On the relationship between transition and inverse opposites in MMTD

Abstract

Measure of medium truth degree MMTD is a new numerical quantification approach processing vague phenomenon, which has found effective application in some fields. MMTD is based on medium logics ML whose major philosophical background is the opposite that limits the application area of MMTD. To counter de-emphasizing `the greatest difference' between the two sites of inverse opposite concept, the idea of weakening polarization and strengthening transition is presented in this paper. After introducing ML and MMTD in brief, the concepts of transition are described with mathematical and logical methods. Some concepts and lemmas that are the non-increment of Minkovski distance, neighbor-point, least truth formula and least medium formula are given to discuss the relations between inverse opposites and transition. Then, predicate mapping P: {T, F}2→{T, M, F} is constructed, and the sufficient condition for converting transition to opposing polarization is established. The theorem and corollaries relate to P show all cases existed transition may be process as inverse opposites, therefore MMTD can find application in wider fields.