Problems of Choquet Integral Practical Applications

Choquet integral with respect to fuzzy measure is a generalization of weighted arithmetic mean aggregation operator. It allows taking into account the phenomenon of dependence between criteria. Due to this it is possible to reflect the expert knowledge more accurately without making the model simplification which is the assumption of independence of the aggregation criteria. The problems of Choquet fuzzy integral applications and possible ways of overcoming them are discussed. Practical applications for this relatively new apparatus are reviewed

Learning weights in the generalized OWA operators

This paper discusses identification of parameters of generalized ordered weighted averaging (GOWA) operators from empirical data. Similarly to ordinary OWA operators, GOWA are characterized by a vector of weights, as well as the power to which the arguments are raised. We develop optimization techniques which allow one to fit such operators to the observed data. We also generalize these methods for functional defined GOWA and generalized Choquet integral based aggregation operators.<br /

An inquiry-based method for Choquet integral-based aggregation of interface usability parameters

summary:The concept of usability of man-machine interfaces is usually judged in terms of a number of aspects or attributes that are known to be subject to some rough correlations, and that are in many cases given different importance, depending on the context of use of the application. In consequence, the automation of judgment processes regarding the overall usability of concrete interfaces requires the design of aggregation operators that are capable of modeling approximate or ill-defined interactions among criteria. In addition, justified expert opinions are given a prominent status in the current practice of usability evaluation, which points to the convenience of including experts as an integral part of the aggregation operator design process. On the basis of these assumptions we review in this paper possible approaches to design a suitable aggregation operation and describe a method for such kind of design process that explicitly models expert-elicited relationships among criteria, enforcing some properties on a Choquet capacity. The method subsequently uses experimental data to fine-tune operator design. A case study is described to illustrate the method, and a comparative study with other common aggregation approaches is also provided