Ten years ago, the author set up a symmetrical model of color vision (Lu, 1989), in which the color-visual mechanism is treated as a fuzzy 3-8 decoder that produces three pairs of opponent color signals (red-cyan, green-magenta, and blue-yellow) instead of two pairs (red-green and blue-yellow) as in a popular model of color vision. It was thought that the mechanism with the three pairs of color signals had higher discrimination and hence could convey more information. To get support from information theory, the author tried to measure sensory information by Shannon¡¯s information measure (Shannon,1949). Yet, the effort yielded no verification. It was also recognized that there were similar problems with semantic information, such as information conveyed by weather forecasts. The problems are three in the main: 1)Similarity between observed or described objects, such as colors, is important to information. Yet, it is difficult to handle the similarity with Shannon¡¯s information theory. 2)On common sense, information conveyed by a lie or wrong prediction should be presented as being negative. However, Shannon¡¯s information measure is always positive. For example, a meteorological observatory always produces correct forecasts while another observatory always provides opposite forecasts. Obviously, the former is better. However, Shannon¡¯s information measure gives them the same evaluation. The reason is that Shannon¡¯s theory does not consider implications or semantic aspects of messages. 3)Information on a single event, such as the prediction ¡°Tomorrow will be very rainy¡±, can not be measured by Shannon¡¯s information measure.
To develop Shannon's information theory, researchers have proposed various generalized information theories or measures (Weaver,1949; Bar-Hillel and Carnap,1952; Brillouin, 1962; De Luca and Termini,1972; Gottinger, 1975; Higashi and Klir,1982; Jumarie, 1987) However, the problems listed are not adequately treated.