scholarly journals Generalised convexity and duality in multiple objective programming

1989 ◽  
Vol 39 (2) ◽  
pp. 287-299 ◽  
Author(s):  
T. Weir ◽  
B. Mond
Keyword(s):  
Multiple Objective Programming ◽  
Multiple Objective ◽  
Duality Theorems ◽  
Converse Duality ◽  
Duality Results ◽  
Objective Programming ◽  
Weak Minima ◽  
Convexity Conditions

By considering the concept of weak minima, different scalar duality results are extended to multiple objective programming problems. A number of weak, strong and converse duality theorems are given under a variety of generalised convexity conditions.

FUZZY MULTIPLE OBJECTIVE PROGRAMMING IN AN INTERVAL PIECEWISE REGRESSION MODEL

2009 ◽  
Vol 17 (03) ◽  
pp. 365-376 ◽  
Author(s):  
JING-RUNG YU ◽  
GWO-HSHIUNG TZENG
Keyword(s):  
Regression Model ◽  
Regression Models ◽  
Heuristic Approach ◽  
Multiple Objective Programming ◽  
Change Points ◽  
Multiple Objective ◽  
Compromise Solution ◽  
Numerical Examples ◽  
Piecewise Regression ◽  
Objective Programming

This study proposes fuzzy multiple objective programming to determine the measure of fitness and the number of change-points in an interval piecewise regression model. To increase the measure of fitness, Tanaka and Lee proposed a conceptual procedure, which is a heuristic approach and becomes complicated for determining the proper polynomial. Therefore, a multiple objective approach is adopted to obtain a compromise solution among three objectives — maximizing the measure of fitness, minimizing the number of change-points and minimizing the width to obtain the interval regression models. By using the proposed method, a better measure of fitness can be obtained. Two numerical examples are used as demonstrations to illustrate our approach in more detail.

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