Abstract
In this manuscript, we extend the traditional multi-attributive border approximation area comparison (MABAC) method for the multiple-criteria group decision-making (MCGDM) with triangular fuzzy neutrosophic numbers (TFNNs) to propose the TFNNs-MABAC method. In the proposed method, we utilize the TFNNs to express the values of criteria for each alternative in MCGDM problems. First, we briefly acquaint the basic concept of TFNNs and describe its corresponding some operation laws, the functions of score and accuracy, and the normalized hamming distance. We then review two aggregation operators of TFNNs. Afterward, we combine the traditional MABAC method with the triangular fuzzy neutrosophic evaluation and provide a sequence of calculation procedures of the TFNNs-MABAC method. After comparing it with some TFNNs aggregation operators and another method, the results showed that our extended MABAC method can not only effectively handle the conflicting attributes, but also practically deal with incomplete and indeterminate information in the MCGDM problem. Therefore, the extended MABAC method is more effective, conformable, and reasonable. Finally, an investment selection problem is demonstrated as a practice to verify the reasonability of our MABAC method.
Highlights
The multi-attributive border approximation area comparison (MABAC) approach has been widely utilized to investigate multiple-criteria group decision-making (MCGDM) problems and has been extensively applied in various case studies by many fabulous researchers
Since the results in terms of ranking order provided by both aggregation operators are different, we investigated further the discrepancy between truth and falsity of the triangular fuzzy neutrosophic number weighted averaging (TFNNWA) and triangular fuzzy neutrosophic number weighted geometric (TFNNWG) results for each alternative through the accuracy function of triangular fuzzy neutrosophic numbers (TFNNs)
We proposed the TFNNs-MABAC method based on some fundamental theories in TFNNs and the traditional MABAC model for MCGDM
Summary
The MABAC (multi-attributive border approximation area comparison) approach has been widely utilized to investigate multiple-criteria group decision-making (MCGDM) problems and has been extensively applied in various case studies by many fabulous researchers. Axioms 2020, 9, 104 a worthy instrument for MCGDM [17,18] problems This theory can capture objects into members of the set through a degree of membership that can be presented by arbitrary values within the real-number interval from 0 to 1. Many recent MCGDM problems have actively involved a group of decision-makers (DMs) in the process of decision-making to minimize the subjectivity of the DMs’ judgment They tend to have their own different opinions to assess alternatives and criteria and usually give their evaluation opinions using the linguistic variables term. Mishra et al [42] utilized interval valued intuitionistic fuzzy sets (IVIFSs) to develop an extension of MABAC method for a programming language assessment.
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