"Uniqueness of Reconstruction for Yager's t-Norm Combination of Probabi" by Nitaya Buntao and Vladik Kreinovich

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Departmental Technical Reports (CS)

Uniqueness of Reconstruction for Yager's t-Norm Combination of Probabilistic and Possibilistic Knowledge

Nitaya Buntao
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

5-2011

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Technical Report: UTEP-CS-11-18

Published in International Journal of Intelligent Systems, 2012, Vol. 27, No. 1, pp. 16-22.

Abstract

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.

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