSs:

Intuitionistic fuzzy sets

IVFSs:

Interval-valued fuzzy sets

MCDM:

Multi-criteria decision-making

MCGDM:

Multi-criteria group decision-making

MVNPWA:

Multi-valued neutrosophic power weighted average

MVNPWG:

Multi-valued neutrosophic power weighted geometric

MVNSs:

Multi-valued neutrosophic sets

MVNWBM:

Multi-valued neutrosophic weighted Bonferroni mean

MVNWGBM:

Multi-valued neutrosophic weighted geometric Bonferroni mean

NSs:

Neutrosophic sets

PMVNNs:

Probability multi-valued neutrosophic numbers

PMVNSs:

Probability multi-valued neutrosophic sets

PROMETHEE:

Preference ranking organization method for enrichment evaluation

QUALIFLEX:

Qualitative flexible multiple criteria method

SNSs:

Simplified neutrosophic sets

TF:

Truth-membership function

TODIM:

An acronym in Portuguese of interactive and multi-criteria decision-making

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Acknowledgements

This paper is supported by the National Natural Science Foundation of China (Nos. 71771140 and 71471172), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045) and Shandong Provincial Social Science Planning Project (Nos. 17BGLJ04, 16CGLJ31 and 16CKJJ27).

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Correspondence to Peide Liu.

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Liu, P., Cheng, S. & Zhang, Y. An Extended Multi-criteria Group Decision-Making PROMETHEE Method Based on Probability Multi-valued Neutrosophic Sets. Int. J. Fuzzy Syst. 21, 388–406 (2019). https://doi.org/10.1007/s40815-018-0572-6

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