An Objective Approach for Constructing a Membership Function Based on Fuzzy Harvda-Charvat Entropy and Mathematical Programming

Author:

Hasuike Takashi, ,Katagiri Hideki,

Abstract

This paper proposes an objective approach to the construction of an appropriate membership function that extends to our previous studies. It is important to set a membership function with subjectivity and objectivity to obtain a reasonable optimal solution that complies with the decision maker’s feelings in real-world decision making. To ensure objectivity and subjectivity of the obtained membership function, an entropy-based approach based on mathematical programming is integrated into the interval estimation considered by the decision maker. Fuzzy Harvda-Charvat entropy, which is a natural extension of fuzzy Shannon entropy, is introduced as general entropy with fuzziness. The main steps of our proposed approach are to set intervals with membership values 0 and 1 to enable a decision maker to judge confidently, and to solve the proposed mathematical programming problem strictly using nonlinear programming. In this paper, the given membership function is assumed to be a piecewise linear membership function as an approximation of nonlinear functions, and each intermediate value of partial linear function is optimally obtained.

Publisher

Fuji Technology Press Ltd.

Subject

Artificial Intelligence,Computer Vision and Pattern Recognition,Human-Computer Interaction

Reference21 articles.

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3. M. R. Civanlar and H. J. Trussell, “Constructing membership functions using statistical data,” Fuzzy Sets and Systems, Vol.18, pp. 1-13, 1986.

4. H. D. Cheng and Y. H. Cheng, “Thresholding based on fuzzy partition of 2D histogram,” Proc. of IEEE Int. Conf. on Pattern Recognition, Vol.2, pp. 1616-1618, 1997.

5. G. Nieradka and B. Butkiewicz, “A method for automatic membership function estimation based on fuzzy measures,” Proc. of IFSA2007, LNAI4529, pp. 451-460, 2007.

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