TY - JOUR

T1 - A constructing algorithm for appropriate piecewise linear membership function based on statistics and information theory

AU - Hasuike, Takashi

AU - Katagiri, Hideki

AU - Tsubaki, Hiroe

N1 - Publisher Copyright:
© 2015 The Authors. Published by Elsevier B.V.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2015

Y1 - 2015

N2 - This paper proposes a constructing algorithm for an appropriate membership function to integrate the fuzzy Shannon entropy with a piecewise linear function into subjective intervals estimation by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in real-world decision making. The main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the initial mathematical programming problem efficiently using previous constructing approaches. In this paper, introducing some natural assumptions in the real-world and performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each appropriate membership value is developed.

AB - This paper proposes a constructing algorithm for an appropriate membership function to integrate the fuzzy Shannon entropy with a piecewise linear function into subjective intervals estimation by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in real-world decision making. The main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the initial mathematical programming problem efficiently using previous constructing approaches. In this paper, introducing some natural assumptions in the real-world and performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each appropriate membership value is developed.

KW - Fuzzy entropy

KW - Mathematical programming

KW - Membership function

KW - Smoothing function

UR - http://www.scopus.com/inward/record.url?scp=84941083827&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941083827&partnerID=8YFLogxK

U2 - 10.1016/j.procs.2015.08.140

DO - 10.1016/j.procs.2015.08.140

M3 - Conference article

AN - SCOPUS:84941083827

VL - 60

SP - 994

EP - 1003

JO - Procedia Computer Science

JF - Procedia Computer Science

SN - 1877-0509

IS - 1

T2 - 19th International Conference on Knowledge Based and Intelligent Information and Engineering Systems, KES 2015

Y2 - 7 September 2015 through 9 September 2015

ER -