Intuitionistic fuzzy sets and their use in image classification

Abstract

In this paper, the problem of classification of images is discussed. Our specific problem is that we need to classify tire images into selected classes which are characterized by some patterns. The theory of intuitionistic fuzzy sets is used for classification of the images. In the first step is showed the way how this type of images could be represented as the vectors. Then the membership and non-membership value to each coordinate are calculated and finally the value of similarity measure between patterns and specific image is computed. Classification is performed with respect to the valued of similarity measure.

Intuitionistic fuzzy negations and their use in image classification

“…Similarly, as in [6] and [7] there were some incorrectly classified images which had some common properties. There were some images in the database, for which the human expert also finds it hard to classify them exactly into one class.…”

“…The classification of tire tread images by using intuitionistic fuzzy set functions was made in some papers also before. For example, in [6] authors used similarity measure defined on intuitionistic fuzzy sets for classification of the images. For similarity measures there could be found many counter-intuitive results, see [8].…”

“…To calculate the value of membership and non-membership function to each coordinate of the image vector, we used the procedure that was described in the paper [4]. To build the database of templates and patterns, we used the same approach as it was mentioned in papers [6] and [7]. For each of the seven classes mentioned in Introduction we choose the so called templates.…”

Some notes on intuitionistic fuzzy equivalence relations and their use on real data

“…Therefore it is important to process the images in such way that the best possible position of tire tread sample will be obtained. On the behalf of this idea there was created number of methods (see [11][12][13]19]) of classifying images into the chosen number of classes. In this part of the paper we use the results of classification of the images on the basis of intuitionistic fuzzy sets and we apply the conditions of intuitionistic fuzzy equivalence relations to obtain new results.…”

“…For pre-processing of the images we developed the specific algorithm (see [11]). After using this algorithm each image is represented by 16 coordinate vector.…”