Canonical triangular interval type-2 fuzzy set linguistic distribution assessment TODIM approach: A case study of FMEA for electric vehicles DC charging piles

Linguistic distribution assessment (LDA) plays a prominent role in describing the subjective uncertainties and objective distribution of decision-maker (DM) opinions. Although there have been several studies on LDA, few of these studies have paid attention to the different understandings of language semantics provided by DMs. To address the issue, type-2 (T2) fuzzy sets (T2FSs) are a well-known approach because T2FSs can accurately model the understanding of individuals with linguistic uncertainty. A trapezium (or trapezoidal) interval type-2 fuzzy set (TrIT2FS) is a common application of T2 fuzzy logic. Accordingly, this paper discusses a novel LDA called a canonical triangular interval type-2 fuzzy set (CTriIT2FS)-LDA in a T2 fuzzy environment. The CTriIT2FS-LDA combines a CTriIT2FS simplified from a TrIT2FS with LDA, which can simplify the computation while retain-ing their advantages. To facilitate the calculation of the CTriIT2FS-LDA, the basic operations of the CTriIT2FSs and the CTriIT2F-LDA, such as the defuzzied (crisp) function, distance measurement, and entropy measurement, are defined. Based on the TODIM approach, a CTriIT2F-LDA-TODIM is developed for FMEA for interval type-2 fuzzy environments. Furthermore, the proposed approach is applied in a practical case for FMEA for the elec-tric vehicle DC charging piles of the State Grid Corporation of China.