Pexider Functional Equations Their Fuzzy Analogs 529

may be interpreted as giving the amount of information I due to two independent events A and B with probabilities p and q, respectively. The functional equation (1.1) is one of Cauchy equations, and has been dealt with extensively (see Aczdl [1-2]). However, it is more often than not that we do not have the exact values of the probabilities p and q because not enough data is available or because p and q partially reflect the decision maker’s subjective opinion. As such, the decision maker will not exactly know the amount of information, I(-), generated by the independent event A, B and A gl B. Rather the decision maker has an amount of belief in each of the possible values of such quantities as I(.). The b.e,h.’e.f is a umber between 0 and 1. The idea of assigning beliefs to possible values has been introduced by Zadeh [12-13] under the name of Fuzzy Set Theory. For this reason I(-) is a "fuzzy" number representing the true information given for a specific probability p resulting from some imprecise measurement. This discussion, along with results obtained by Kreinovich and Decba [9] for another Cauchy equation m(x + U) re(x)+ re(U) (1.2)