Constructing shadowed set based on game analysis of uncertainty and decision cost

Abstract

As a three-way approximation scheme to deal with fuzzy set, shadowed set approximately divides fuzzy objects with uncertainty into elevated, reduced, and shadow areas by a pair of decision thresholds α,β, thus effectively reducing the uncertainty of information. However, the current construction of shadowed set is all based on a single principle, lacking the comprehensive consideration of multiple principles, and these construction principles focus on the rationality of semantic interpretation of model construction process and threshold determination, and lack of consideration of the validity of partition results. To resolve these issues, this paper proposes a new shadowed set model through the game analysis between uncertainty and decision cost (UC-GTSS). First, Combining shadowed set construction with game theory, UC-GTSS is proposed based on game competition mechanism. Through the game analysis of uncertainty and decision cost, the optimal α,β is found, and a game payoff fusion algorithm based on Topsis is proposed. Second, the definition of UC-GTSS model expression, game player, strategy, payoff function, equilibrium analysis, optimization α,β determination and the influence of model parameters are analyzed and discussed. Third, the UC-GTSS model is extended and discussed based on the validity of the partition results, such as the game between approximate classification accuracy and coverage, the game between the Gini coefficient of the partition areas. Finally, through the analysis of algorithms, instances and data experiments, the construction process, validity, and rationality of UC-GTSS and its extended model are demonstrated.