Application of Fuzzy Integrals Based on c-Credibility Measures in Image Processing

Aggregation functions can play a very important role in decision-making theory, and integrals based on fuzzy measures are one such example. Among the most famous are Sugeno and Choquet integrals. Also, from credibility theory comes a class of fuzzy measures, so-called credibility measures. This paper establishes some new properties of the c-credibility measure and the construction procedure of such a measure on a given set, based on the Extension theorem of credibility. Some generalizations of this measure can be used to define a new fuzzy integral based on it. We consider some properties of this integral, such as e.g. preservation of order and properties of additivity. Such integrals can serve as an aggregation of some measures of similarity of parts of an object, thus giving an answer as to whether the object under consideration is similar to another composed of parts of the same type. In some earlier works, the similarity of the images of two faces was analyzed with rega rds to the measurements of the appropriate parts. The efficiency of this method is compared with similar methods on selected image databases while varying the parameters that define the new integral.