Abstract
Usually, trapezoid truth value (TTV) is investigated in the one-dimensional truth value space V=[0,1]. This paper proposes another viewpoint about the logical operations of TTV. In 1993, T.Oda introduced the Fuzzy-set Concurrent Rating (FCR) method. The two-items type FCR method uses two independent rating scales for a question. Several equations have been proposed to measure the degree of contradiction or irrelevancy in the paired responses. In order to define the indexes for utilizing the paired data obtained by using the FCR method, the two-dimensional Hyper Logic Space (HLS) model is developed. The new model of TTV is derived from the study of the HLS model. The HLS is a kind of extended fuzzy logic. It treats the Truthfulness (T) and the Falseness (F) of the proposition independently. In 1990, Mukaidono and Kikuchi independently treated T and F in their Between Fuzzy Logic (BFL) model. The difference between the HLS and the BFL is, only the definitions of each negation operations. The HLS satisfies the Kleene's law while the BFL does not. In this paper, the outline of the FCR method, the BFL model and the HLS model are also introduced for the understanding of the new TTV model.
