A fuzzy set theoretic approach to weak known-signal detection

Abstract In this paper locally optimum detection of known signals is considered when the observations provide us with fuzzy information, and a useful expression of the test statistic of the locally optimum fuzzy detector for known signals is obtained. The structure of the locally optimum fuzzy detector is obtained and compared to that of the classical (crisp) locally optimum detector. Several properties of the locally optimum fuzzy nonlinearity, which constitutes the locally optimum fuzzy detector, are also described.

[1]  Saleem A. Kassam,et al.  Optimum Quantization for Signal Detection , 1977, IEEE Trans. Commun..

[2]  Rick S. Blum,et al.  Asymptotically optimum quantization with time invariant breakpoints for signal detection , 1991, IEEE Trans. Inf. Theory.

[3]  John B. Thomas,et al.  Detectors for discrete-time signals in non-Gaussian noise , 1972, IEEE Trans. Inf. Theory.

[4]  Iickho Song,et al.  Locally optimum detection of signals in a generalized observation model: The random signal case , 1990, IEEE Trans. Inf. Theory.

[5]  M. Gorzałczany,et al.  Decision making in signal transmission problems with interval-valued fuzzy sets , 1987 .

[6]  Peter No,et al.  Digital Coding of Waveforms , 1986 .

[7]  Peter F. Swaszek,et al.  Locally optimal detection in multivariate non-Gaussian noise , 1984, IEEE Trans. Inf. Theory.

[8]  Jihoon Kim,et al.  A suboptimum quantization-detection scheme using input amplitude compression , 1990, Signal Process..

[9]  M. Gorzałczany.  A method for inference in approximate reasoning based on interval-valued fuzzy sets , 1987 .

[10]  M. Reha Civanlar,et al.  Digital signal restoration using fuzzy sets , 1986, IEEE Trans. Acoust. Speech Signal Process..

[11]  Iickho Song,et al.  A fuzzy decision problem based on the generalized Neyman-Pearson criterion , 1992 .

[12]  María Angeles Gil,et al.  The likelihood ratio test for goodness of fit with fuzzy experimental observations , 1989, IEEE Trans. Syst. Man Cybern..

[13]  L. Zadeh.  Probability measures of Fuzzy events , 1968 .

[14]  Pedro Gil,et al.  On the use of Zadeh's probabilistic definition for testing statistical hypotheses from fuzzy information , 1986 .