General Fuzzy Measures Research Articles

Identification of general fuzzy measures by genetic algorithms based on partial information

This study develops an identification procedure for general fuzzy measures using genetic algorithms. In view of the difficulty in data collection in practice, the amount of input data is simplified through a sampling procedure concerning attribute subsets, and the corresponding detail design is adapted to the partial information acquired by the procedure. A specially designed genetic algorithm is proposed for better identification, including the development of the initialization procedure, fitness function, and three genetic operations. To show the applicability of the proposed method, this study simulates a set of experimental data that are representative of several typical classes. The experimental analysis indicates that using genetic algorithms to determine general fuzzy measures can obtain satisfactory results under the framework of partial information.

Improved feature selection and classification by the 2-additive fuzzy measure

This paper focusses on the investigation of a pattern recognition method based on the fuzzy integral. Until now this method has used a general fuzzy measure, which is characterized by exponential complexity. Naturally this led to some difficulties in practical applications of this pattern recognition method. In this paper, a heuristic algorithm for the identification of the 2-additive fuzzy measure, which is a particular type of k-additive fuzzy measures, is proposed. This algorithm can be used to reduce complexity of feature selection and classifier design. A further topic considered in this paper is the development of a feature selection algorithm for the fuzzy integral classifier. The proposed heuristic algorithm is based on two feature-evaluation criteria such as the importance and the interaction indexes. They were earlier defined in the literature using the semantic interpretation of the fuzzy measure. To validate the proposed algorithms, the feature selection algorithm and the pattern recognition method based on the fuzzy integral are applied to a problem of acoustic quality control.

AGGREGATION AND COMPLETION OF RANDOM SETS WITH DISTRIBUTIONAL FUZZY MEASURES

The two known information theories, probability and possibility theory, are based on t-conorm decomposable fuzzy measures, so that bijective mappings exist between their set-valued measures and their point-valued distributions. Further, their random set (Dempster-Shafer evidence theoretical) interpretations have simple topological structures, with bijective mappings between the subset focal elements and the point singletons. We introduce the concepts of distributional and aggregable random sets and random set completion, and first use them as a model in which to cast probability and possibility measures and distributions. Then, towards the goal of deriving new forms of information theory, general Sugeno conorm decomposable fuzzy measures and ring-like aggregable random sets with set-intersection structural aggregation are examined, but it is shown that in these two cases no new information theories are forthcoming.

Fuzzy t-conorm integral with respect to fuzzy measures: Generalization of Sugeno integral and Choquet integral

Abstract This article discusses integrals with respect to Sugeno's fuzzy measures. Sugeno integrals and Choquet integrals with respect to general fuzzy measures are generalized in the setting of a t-conorm algebraic system. First t-conorm integrals with respect to decomposable measures based on t-conorm algebraic system are defined. They are a modification of the Weber integral. Secondly they are extended to fuzzy t-conorm integrals with respect to general fuzzy measures. The extension is made in the same way as the extension of the Lebesgue integral to the Choquet integral. The class of fuzzy t-conorm integrals includes Choquet integrals and Sugeno integrals. Properties of the integrals, especially their representation, are discussed.

A model of human evaluation process using fuzzy measure

This paper presents a mathematical model for the human subjective evaluation process using fuzzy integrals based on the general fuzzy measure. First, the concept of overlap coefficient is introduced to describe the properties of a given fuzzy measure and to characterize the human evaluation process. Further, a new algorithm is developed to identify the fuzzy measure with full degrees of freedom. Lastly, the model and the identification scheme are applied to two practical examples: prediction of wood strength by an experienced inspector and trouble evasive actions taken by a computer game player.