Abstract
Multi-attribute group decision-making (MAGDM) is widely applied to various areas for solving real-life problems, including technology selection, credit assessment, strategic planning evaluation, supplier selection, etc. To describe the complex and imprecise cognition, it is more convenient to provide the decision-making information in linguistic terms rather than concrete numerical values. Thus, several linguistic models, such as the fuzzy linguistic approach (FLA), hesitant fuzzy linguistic term sets (HFLTSs), hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), and probabilistic linguistic term sets (PLTS) have been proposed successively. Due to the flexibility and comprehensiveness of PLTS, it has aroused growing concern. However, it also has a big limitation of requiring the membership degree to be 1 by default, and it does not consider the degree of non-membership and hesitancy of a linguistic variable. Therefore, the probabilistic hesitant intuitionistic fuzzy linguistic term sets (PHIFLTSs) have been presented to extend the PLTS by combining the membership and non-membership in symmetry to depict the evaluation of the experts. To overcome the existing shortcomings and enrich the methodology framework of PHIFLTSs, some novel operational laws are defined to extend the applicability and methodology of the PHIFLTSs in MAGDM. Furthermore, the distance and correlation measures for the PHIFLTSs are improved to make up the shortage of the current distance measures. In addition, the unbalanced linguistic terms are taken into account to represent the cognitive complex information of experts. At last, a MAGDM model based on the multiplicative multi-objective optimization by ratio analysis (MULTIMOORA) approach with the use of the developed novel operational laws and correlation measures is presented, which results in more accuracy and effectiveness. A real-word application example is presented to demonstrate the working of the proposed methodology. Moreover, a thorough comparison is done with related existing works in order to show the validity of this methodology.
Highlights
Multi-attribute group decision-making (MAGDM) is usually described as the process of selecting the optimal option that has the highest degree of satisfaction from a series of finite alternatives, which are evaluated by multiple experts over multiple attributes
The method in [27] does not consider the situations of unbalanced linguistic terms on the PHIFLTSs environment; this paper selects the second type of linguistic scale function for all attributes to deal with the semantics of unbalanced LTSs; Table 10 shows the difference of the ranking orders between the work in [27] and this paper, which is due to the effect of the innovation in the basic operational laws, the unbalance LTSs, the distance measure and the MULTIMOORA approach proposed in this paper
We proposed a new MAGDM model based on the MULTIMOORA approach under the PHIFLTSs environment, which has the following superiorities: (1)
Summary
Multi-attribute group decision-making (MAGDM) is usually described as the process of selecting the optimal option that has the highest degree of satisfaction from a series of finite alternatives, which are evaluated by multiple experts over multiple attributes. To overcome the above-stated limitations and enrich the theories and methods of the PHIFLTSs, this paper focuses on the following four main aspects: This paper proposes some novel operational laws for the probabilistic hesitant intuitionistic fuzzy linguistic term sets to enrich the computation between PHIFLTSs and to improve the applicability and methodology in multi-attribute group decision-making models. This paper presents a MAGDM model based on the MULTIMOORA approach with the use of the developed novel operational laws and correlation measures Based on these four innovative strands of research, the following main goals of this paper are two-fold: (1) with the use of the proposed novel operational laws, distance, and correlation measure, and the unbalanced linguistic terms PHIFLTSs, to provide new theories and methods for the PHIFLTSs to overcome the existing defects; (2) with the use of the MULTIMOORA ranking approach, to propose a new multi-attribute group decision-making method for the PHIFLTSs to obtain superiority concerning time consumption, robustness, simplicity, and effectiveness at the decision making level.
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