Fuzzy programming technique to solve multi-objective geometric programming problems. (English) Zbl 0786.90086
Summary: A fuzzy programming technique is used to solve a multi-objective geometric programming problem as a vector minimum problem. A fuzzy membership function is defined for the multi-objective geometric programming problem. Two numerical examples are presented to illustrate the method.
MSC:
| 90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |
| 90C30 | Nonlinear programming |
| 90C29 | Multi-objective and goal programming |
References:
| [1] | Beightler, C. S.; Phillips, D. T., Applied Geometric Programming (1976), John Wiley & Sons: John Wiley & Sons New York · Zbl 0344.90034 |
| [2] | Duffin, R. J.; Peterson, E. L.; Zener, C., Geometric Programming — Theory and Application (1967), John Wiley & Sons: John Wiley & Sons New York · Zbl 0171.17601 |
| [3] | Ecker, J. G.; Kupferschmid, M., An ellipsoid algorithm for non-linear programming, Mathematical Programming, 27, 83-106 (1983) · Zbl 0526.90074 |
| [4] | Kuester, J. L.; Mize, J. H., Optimization Techniques with Fortran (1973), McGraw-Hill: McGraw-Hill New York · Zbl 0268.65039 |
| [5] | Zimmermann, H.-J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 46-55 (1978) · Zbl 0364.90065 |
| [6] | Zimmermann, H.-J., Fuzzy Set Theory and its Applications (1990), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht-Boston |
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