Fuzzy measures for fuzzy signal-to-noise ratios

摘要

Signal-to-noise ratios (SNRs) are widely applicable in quality engineering for improving product quality. In real-world applications, the observations are sometimes described in linguistic terms, or are only approximately known, rather than equated with randomness. To deal with imprecise data, the notion of fuzziness was introduced. This paper develops a procedure to calculate the SNR with fuzzy observations. The idea is based on the extension principle. A pair of mathematical programs was formulated to calculate the lower and upper bounds of the fuzzy SNR at possibility level alpha. From different values of alpha, the membership function of the SNR was approximated. Three different types of SNRs are discussed: "higher the better," "lower the better," and "nominal the best." Because the SNR is expressed by a membership function rather than by a crisp value, more information is provided for making decisions.