An efficient hybrid direct-vague fuzzy moves system using fuzzy-rules-based precise rules

Abstract

In this paper, a game transformation is proposed to enable a player to get a globally reasonable goal which is not only as advantageous to his own side as possible but also as disadvantageous to his opponent as possible. The Theory of Fuzzy Moves (TFM), based on the Theory of Moves (TOM) and game theory, is suitable for making a player reach a relatively good fuzzy outcome. Through analysis, we have found that only some of the fuzzy moves' rules are vague (i.e. fuzzy), and the others are direct (i.e. precise). We have found that (1) for the direct rules, the hybrid system is fault-tolerant and stable; (2) for the vague rules, the hybrid system is sensitive for the relevant players' fuzzy payoffs and globally strategic goals since there exist sensitive points or curves. Through the mathematical simplification of the vague rules' inference, we can finally construct the hybrid direct-vague fuzzy moves system by directly using the simple mathematical mapping functions without using the conventional fuzzification, fuzzy inference, and defuzzification. Importantly, the hybrid direct-vague fuzzy moves system with the simple mapping functions can run much more quickly than the fuzzy moves system with the complex fuzzy mapping functions. Finally, some typical examples of globally optimal fuzzy moves have shown that the hybrid direct-vague fuzzy moves system is stable and fault-tolerant enough to deal with the fuzzy moves in dynamic and uncertain situations.