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Triangular Fuzzy Neutrosophic Preference Relations and Their Application in Enterprise Resource Planning Software Selection

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Abstract

Enterprise resource planning (ERP) system selection is one of the most important topics in an ERP implementation program that ensures the success of the system. Because of the inherent complexity of ERP systems, it is difficult and time consuming for the organization to select the suitable ERP software. This paper employs triangular fuzzy neutrosophic preference relations (TFNPRs) to express the recognitions of decision-makers (DMs) for the choice of ERP software. Preference relation is a powerful tool to express complex decision problems, and the triangular fuzzy neutrosophic number (TFNN) is a good choice to represent the recognitions of the DMs; this paper combines preference relation with TFNN to define the concept of triangular fuzzy neutrosophic preference relations (TFNPRs). To rank the evaluated ERP systems logically, a multiplicative consistency concept for TFNPRs is defined. Then, several multiplicative consistency-based 0–1 mixed programming models are established for estimating missing values in incomplete TFNPRs and for deriving multiplicatively consistent TFNPRs from inconsistent ones, respectively. For group decision-making (GDM), a Manhattan distance measure-based consensus index is defined to measure the agreement degrees of the DMs’ opinions. A multiplicative consistency and consensus-based algorithm to GDM with TFNPRs is provided that can cope with incomplete and inconsistent TFNPRs. Meanwhile, an illustrative example about the selection of ERP software is offered to show the utilization of the new method, and comparison analysis is performed with several previous methods about ERP software selection. The new method adopts TFNPRs that can express the fuzzy truth-membership degree, the fuzzy indeterminacy-membership degree and the fuzzy falsity-membership degree of the recognitions of the DMs. It extends the application of preference relations and endows the DMs with more flexibility to denote their recognitions. Furthermore, the new method is based on the multiplicative consistency and consensus analysis that ensures the rational and representative ranking of the considered objects.

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Funding

This study was funded by the National Natural Science Foundation of China (Nos. 71571192, 71874112, and 71771025), the Innovation-Driven Project of Central South University (No. 2018CX039), the Beijing Intelligent Logistics System Collaborative Innovation Center (No. 2019KF-09), the Major Project for National Natural Science Foundation of China (Nos. 91846301, 71790615), and the State Key Program of National Natural Science of China (No. 71431006).

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Authors and Affiliations

  1. School of Information, Beijing Wuzi University, Beijing, 101149, China

    Fanyong Meng

  2. School of Business, Central South University, Changsha, 410083, China

    Fanyong Meng, Na Wang & Yanwei Xu

Authors
  1. Fanyong Meng
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  2. Na Wang
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  3. Yanwei Xu
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Correspondence to Na Wang.

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Appendix. The Tables of the Case Study

Appendix. The Tables of the Case Study

Table 1 Criteria for selecting ERP software
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Table 2 TFNPR \( {\tilde{P}}^{(1)} \) provided by the DM e1
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Table 3 TFNPR \( {\tilde{P}}^{(2)} \) provided by the DM e2
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Table 4 TFNPR \( {\tilde{P}}^{(3)} \) provided by the DM e3
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Table 5 TFNPR \( {\tilde{P}}^{(4)} \) provided by the DM e4
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Table 6 Missing values in TFNPRs
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Table 7 Optimal objective function values of models (17) and (21)
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Table 8 0–1 indicator variables obtained from models (18) and (22)
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Table 9 Multiplicatively consistent TFNPR \( {\tilde{Q}}^{(1)} \)
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Table 10 Multiplicatively consistent TFNPR \( {\tilde{Q}}^{(2)} \)
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Table 11 Multiplicatively consistent TFNPR \( {\tilde{Q}}^{(3)} \)
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Table 12 Multiplicatively consistent TFNPR \( {\tilde{Q}}^{(4)} \)
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Table 13 Comprehensive TFNPR \( \tilde{R} \)
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Table 14 Comprehensively multiplicatively consistent TFNPR \( \tilde{B} \)
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Meng, F., Wang, N. & Xu, Y. Triangular Fuzzy Neutrosophic Preference Relations and Their Application in Enterprise Resource Planning Software Selection. Cogn Comput 12, 261–295 (2020). https://doi.org/10.1007/s12559-019-09640-4

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