### Abstract

The aim of this paper is to introduce a novel statement of fuzzy mathematical programming problems and to provide a method for finding a fair solution to these problems. Suppose we are given a mathematical programming problem in which the functional relationship between the decision variables and the objective function is not completely known. Our knowledge-base consists of a block of fuzzy if-then rules, where the antecedent part of the rules contains some linguistic values of the decision variables, and the consequence part consists of a linguistic value of the objective function. We suggest the use of Tsukamoto's fuzzy reasoning method to determine the crisp functional relationship between the objective function and the decision variables, and solve the resulting (usually nonlinear) programming problem to find a fair optimal solution to the original fuzzy problem.

Original language | English |
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Pages (from-to) | 111-120 |

Number of pages | 10 |

Journal | Fuzzy Sets and Systems |

Volume | 119 |

Issue number | 1 |

DOIs | |

Publication status | Published - Apr 1 2001 |

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### Keywords

- Fuzzy optimization
- Linguistic variable
- Soft constraints
- Tsukamoto's fuzzy reasoning

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Science Applications
- Computer Vision and Pattern Recognition
- Information Systems and Management
- Statistics, Probability and Uncertainty
- Electrical and Electronic Engineering
- Statistics and Probability

### Cite this

*Fuzzy Sets and Systems*,

*119*(1), 111-120. https://doi.org/10.1016/S0165-0114(98)00465-5

**Optimization under fuzzy if-then rules.** / Carlsson, Christer; Fullér, R.

Research output: Contribution to journal › Article

*Fuzzy Sets and Systems*, vol. 119, no. 1, pp. 111-120. https://doi.org/10.1016/S0165-0114(98)00465-5

}

TY - JOUR

T1 - Optimization under fuzzy if-then rules

AU - Carlsson, Christer

AU - Fullér, R.

PY - 2001/4/1

Y1 - 2001/4/1

N2 - The aim of this paper is to introduce a novel statement of fuzzy mathematical programming problems and to provide a method for finding a fair solution to these problems. Suppose we are given a mathematical programming problem in which the functional relationship between the decision variables and the objective function is not completely known. Our knowledge-base consists of a block of fuzzy if-then rules, where the antecedent part of the rules contains some linguistic values of the decision variables, and the consequence part consists of a linguistic value of the objective function. We suggest the use of Tsukamoto's fuzzy reasoning method to determine the crisp functional relationship between the objective function and the decision variables, and solve the resulting (usually nonlinear) programming problem to find a fair optimal solution to the original fuzzy problem.

AB - The aim of this paper is to introduce a novel statement of fuzzy mathematical programming problems and to provide a method for finding a fair solution to these problems. Suppose we are given a mathematical programming problem in which the functional relationship between the decision variables and the objective function is not completely known. Our knowledge-base consists of a block of fuzzy if-then rules, where the antecedent part of the rules contains some linguistic values of the decision variables, and the consequence part consists of a linguistic value of the objective function. We suggest the use of Tsukamoto's fuzzy reasoning method to determine the crisp functional relationship between the objective function and the decision variables, and solve the resulting (usually nonlinear) programming problem to find a fair optimal solution to the original fuzzy problem.

KW - Fuzzy optimization

KW - Linguistic variable

KW - Soft constraints

KW - Tsukamoto's fuzzy reasoning

UR - http://www.scopus.com/inward/record.url?scp=0039149103&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039149103&partnerID=8YFLogxK

U2 - 10.1016/S0165-0114(98)00465-5

DO - 10.1016/S0165-0114(98)00465-5

M3 - Article

VL - 119

SP - 111

EP - 120

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

SN - 0165-0114

IS - 1

ER -