Fuzzy approaches for multiple objective linear fractional optimization. (English) Zbl 0546.90094

Summary: The problem of finding a solution to a multiple objective linear fractional program arises in several real world situtions. In this paper we advocate that fuzzy sets theory provides a basis for solving this problem with sufficent consistency and rigorousness. After representing imprecise aspirations of the decision maker by structured linguistic variables or converting the original problem via approximations or change of variables into a multiple objective linear program, techniques of fuzzy linear programming may be used to reach a satisfactory solution. It is shown that under reasonable restrictions, this solution is efficient (Pareto optimal) for the original problem. Numerical examples are also included for illustration.


90C32 Fractional programming
90C05 Linear programming
90C31 Sensitivity, stability, parametric optimization
03E72 Theory of fuzzy sets, etc.
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[1] Baptistella, L.F.B.; Ollero, A., Fuzzy methodologies for interactive multicriteria optimization, Note interne LAAS-ASC, 79-I-57, (1979) · Zbl 0442.90088
[2] Ecker, J.G.; Kouada, I.A., Finding all efficient extreme points for multiple objective linear programs, Math. programming, 14, 249-261, (1978) · Zbl 0385.90105
[3] Geoffrion, A.M.; Dyer, J.S.; Feinberg, A., An interactive approach for multi-criterion optimization, with an application to the operation of an Academic department, Management sci, 19, 357-368, (1972) · Zbl 0247.90069
[4] Kornbluth, J.S.H.; Steuer, R.E., Multiple objective linear fractional programming, Management sci, 27, 1024-1039, (1981) · Zbl 0467.90064
[5] Kornbluth, J.S.H.; Steuer, R.E., Goal programming with linear fractional criteria, Europ. J. oper. res, 8, 58-65, (1981) · Zbl 0486.90077
[6] Kreyszig, E., Functional analysis, (), 143-165
[7] Kuz’min, V.R., A parametric approach to description of linguistic values of variables and hedges, Fuzzy sets and systems, 6, 27-41, (1981)
[8] Luhandjula, M.K., Compensatory operators in fuzzy linear programming with multiple objectives, Fuzzy sets and systems, 8, 245-252, (1982) · Zbl 0492.90076
[9] Luhandjula, M.K., Linear programming under randomness and fuzziness, Fuzzy sets and systems, 10, 45-55, (1983) · Zbl 0514.90067
[10] Schaible, S., Fractional programming, (), 479-493
[11] Vadja, S., Probabilistic programming, (1972), Academic Press New York
[12] Zadeh, L.A.; Zadeh, L.A.; Zadeh, L.A., The concept of linguistic variable and its application to approximate reasoning, part I, II, III, Information sci, Information sci, Information sci, 9, 43-80, (1975) · Zbl 0404.68075
[13] Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision process, IEEE trans. syst. man. cybernet, 3, 28-44, (1973) · Zbl 0273.93002
[14] Zimmermann, H.J., Fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems, 1, 45-55, (1978) · Zbl 0364.90065
[15] Zimmermann, H.J., Trends and new approaches in European operational research, J. opl. res. soc, 33, 597-603, (1982)
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