Fuzzy rule-based approach with z-numbers in solving group multi-attribute decision making problems

Multi-Attribute Decision Making (MADM) process is the most well-known branch of decision making and it is one of the most important tasks that have received a lot of attentions in many areas. In solving MADM issues, the parameters of decision making are often faced problems, such as imprecise, vague, uncertainty or incomplete information which lead to inaccurate decision-making. To cope up with these problems, the researchers apply fuzzy set theory as the best-developed approach. Among different fuzzy methods, fuzzy rule- based system (FRBS) due to its flexibility, simplicity, and experts' knowledge modeling is an adequate technique to solving MADM problems. The main objective of this research is to apply experts' opinions by Z-numbers in MADM issues as improvement in ranking performance in decision making process. Based on extensive literature review on MADM issues using FRBS and Z-numbers, two main problems are addressed in this work. The first problem is inaccurate ranking results drew from the process of aggregating experts' opinions before converting them into one opinion due to data losses, and the second problem is regarding inadequate information in the experts' opinion, which lead to some degree of decision uncertainties. Indeed, in FRBS research to ranking, the reliability level (Z-numbers) in experts' opinions within the decision-making process has not been taken into account. Whereas, the Z-numbers play a key role in decision-making process to reach more precise decisions affecting the final ranking results. The methods which have been applied and proposed in this study were aimed to increase the accuracy of decision making in solving MADM problems with easing computational process. In the FRBS-TOPSIS method, the initial data preparation is conducted and later FRBS are applied to rank the experts' opinions individually to obtain the final score of alternatives. Finally, aggregation of experts' opinions is performed by applying TOPSIS conventional technique. The proposed method was compared using the published data from another study by obtaining the final score of each alternative for all experts individually. In the Z-FRBS approach, by considering experts' opinion in form of Z-numbers to deal with inadequate information and modeling experts' knowledge through FRBS, the process of making decision is performed without using conventional techniques which resulted in a more accurate solving MADM problems. The effectiveness and validity of the main method is approved with an illustrative example, sensitivity analysis, and comparison with three others validated method. In one of the comparisons, the findings showed among 25 alternatives, the Spearman Rho Coefficient (SRC) amount as decision making accuracy in the proposed method increased from 0.850 to 0.862. Indeed, based on the achieved results, with using the data from the other three methods, it is proven that the Z-FRBS method has made more efficient and accurate decisions than the compared methods in solving MADM problems. The advantages of the proposed methods are improvement in ranking performance by means of FRBS, easing computational process, and flexibility.

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