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Statistical test of fuzzy hypotheses using linguistic variable

Hypothesis testing of population parameters plays an important role in statistical analysis. This work extends this topic to the fuzzy environment for wider application. Developing a method of testing fuzzy hypotheses using linguistic variables is of priority concern. The method is based on Zadeh’s extension principle: the fuzzy population mean in the null hypothesis is converted to fuzzy numbers using conversion scales proposed by Chen and Hwang(1992). The intersection of two membership functions yields a matched ratio, which can specify the degree of acceptability of the null hypothesis; thus, the deficiency due to the binary decision of the classical method can be avoided. The proposed test yields two important conclusions. Using linguistic variables, candidates with the same scores can be differentiated by MR. Moreover, differences between intervals of successive linguistic variables can be overcome. The method proposed here better reflects the real situation than conventional methods.