Recursive Aggregation Of OWA Operators Based On Non-additive Measure With ?-? Rules And Its Integrator Design

As is known to all,Ordered Weighted Averaging(OWA)operators have been widely used in many fields,such as neural network,expert system,information fusion,fuzzy logic control,decision analysis,market supply survey etc.Therefore,there are many studies on the OWA operators.However,when using the recursive forms of OWA operators to make evaluation of the multi-attribute decision,the weight vector is not able to be measured independently and the attribute index is mostly related with each other,namely it may not satisfy countable additivity of the classic probability measures.On the other hand,due to the fuzziness and uncertainty of objective things and the compiexity of human brain thinking,in the process of decision-making and evaluation for the muiti-attribute decision making,decision makers are more willing to appiy the natural language to describe evaluation results.In this article,the fact that uncertain attribute indexes are related to each other is fused to the process of decision problem by non-additive measure with?-? rules,and the recursive aggregation theory and integrator design of the OWA operators based on fuzzy measures and natural language variables are systematically researched.First of all,taking the fuzziness and uncertainty of data into consideration,the OWA operators based on non-additive measure with ?-? rules are proposed,with the help of non-additive measures based on ?-? rules.In addition,the definitions of orness measure and andness measure are given.Then,by means of the OWA operators based on non-additive measure with ?-?rules,the recursive aggregation theory of the OWA operators based on non-additive measure with ?-? rules is presented,including left recursive form,right recursive form and a more general recursive form.Meanwhile the calculation methods and relevant properties are discussed.Finally,according to the OWA operators based on non-additive measure with?-? rules and recursive aggregation forms,integrator for classic date environment and uncertain date environment are designed with the help of genetic algorithm and the process of calculation are demonstrated by illustrative examples.