| Summary: | 碩士 === 中原大學 === 數學系 === 88 === In the reliability theory, studies always focus on the states of system and its components under nonfuzzy(crisp) situation (see [1, 2, 7, 9]). Since Zadeh proposed the idea of fuzzy sets in 1965, the reliability theory in fuzzy environment has been studied (see [5, 6, 8, 10]).
In this thesis we explore fuzzy-state structure functions and its possibility reliability by the Zadeh`s extension principle with triangular fuzzy numbers. First we review definitions and properties of coherent systems and its reliability functions. Then we propose coherent systems with triangular fuzzy numbers and their series and parallel fuzzy reliability systems. Finally we give some definitions and properties of possibility reliability functions with fuzzy states. Furthermore, we have possibility reliability function of series and parallel fuzzy systems.
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