Abstract
Decisions strongly rely on information, so the information must be reliable, yet most of the real-world information is imprecise and uncertain. The reliability of the information about decision analysis should be measured. Z-number, which incorporates a restraint of evaluation on investigated objects and the corresponding degree of confidence, is considered as a powerful tool to characterize this information. In this paper, we develop a novel approach based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method and the power aggregation operators for solving the multiple criteria group decision making (MCGDM) problem where the weight information for decision makers (DMs) and criteria is incomplete. In the MCGDM, the evaluation information made by DMs is represented in the form of linguistic terms and the following calculation is performed using Z-numbers. First, we establish an optimization model based on similarity measure to determine the weights of DMs and a linear programming model with partial weight information provided by DMs based on distance measure to determine the weights of criteria. Subsequently, decision matrices from all the DMs are aggregated into a comprehensive evaluation matrix utilizing the proposed ZWAPA operator or ZWGPA operator. Then, those considered alternatives are ranked in accordance with TOPSIS idea and the feature of Z-evaluation. Finally, a practical example about supplier selection is given to demonstrate the detailed implementation process of the proposed approach, and the feasibility and validity of the approach are verified by comparisons with some existing approaches.
Highlights
We develop a novel approach based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method and the power aggregation operators for solving the multiple criteria group decision making (MCGDM) problem where the weight information for decision makers (DMs) and criteria is incomplete
Since the fuzzy set theory was coined by Zadeh [1], it has been widely used in many application fields as a tool that is capable of capturing the certainty of information and depicting people’s subjective thinking, especially decisionmaking problems with uncertain, imprecise even incomplete information
Kang and his team focused on solving supplier selection problem by utilizing the methodology presented in that paper including two parts: one changed a Z-number to a traditional fuzzy number according to the fuzzy expectation; the other worked out the optimal priority weight for supplier selection with the improved genetic algorithm and the extended fuzzy AHP under Znumber environment in [25]
Summary
Since the fuzzy set theory was coined by Zadeh [1], it has been widely used in many application fields as a tool that is capable of capturing the certainty of information and depicting people’s subjective thinking, especially decisionmaking problems with uncertain, imprecise even incomplete information. Authors in [24] employed the same way to transform Z-numbers to fuzzy numbers before ordering Z-numbers, the whole course that rank Z-numbers was analogous to [23], and the research made lots of analysis and discussion on different Z-number combinations to investigate the effectiveness of the proposed ranking approach Kang and his team focused on solving supplier selection problem by utilizing the methodology presented in that paper including two parts: one changed a Z-number to a traditional fuzzy number according to the fuzzy expectation; the other worked out the optimal priority weight for supplier selection with the improved genetic algorithm and the extended fuzzy AHP under Znumber environment in [25].
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