A solution algorithm for fuzzy linear programming with piecewise linear membership functions

Inuiguchi, Masahiro; Ichihashi, Hidetomo; Kume, Yasufumi

doi:10.1016/0165-0114(90)90123-n

Cited by 73 publications

(43 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 1986 Carlsson and Korhonen suggested an approach that accepts all coefficients as fuzzy and presents a parametric solution. In 1987 Werners (Werners, 1987) studied on an interactive model and in 1990 Inuiguchi et al (Inuiguchi et al, 1990) studied a FLP with partial linear membership functions. In recent years in 2000 Tanaka et al, in 2001 Jamison andLodwick (Jamison andLodwick, 2001), in 2001 Chiang, Liu (Liu, 2001), in 2002 Bector and Chandra contributed the theory and methodolgy (Paksoy, 2002).…”

Section: Fuzzy Linear Programmingmentioning

confidence: 99%

Interactive fuzzy linear programming and an application sample at a textile firm

Ertuğrul

Tuş

2007

Fuzzy Optim Decis Making

View full text Add to dashboard Cite

The purpose of this study is to examine Interactive Fuzzy Linear Programming (IFLP) model by using Zimmermann, Werners, Chanas and Verdegay's approaches that provide best decision-making under fuzzy environments. In this study, it is used the method which can model the fuzzy structure of the real world and which operates with the decision maker interactively, which aims at obtaining the best solution by continuing this interactiveness in the solution process, which includes fuzziness with more realistic approach to the system. It is showed that the importance of fuzziness concept for IFLP problems, how it is applied on real-world problems and its effects.

show abstract

Section: Fuzzy Linear Programmingmentioning

confidence: 99%

Interactive fuzzy linear programming and an application sample at a textile firm

Ertuğrul

Tuş

2007

Fuzzy Optim Decis Making

View full text Add to dashboard Cite

show abstract

“…Moreover, Inuiguchi et al [14] considered solving fuzzy linear programming problems in view of fuzzy linear inequalities. Recently, Hu and Fang [15] studied a system of fuzzy inequalities with linear membership functions which can be converted to a regular convex programming problem.…”

Section: Introductionmentioning

confidence: 99%

An approach for solving fuzzy implicit variational inequalities with linear membership functions

Lan

2008

Computers & Mathematics with Applications

View full text Add to dashboard Cite

In this paper, we consider a class of fuzzy implicit variational inequalities with linear membership functions. By using the "tolerance approach", we show that solving such problems can be reduced to a semi-infinite programming problem. A version of the "method of centres" with "entropic regularization" techniques, only used a quasi-Newton line search using MATLAB software is required in our implementation. We also give a numerical example to illustrate the validity of our approach.

show abstract

“…Normally, a fuzzynumbered approach is employed for such generalized case. For example, for fuzzy numbers in linear forms, the symmetric triangular fuzzy numbers were used by Tong (1994) and Lui (2001); and for non-linear fuzzy numbers, exponential logistic by Carlsson and Korhonen (1986) and Vasant (2003), piecewise linear by Inuiguchi, Ichihashi and Kume (1990) and Hu and Fang (1999), and so-called epsilon-delta relation by Ramı´k and Rommelfanger (1996) were also proposed. An overview can be referred to Dombi (1990) or Rommelfanger (1996).…”

Section: Introductionmentioning

confidence: 99%

Preference Approach to Fuzzy Linear Inequalities and Optimizations

Wang

2005

Fuzzy Optim Decis Making

View full text Add to dashboard Cite

In this study we first present the preference structures in decision making as a generalized non-linear function. Then, we incorporate it into a fuzzy linear inequality of which the progressive and conservative manners are described by the concept of target hyperplanes. Thus, one's preference domain is said to be bounded by such soft constraint. When facing different situations, a membership function is defined as an evaluation function for incorporating one's optimistic or pessimistic attitude into this soft constraint. Once a goal is pursued, the problem is transformed into a symmetric fuzzy linear program. Based on max-min principle, an auxiliary crisp model in the form of a generalized fractional program is derived. Then, Dinkelbach-type-2 and the bisection algorithms are adopted for solution. Finally their simulation results of an uncertain production scheduling problem are reported.

show abstract

A solution algorithm for fuzzy linear programming with piecewise linear membership functions

Cited by 73 publications

References 9 publications

Interactive fuzzy linear programming and an application sample at a textile firm

Interactive fuzzy linear programming and an application sample at a textile firm

An approach for solving fuzzy implicit variational inequalities with linear membership functions

Preference Approach to Fuzzy Linear Inequalities and Optimizations

Contact Info

Product

Resources

About