Uniqueness of reconstruction for Yager's t‐norm combination of probabilistic and possibilistic knowledge

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 the product t‐norm; in this paper, we extend this result to a general class of t‐norms. © 2011 Wiley Periodicals, Inc.