Abstract:

In the fuzzy logic system L* with valuation lattice ［0,1］, based on conditional probability and using the randomization method of valuation set, the concept of conditional randomized truth degree of formulas is introduced. The MP rule and HS rule of conditional randomized truth degrees are proved. The concepts of conditional randomized similarity and conditional pseudometric between formulas are presented and conditional randomized logic metric space is built. Several properties of conditional pseudometric are deduced and it is proved that the logical operations are continuous on conditional randomized logic metric space. Then the theory of approximate reasoning under certain information is studied.

Key words: conditional randomized truth degree; conditional randomized similarity; conditional randomized logic metric space; approximate reasoning