Fitting Aggregation Operators
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This paper treats the problem of fitting aggregation operators to empirical data. Specifically, we are interested in modelling of the conjunction in human language. To our knowledge, the first attempt to see how humans “interpret” the conjunction for graded properties is due to the paper . In that case, simply the minimum t-norm came out. Our results are different because our approach to the resolution is different. We have experimentally rated simple statements and their conjunctions. Then we have tried, on the basis of measured data, to find a suitable function, which corresponds to human conjunction. First, we discuss methods applicable to associative operators, t-norms. Next, we propose an algorithm for approximation of the t-norm’s generator based on the weighting method and Lawson-Hanson’s algorithm. Suitable modifications of the algorithm can generalize our solutions to aggregation operators. In this way we get new results for generated means which are well-known representatives of aggregation operators. Empirically measured data suggest that people do not understand conjunction necessarily as a commutative operation. Finally, we investigate the modelling of the conjunction via generated Choquet integral.
KeywordsAggregation Operators Choquet Integral Understand Conjunction Commutative Operation Restricted Optimization Problem
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