Conditioning in possibility theory with strict order norms

✍ Scribed by Bernard De Baets; Elena Tsiporkova; Radko Mesiar

• Book ID: 104292572
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 615 KB
• Volume: 106
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(97)00245-5

✦ Synopsis

The general order-norm-based approach of defining the conditional possibility H(AIB ) as the greatest solution of the equation °o°J(x, H(B)) = H(A fq B), with oj-a t-norm, and of defining the conditional necessity N(A I B) as the smallest solution of the equation 6a(x, N(co B))= N(A U co B), with ~ a t-conorm, is carefully studied. In particular, it is investigated under which conditions the conditional possibilities (resp. necessities) again establish a possibility (resp. necessity) measure. Due to the new characterization of strict t-norms (resp. t-conorms) presented in this paper, it is shown that, in general, only a strict t-norm (resp. t-conorm) can be used, or, in other words, a transformation of the algebraic product (resp. probabilistic sum) by means of an order preserving permutation of the unit interval. This indicates that the algebraic product not only has a probabilistic, but also a surprising possibilistic nature. (~) 1999 Elsevier Science B.V. All rights reserved.