POSSIBILITY, PROBABILITY AND RELATIVE INFORMATION - A UNIFIED APPROACH VIA GEOMETRIC-PROGRAMMING

The theory of possibility (Zadeh, Sugeno) and the theory of relative information (Jumarie) both aim to deal with the meaning of information, but their mathematical frameworks are quite different. In the first approach, possibility is described either by fuzziness (Zadeh) or by generalized measures (Sugeno), and in the second, possibility is obtained as the result of observing probability via an observation process with informational invariance. Shows that a combination of (classical) information theory with generalized maximum likelihood via geometric programming exhibits a link between relative information, fuzziness and possibility. Some consequences are outlined.