1.       INTRODUCTION

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.

  To resolve the above problems, first, with the help of the concepts of fuzzy set and similarity relation, the author developed an information measure ( Equation (35) ) that can be used to measure semantic information when language is always correctly used . Later, the author  found that three types of probabilities: objective, subjective, and logical probabilities (Section 2.1) could be put into a mutual information formula at the same time so that the measure of information conveyed by a lie or a wrong prediction may be negative.  Sensory information could also be reasonably measured with the same formula. Measurement of  the information of single event  becomes tenable  (Lu, 1991).  Further, the author  found the coding meanings of the generalized entropy and generalized mutual information (Lu, 1994) and the meaning of optimizing communication. The new generalized information theory is seemingly a more natural and full extension of Shannon's information theory.

  The new information theory is compatible with  research results, such as by Weaver (1949), Bar-Hillel and Carnap (1952), Popper (1968),  Kullback (1959),  Theil (1967),  Aczel and Forte (1986), Zadeh (1965,1986) and Wang (1987).