Fuzzy system reliability analysis using T ω (the weakest t ‐norm) based arithmetic operations on L‐R type interval valued vague sets

Purpose – The purpose of this research is to develop a new approach for analyzing the fuzzy reliability of a series and parallel system. Also to introduce definition of L‐R type interval valued triangular vague set and certain T ω‐based arithmetic operations between two L‐R type interval valued triangular vague sets. Design/methodology/approach – In the proposed approach using a fault tree an interval valued vague fault tree is developed for the system in which the fuzzy reliability of each component of the system is represented by a L‐R type interval valued triangular vague set. Then with the help of a developed interval valued vague fault tree an algorithm is developed to analyze the fuzzy system reliability. Findings – For numerical verification of the proposed approach the fuzzy reliability of the basement flooding has been analyzed using the existing approaches and the proposed approach. Comparing the results of existing approaches and the proposed approach, it has been shown that the uncertainty about the reliability is minimized using the proposed approach and the results are exact. While using the existing approaches the results are approximate due to approximate product of triangular vague sets and interval valued triangular vague sets. Originality/value – The paper introduces a new approach for analyzing the fuzzy system reliability using T ω‐based arithmetic operations over L‐R type interval valued triangular vague sets.