Yager ’ s Combination of Probabilistic and Possibilistic Knowledge : Beyond t-Norms

Often, about the same real-life system, we have both measurement-related probabilistic information expressed by a probability measure P (S) and expert-related possibilistic information expressed by a possibility measure M(S). To get the most adequate idea about the system, we must combine these two pieces of information. For this combination, R. Yager – borrowing an idea from fuzzy logic – proposed to use a t-norm f&(a, b) such as the product f&(a, b) = a ·b, i.e., to consider a set function f(S) = f&(P (S),M(S)). A natural question is: can we uniquely reconstruct the two parts of knowledge from this function f(S)? In our previous paper, we showed that such a unique reconstruction is possible for strictly Archimedean t-norms; in this paper, we extend this result to a more general class of combination operations. c ©2013 World Academic Press, UK. All rights reserved.