Information Complexity and Fuzzy Control

1 Preamble Our article analyzes complexity of extracting information from fuzzy data. Such process can be properly viewed as contributing information, hence also alleviating uncertainty about the result of the process itself. Notion of information has been utilized frequently, both formally and informally. In the formal vein, Shannon entropy of probabilistic distributions is foremost, followed by host of less perfect variants. In the theory of possibility [3], based on fuzzy sets, there is U-uncertainty and several related functions [7, 16]. Both these concepts can be introduced axiomatically, using general rules of combining information [7]. Such rules deal with combining independent events, restricting ranges of possible outcomes, and other operations on distributions. Specialized to either probability or possibility theories, they become axioms, which can be shown sufficient to characterize the respective information measures uniquely [16]. Independent of those methods, a question of complexity of computing numerical answers to analytical queries has been studied [18, 19]. Here the