Abstract
This paper develops a constructing algorithm for an appropriate membership function as objectively as possible. It is important to set an appropriate membership function for real-world decision making. The main academic contribution of our proposed algorithm is to integrate a general continuous and nonlinear function with fuzzy Shannon entropy into subjective interval estimation by a heuristic method under a given probability density function based on real-world data. Two main steps of our proposed approach are to set membership values a decision maker confidently judges whether an element is included in the given set or not and to obtain other values objectively by solving a mathematical programming problem with fuzzy Shannon entropy. It is difficult to solve the problem efficiently using previous constructing approaches due to nonlinear function. In this paper, the given nonlinear membership function is approximately transformed into a piecewise linear membership function, and the appropriate values are determined. Furthermore, by introducing natural assumptions in the real-world and interactively adjusting the membership values, an algorithm to obtain the optimal condition of each appropriate membership value is developed.
| Original language | English |
|---|---|
| Title of host publication | Procedia Computer Science |
| Publisher | Elsevier |
| Pages | 32-37 |
| Number of pages | 6 |
| Volume | 61 |
| DOIs | |
| Publication status | Published - 2015 |
| Event | Complex Adaptive Systems, 2015 - San Jose, United States Duration: 2015 Nov 2 → 2015 Nov 4 |
Other
| Other | Complex Adaptive Systems, 2015 |
|---|---|
| Country | United States |
| City | San Jose |
| Period | 15/11/2 → 15/11/4 |
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Keywords
- Fuzzy entropy
- Interactive algorithm
- Mathematical programming
ASJC Scopus subject areas
- Computer Science(all)
Cite this
An Interactive Algorithm to Construct an Appropriate Nonlinear Membership Function Using Information Theory and Statistical Method. / Hasuike, Takashi; Katagiri, Hideki; Tsubaki, Hiroe.
Procedia Computer Science. Vol. 61 Elsevier, 2015. p. 32-37.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - An Interactive Algorithm to Construct an Appropriate Nonlinear Membership Function Using Information Theory and Statistical Method
AU - Hasuike, Takashi
AU - Katagiri, Hideki
AU - Tsubaki, Hiroe
PY - 2015
Y1 - 2015
N2 - This paper develops a constructing algorithm for an appropriate membership function as objectively as possible. It is important to set an appropriate membership function for real-world decision making. The main academic contribution of our proposed algorithm is to integrate a general continuous and nonlinear function with fuzzy Shannon entropy into subjective interval estimation by a heuristic method under a given probability density function based on real-world data. Two main steps of our proposed approach are to set membership values a decision maker confidently judges whether an element is included in the given set or not and to obtain other values objectively by solving a mathematical programming problem with fuzzy Shannon entropy. It is difficult to solve the problem efficiently using previous constructing approaches due to nonlinear function. In this paper, the given nonlinear membership function is approximately transformed into a piecewise linear membership function, and the appropriate values are determined. Furthermore, by introducing natural assumptions in the real-world and interactively adjusting the membership values, an algorithm to obtain the optimal condition of each appropriate membership value is developed.
AB - This paper develops a constructing algorithm for an appropriate membership function as objectively as possible. It is important to set an appropriate membership function for real-world decision making. The main academic contribution of our proposed algorithm is to integrate a general continuous and nonlinear function with fuzzy Shannon entropy into subjective interval estimation by a heuristic method under a given probability density function based on real-world data. Two main steps of our proposed approach are to set membership values a decision maker confidently judges whether an element is included in the given set or not and to obtain other values objectively by solving a mathematical programming problem with fuzzy Shannon entropy. It is difficult to solve the problem efficiently using previous constructing approaches due to nonlinear function. In this paper, the given nonlinear membership function is approximately transformed into a piecewise linear membership function, and the appropriate values are determined. Furthermore, by introducing natural assumptions in the real-world and interactively adjusting the membership values, an algorithm to obtain the optimal condition of each appropriate membership value is developed.
KW - Fuzzy entropy
KW - Interactive algorithm
KW - Mathematical programming
UR - http://www.scopus.com/inward/record.url?scp=84962667098&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84962667098&partnerID=8YFLogxK
U2 - 10.1016/j.procs.2015.09.140
DO - 10.1016/j.procs.2015.09.140
M3 - Conference contribution
VL - 61
SP - 32
EP - 37
BT - Procedia Computer Science
PB - Elsevier
ER -