Abstract
In this paper, we analyze the reliability of fuzzy system (particularly, series and parallel system) with independent and non-identically distributed components using the new operations of TA [F. Abbasi, T. Allahviranloo and S. Abbasbandy, A new attitude coupled with fuzzy thinking to fuzzy rings and fields, Journal of Intelligent and Fuzzy Systems 29 (2015) 851–861.] due to the smaller results support, easier calculations and special properties than operations based on the extension principle (in the domain of the membership function) and the interval arithmetic (in the domain of the [Formula: see text]-cuts). we propose the new fuzzy arithmetic operations based on transmission average(TA) on LR type flat fuzzy numbers. In the proposed formulae, LR type flat fuzzy numbers are not restricted to have the same [Formula: see text] and [Formula: see text] shape functions. This allows arithmetic operator for arithmetic involving LR type flat fuzzy numbers of different and general shape. Finally, an imprecise failure to start of an automobile is considered in fuzzy environment. The reliability of components of the proposed model is considered as LR type flat fuzzy numbers.
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