Interval-Valued and Set-Valued Extensions of Discrete Fuzzy Logics, Belnap Logic, and Color Optical Computing

Abstract

It has been recently shown that in some applications, e.g., in ship navigation near a harbor, it is convenient to use combinations of basic colors – red, green, and blue – to represent different fuzzy degrees. In this paper, we provide a natural explanation for the efficiency of this empirical fact: namely, we show: (1) that it is reasonable to consider discrete fuzzy logics, (2) that it is reasonable to consider their interval-valued and set-valued extensions, and (3) that a set-valued extension of the 3-valued logic is naturally equivalent to the use of color combinations.