Best-Worst Multi-Attribute Decision Making Method Based on New Possibility Degree With Probabilistic Linguistic Information

Abstract

A Best-Worst multi-attribute decision-making (MADM) method based on a new possibility degree is put forward to deal with MADM problems with probabilistic linguistic evaluation information. Firstly, a new possibility degree for pairwise comparisons with probabilistic linguistic term sets (PLTSs) is defined. Secondly, starting from the new possibility degree, two different ideas of Best-Worst Method (BWM) for getting the optimal attribute weights are put forward. Thirdly, combining the new probabilistic linguistic possibility degree and the two BWM ideas, two optimization models for determining the attribute weights are constructed, respectively. Moreover, consistency ratios for two new BWM models are proposed to check the reliability of the pairwise comparisons. Meanwhile, the state of optimal solutions for the new BWM models is analyzed. Finally, a new Best-Worst MADM method under probabilistic linguistic information is presented, which is applied to a practical example of selecting optimal green enterprises. Some comparative analyses are given to show the rationality and validity of the proposed method.INDEX TERMS Multi-attribute decision-making (MADM), probabilistic linguistic term sets (PLTSs), possibility degree, attribute weight, Best-Worst Method (BWM), green evaluation.

Interval Type-2 Trapezoidal Fuzzy Decision- Making Method With Consistency-Improving Algorithm and DEA Model

“…4Compared with FMCGDM method investigated by Kundu et al [57], IT2TFDM method and FMCGDM method in [57] generate the different decision-making results. In fact, based on the original IT2TrFPR x is more important than 3 x , i.e., 23 xx . Thus, the proposed IT2TFDM method can output more accurate result.…”

“…It is known that one of the necessary steps is to check the quality of preference evaluation information, in which consistency and its measurement play significant roles [23][24][25][26][27]. With the interesting consistency properties, Herrera-Viedma et al [28] designed an approach to construct consistent FPRs.…”

Risk-Based Multi-Attribute Decision-Making for Normal Cloud Model Considering Pre-Evaluation Information

“…In a MADM problem, attribute weight is crucial to aggregate the information of decision-makings, which should not only reflect the DM's subjective judgments but also adequately represent the information involved in the decision-making. In terms of determining the incomplete attribute weights, various methods have been developed, such as trapezoidal fuzzy neutrosophic entropy-based [37] and similarity degrees-based [38] weight determination approaches for completely unknown attribute weights, relative closenessbased [39] and group satisfaction-based [40] linear programming models, Best-Worst Method [2], and maximum deviation method [36] for incompletely known attribute weights.…”

“…Here, we only discuss decision-makings with incompletely known attribute weights. Compared with other methods [2], [39], [40], an optimization model with the maximum deviation [36], aiming at sorting the alternatives by the weight of each attribute, is more effective for sorting alternatives with certain distinction degree. The greater contribution of one attribute on the summation of weighted values' deviations of the alternatives indicates the greater importance of the attribute, and thus a higher weight value is assigned, and vice versa [22].…”

“…M ULTI-ATTRIBUTE decision making (MADM) is a process of ranking alternatives or selecting the best alternative from several alternatives with respect to a set of attributes [1]. In decision-making practice, decision-makers (DMs) prefer to use linguistic terms to express their preferences due to the fact that this expression is not only intuitive and easy to express but can well align human source [2]- [4]. However, most of existing methods based on linguistic terms rely on the conversion between linguistic information and exact numbers, and thus ignore the randomness and fuzziness which are the two key aspects of various uncertainties involved in the linguistic expression [5].…”