Feature Based Defuzzification in ℤ2 and ℤ3 Using a Scale Space Approach

Abstract

A defuzzification method based on feature distance minimization is further improved by incorporating into the distance function feature values measured on object representations at different scales. It is noticed that such an approach can improve defuzzification results by better preserving the properties of a fuzzy set; area preservation at scales in-between local (pixel-size) and global (the whole object) provides that characteristics of the fuzzy object are more appropriately exhibited in the defuzzification. For the purpose of comparing sets of different resolution, we propose a feature vector representation of a (fuzzy and crisp) set, utilizing a resolution pyramid. The distance measure is accordingly adjusted. The defuzzification method is extended to the 3D case. Illustrative examples are given.

Defuzzification of spatial fuzzy sets by feature distance minimization

“…Suggestions how to design a defuzzification method appropriate for a particular application are given, together with a discussion about the behaviour of the algorithm depending on different parameter settings. The proposed method has been further developed and successfully adjusted to particular tasks in [35,36]. In our opinion, the flexibility of the proposed defuzzification method and the essential simplicity of its main idea, presented in this paper, are an appealing starting point for further studies and development.…”

“…The computational complexity may, however, be significant for higher dimensional images. In our study presented in [36], the method proposed in this paper is extended and applied to 3D images.…”

Defuzzification by Feature Distance Minimization Based on DC Programming

“…In [12], four methods where suggested, SA being recommended as the preferred one. However, SA is non-deterministic and computationally demanding, which appeared to be a serious disadvantage when the defuzzification method is extended to 3D [5]. This motivated the work on adapting a deterministic optimization method to the defuzzification by feature distance minimization, presented in this paper.…”

“…We use the SA algorithm as described in [12] and further refined in [4,5], with the following parameter settings: The initial configuration is obtained by the optimal α-cut; The initial temperature, T 0 is 0.1; The number of perturbations tested at each temperature level is 10 000, after which the temperature is reduced one level, T k+1 = 0.995T k ; The temperature is successively lowered until 50 000 successive perturbations does not provide any step that gives a reduction in distance, after which a new re-annealing is restarted from the currently best found solution; After 10 re-annealings the process is stopped and the best found configuration is used. For more details see [5].…”

“…The minimization task of finding an optimal binary configuration requires, due to the large search space, application of some appropriate optimization method. An algorithm which is successfully adapted and mostly used for this task so far is Simulated Annealing (SA) [4,5,12].…”