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Design experts need to fully understand the failure risk of a product to improve its quality and reliability. However, design experts have different understandings of and concepts in the risk evaluation process, which will lead to cognitive asymmetry in the product’s redesign. This phenomenon of cognitive asymmetry prevents experts from improving the reliability of a product, increasing the risk of product development failure. Traditionally, failure mode and effects analysis (FMEA) has been widely used to identify the failure risk in redesigning products and a system’s process. The risk priority number (RPN), which is determined by the risk factors (RF), namely, the occurrence (O), severity (S), and detection (D), is the index used to determine the priority ranking of the failure modes (FM). However, the uncertainty about the evaluation information for the RF and the coupling relationship within the FM have not been taken into account jointly. This paper presents an integrated approach for FMEA based on an interval-valued intuitionistic fuzzy set (IVIFS), a fuzzy information entropy, a non-linear programming model, and fuzzy PROMETHEE Ⅱ to solve the problem of cognitive asymmetry between experts in the risk evaluation process. The conclusions are as follows: Firstly, an IVIFS is used to present the experts’ evaluation information of the RF with uncertainty, and the fuzzy information entropy is utilized to obtain the weight of the experts to integrate the collective decision matrix. Secondly, a simplified non-linear programming model is utilized to obtain the weight of the RF to derive the weighted preference index of the FM. Subsequently, the coupling relationship within the FM is estimated by fuzzy PROMETHEE Ⅱ, where the net flow is given to estimate the priority ranking of the FM. Finally, the proposed approach is elaborated on using a real-world case of a liquid crystal display. Methods comparison and sensitivity analyses are conducted to demonstrate the validity and feasibility of the proposed approach.

Abstract. Large group decision making considering multiple attributes is imperative in many decision areas. The weights of the decision makers (DMs) is difficult to obtain for the large number of DMs. To cope with this issue, an integrated multiple-attributes large group decision making framework is proposed in this article. The fuzziness and hesitation of the linguistic decision variables are described by interval-valued intuitionistic fuzzy sets. The weights of the DMs are optimized by constructing a non-linear programming model, in which the original decision matrices are aggregated by using the interval-valued intuitionistic fuzzy weighted average operator. By solving the non-linear programming model with MATLAB ® , the weights of the DMs and the fuzzy comprehensive decision matrix are determined. Then the weights of the criteria are calculated based on the information entropy theory. At last, the TOPSIS framework is employed to establish the decision process. The divergence between interval-valued intuitionistic fuzzy numbers is calculated by interval-valued intuitionistic fuzzy cross entropy. A real-world case study is constructed to elaborate the feasibility and effectiveness of the proposed methodology.Keywords. Multiple-attributes large group decision making, optimization of weights of DMs, non-linear programming model, TOPSIS.

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