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The measurement of performance of a process considering both the location and the dispersion of information about the process is referred to as the process capacity indices (PCIs) of interest, C pk . This information is presented by the mean and standard deviation of the producing process. Linguistic variables are used to express the evaluation of the quality of a product. Consequently, C pk is defined with fuzzy numbers. Lee [Eur. J. Oper. Res. 129(2001) 683-688] constructed the definition of the C pk index estimation presented by fuzzy numbers and approximated its membership function using the "min"-norm based Zadeh's extension principle of fuzzy sets. However, Lee's result was shown to be invalid by Hong [Eur. J. Oper. Res. 158(2004) 529-532]. It is well known that T w (the weakest t-norm)-based addition and multiplication preserve the shape of L-R fuzzy numbers. In this paper, we allow that the fuzzy numbers are of L-R type. The object of the present study is to propose a new method to calculate the C pk index under T w -based fuzzy arithmetic operations.

CpkIndex Estimation under Tw(the weakest t-norm)-based Fuzzy Arithmetic Operations

C_pkIndex Estimation under T_w(the weakest t-norm)-based Fuzzy Arithmetic Operations