Abstract
This paper proposes a mathematical programming approach to construct an appropriate membership function extending our previous studies. It is important to set a membership function with both subjectivity and objectivity to obtain a reasonable optimal solution based on decision maker's feelings in real-world decision making. In order to ensure objectivity of obtained membership function as well as subjectivity, an entropy-based approach based on mathematical programming is integrated into interval estimation considered by the decision maker. As a general entropy with fuzziness, fuzzy Harvda-Charvat entropy is introduced, which is a natural extension of fuzzy Shannon entropy. In addition, qualitative and subjective evaluations based on the pairwise comparison are introduced to represent the differences between two membership values. The main step of our revised approach is 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 approximation of nonlinear functions, and each intermediate value of partial linear function is optimally obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 4443-4452 |
| Number of pages | 10 |
| Journal | Journal of Intelligent and Fuzzy Systems |
| Volume | 32 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2017 |
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Keywords
- Harvda-Charvat entropy
- mathematical programming
- Membership function
- scale for measuring
ASJC Scopus subject areas
- Statistics and Probability
- Engineering(all)
- Artificial Intelligence
Cite this
An objective formulation of membership function based on fuzzy entropy and pairwise comparison. / Hasuike, Takashi; Katagiri, Hideki.
In: Journal of Intelligent and Fuzzy Systems, Vol. 32, No. 6, 2017, p. 4443-4452.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An objective formulation of membership function based on fuzzy entropy and pairwise comparison
AU - Hasuike, Takashi
AU - Katagiri, Hideki
PY - 2017
Y1 - 2017
N2 - This paper proposes a mathematical programming approach to construct an appropriate membership function extending our previous studies. It is important to set a membership function with both subjectivity and objectivity to obtain a reasonable optimal solution based on decision maker's feelings in real-world decision making. In order to ensure objectivity of obtained membership function as well as subjectivity, an entropy-based approach based on mathematical programming is integrated into interval estimation considered by the decision maker. As a general entropy with fuzziness, fuzzy Harvda-Charvat entropy is introduced, which is a natural extension of fuzzy Shannon entropy. In addition, qualitative and subjective evaluations based on the pairwise comparison are introduced to represent the differences between two membership values. The main step of our revised approach is 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 approximation of nonlinear functions, and each intermediate value of partial linear function is optimally obtained.
AB - This paper proposes a mathematical programming approach to construct an appropriate membership function extending our previous studies. It is important to set a membership function with both subjectivity and objectivity to obtain a reasonable optimal solution based on decision maker's feelings in real-world decision making. In order to ensure objectivity of obtained membership function as well as subjectivity, an entropy-based approach based on mathematical programming is integrated into interval estimation considered by the decision maker. As a general entropy with fuzziness, fuzzy Harvda-Charvat entropy is introduced, which is a natural extension of fuzzy Shannon entropy. In addition, qualitative and subjective evaluations based on the pairwise comparison are introduced to represent the differences between two membership values. The main step of our revised approach is 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 approximation of nonlinear functions, and each intermediate value of partial linear function is optimally obtained.
KW - Harvda-Charvat entropy
KW - mathematical programming
KW - Membership function
KW - scale for measuring
UR - http://www.scopus.com/inward/record.url?scp=85019717568&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85019717568&partnerID=8YFLogxK
U2 - 10.3233/JIFS-169210
DO - 10.3233/JIFS-169210
M3 - Article
VL - 32
SP - 4443
EP - 4452
JO - Journal of Intelligent and Fuzzy Systems
JF - Journal of Intelligent and Fuzzy Systems
SN - 1064-1246
IS - 6
ER -