A new approach for heterogeneous linguistic failure mode and effect analysis with incomplete weight information

Failure mode and effects analysis (FMEA) is an important technique in safety and reliability analysis, which has been widely used to identify and eliminate known or potential failure. In the process of evaluating failure modes (FMs), experts usually adopt different types of linguistic information to reflect their judgments, and the weights of experts or criteria are often incompletely known. This study aims to develop a novel approach to solve heterogeneous linguistic FMEA problem, in which the ratings of FMs are described by different types of linguistic information, and the information about the importance of experts and criteria is incomplete. Firstly, we propose a linguistic distribution assessment Shapley Choquet ordered averaging (LDASCOA) operator, and discuss some properties of the operator, such as idempotency, monotonicity, boundary and commutativity. Secondly, we present a new idea to convert different types of linguistic information to linguistic distribution assessments (LDAs). Thirdly, to obtain collective linguistic distribution assessment decision matrix and necessary weights, we construct a model to determine the optimal fuzzy measures on expert set with respect to each criterion considering the interactions among elements in the expert set. Fourthly, a new approach to determine the priority of FMs is proposed by defining linguistic distribution assessment ideal variate (LDAIV) and linguistic distribution assessment nadir variate (LDANV), as well as calculating the relative correlation coefficient of each failure. Finally, an illustrative example is given to demonstrate the calculation process of the developed approach, and the advantages are verified by comparing the evaluation result of the developed approach with that of existing methods.