Signal-to-Noise Ratios Using Fuzzy Numbers

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 a. From different values of a, the membership function of the SNR was approximated. Three different types of SNRs are discussed: the higher-the-better, the lower-the-better, and the nominal-the-best. Since the SNR is expressed by a membership function rather than by a crisp value, more information is provided for making decisions. The methodology developed in this paper can also be applied to calculate the SNR with imprecise linguistic terms.