Fuzzy Measures and the Entropy of Fuzzy Partitions

Using an additive fuzzy measure a notion of the entropy of a finite fuzzy partition has been defined [D. Dumitrescu, On fuzzy partitions, in "Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca. 1983;" pp. 57-60; D. Dumitrescu and M. Barbu, Fuzzy entropy and processes, in "Itinerant Seminar on Functional Equations. Approximation and Convexity, Cluj-Napoca, 1985," pp. 71-74]. This notion contains as a particular case a well-known concept of entropy [M. A. Gil et al., Fuzzy Sets and Systems15 (1985), 65-78; H. Tanaka et al., Kybernetes5 (1976), 25-30; I. J. Taneja, Bivariate entropies of finite partitions of fuzzy sets, in "Preprints of Second IFSA Congress, Tokyo, 1987," Vol. 2, pp. 696-699]. The aim of this paper is to review some basic properties of the considered entropy.