Detecting fixed amplitude signals in a fuzzy Gaussian environment

In practical signal detection scenarios, parameters of a random process are often uncertain. In this paper, we model such uncertainties as fuzzy parameters of a stationary random process. A fuzzy Neyman-Pearson hypothesis test concept which accepts any number of fuzzy parameters is presented. A suitable decision rule is developed by applying theory for ordering fuzzy numbers, and stated in terms of a fuzzy threshold. A defuzzifying threshold is then applied to produce a crisp decision rule. The concepts developed here are applied to Neyman-Pearson detection of a fuzzy fixed amplitude signal in Gaussian noise with fuzzy variance.