The Distribution of Quasi-truth Degrees in 4-valued Lukasiewicz Logic System (II)

For the approximate reasoning method based on truth degree extended to the case of non-uniform assignment, we define assignment weight vector in discrete probability space and quasi-truth degree of formula in Lukasiewicz 4-valued logic system which is popularized from truth degree of formula. We also prove that the set of quasi-truth degree of all formulas in the range of [0, 1] is dense when assignment weight vector is (a/8, b/8, c/8, d/8) and (1/15, 2/15, 4/15, 8/15). Finally, we give three types of approximate reasoning models, so provide a possible structure of approximate reasoning theory.