Method to Construct Elementary Dependent Function Based on Weights of Characteristics

Extension theory is the theoretical foundation of artificial intelligence and widely used in many fields such as optimal estimation and predictive control, manufacturing and design science. Dependent function is the core of extension set. According to the fact that decision-makers have different preferences for characteristics of basic-element, we defined the weighted distance between the point and the field within the multi-dimensional space, and constructed the location value and the elementary dependent function that has one variable and some dimensions based on the finite nested field. Some properties are also discussed. The proposed functions allow extension theory with a broader scope.