An integrated weighted multi-criteria decision making method using Z-number and its application in failure modes and effect analysis

Abstract

In this study, a new technique of $Z$-number preference ranking by similarity to the ideal solution is proposed for estimating risk in failure mode and effects analysis. The method ranks all identified faults using subjective and objective weights of risk factors. The subjective weights are calculated by the $Z$-number analytical hierarchy process, and the objective weights are calculated using the $Z$-number Shannon entropy measure. The combination of the subjective and objective weights of the risk factors is used to prioritize the failure modes. Firstly, the expert team is asked to rate the failure modes concerning the risk factors in linguistic terms consisting of two parts, possibility and reliability. The experts’ evaluation is then converted into $Z$-numbers, treating the two components as triangular fuzzy numbers. This method also incorporates the experts’ weights to aggregate the individual ratings by the average method. The method ranks the failure modes by calculating the distance of each failure mode from the $Z$-number positive ideal solution and $Z$-number negative ideal solution. The proposed methodology is illustrated through a flowchart. The strategy is further explained by applying it to a case study of the operation of a crane in a steel mill. Furthermore, the validity and effectiveness of the proposed technique are verified by presenting a comparative analysis of outcomes with the existing techniques. Finally, the sensitivity of the proposed study is also tested and explained by using various diagrams. In the proposed strategy, conversion of $Z$-numbers into fuzzy numbers is avoided, which means there is little loss of information as compared to the existing techniques, which, in turn, lead to optimal decisions.