Research Of Logical Foundation On Negative Information And Mathematics In The Field Of Information Processing

In chapter one of this paper, we proposed that negation relation in information should differentiate contradictory negation and opposite negation relations, and discovered a sort of character of some opposite concepts: one pair of opposite concepts are fuzzy concepts if and only if there is a medium concept between them. Five kinds of contradictory negation and opposite relations (CDC, CFC, ODC, OFC and ROM) in the distinct information and fuzzy information were, from the conceptual point of view , confirmed, and formalization definitions of them were discussed. Furthermore, we studied these different negation relations using the medium predicate logic MF and the infinite valued semantic modelФof MF, and obtained the conditions of processing these different negation relations. Meanwhile, flaws of current mathematics and logic theories were discussed from the view of representation and processing of these relations. In chapter two, To process fuzzy phenomenon existing widely in social life,one new method with measuring truth grade,having background of medium mathematics system,was proposed.After establishing standard pointer of the predicate,the relation between truths of the predicate and areas of numerical value was described.The individual truth grade function, and on which the method of representation of one-variate predicate that is based,were presented.Additional,theλtruth?grade?cut set and the product of number with the predicate were advanced to give medium decomposition theorem about one-variate fuzzy predicate.Hence the quantitative relation between one-variate fuzzy predicate and distinct predicate was constructed.In chapter three, we extended decomposition theorem to general decomposition theorem, and gave the definition of cut segment matrix and investigated some properties of it. At last, in chapter four , we obtained the tenth to thirteenth values and the corresponding trees for these values by way of one new method. Based on this, we further investigated and got the fourteenth to thirty-third values and the corresponding trees.