The Choquet Integral And Time Series Evaluations Based On Non-Additive Measures And Intuitionistic Fuzzy Language Variables

Weighted moving average is closely related to time series analysis.However,when using the weighted moving average to make forecasting of the future direction,the weight vector is not able to be measured independently,namely it may not satisfy countable additivity of the classic probability measures.Thus,Choquet integral based on non-additive measures has been applied to the decision analysis based on interaction.On the other hand,due to the fuzziness and uncertainty of objective things,in the process of evaluation and evaluation,decision makers are more willing to adopt the natural language to solve problems.In this article,the fact that uncertain attribute indexes are related to each other is fused to the process of evaluation by fuzzy measures,and the model of Choquet integral and time series evaluation based on non-additive measures and interval-valued intuitionistic fuzzy language variables is systematically discussed.First of all,taking the fuzziness and uncertainty of data into consideration,the calculation of moving weighted average for a series of fuzzy-numbers could be transformed into a Choquet integration,with the help of non-additive measures based on ?-? rules.And through the established convolution formula Choquet integral,the weighted moving averages for a series of fuzzy-numbers based on non-additive measures with ?-? rules are given and discussed,including the calculus methods and algorithms.Then,by means of interval intuitionistic uncertain linguistic variables,the Choquet integral operator(IVIULC)based on interval-valued intuitionistic uncertain linguistic variables is presented,and through the given algorithm,the fuzzy measures g? and parameter ? are calculated;according to fuzzy transformation,on the base of time series decompositon,the evaluation model of interval-valued intuitionistic fuzzy uncertain language is discussed by the Choquet integral operator(IVIULC)in the setting of the interval-valued intuitionistic uncertain language.Finally,the specific steps and example of time series trend evaluation and composition are also given.