Cao, Bingyuan Fuzzy geometric programming. I. (English) Zbl 0804.90135 Fuzzy Sets Syst. 53, No. 2, 135-153 (1993). Summary: First, the concepts of fuzzy valuation convex (or concave) function and fuzzy convex-geometric programming problem are based on a fuzzy valuation set in this paper. Secondly, fuzzy posynomial geometric programming and its dual-form properties concerned are discussed by means of a fuzzy geometric inequality and of a fuzzy dual theory. Lastly, direct and dual algorithms of fuzzy posynomial geometric programming are respectively deduced by the aid of a fuzzy fixed-point theorem and the notion of \(\alpha\), \(\beta\)-cut. Cited in 1 ReviewCited in 11 Documents MSC: 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming 90C30 Nonlinear programming Keywords:fuzzy convex-geometric programming; fuzzy posynomial geometric programming; fuzzy geometric inequality; fuzzy fixed-point theorem PDFBibTeX XMLCite \textit{B. Cao}, Fuzzy Sets Syst. 53, No. 2, 135--153 (1993; Zbl 0804.90135) Full Text: DOI References: [1] Avriel, M., Nonlinear Programming Analysis and Methods (1976), Prentice Hall: Prentice Hall Englewood Cliffs, NJ · Zbl 0361.90035 [2] Cao, B. Y., Solution and theory of question for a kind of fuzzy positive geometric program, (Proc. 2nd IFSA Congress, Vol. 1 (July 1987)), 205-208, Tokyo [3] Cao, B. Y., Study of fuzzy positive geometric programming dual form, (Proc. 3rd IFSA Congress. Proc. 3rd IFSA Congress, Seattle (August 1989)), 775-778 [4] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049 [5] Duffin, R. J., Cost minimization problems treated by geometric means, Operations Res., 10, 668-675 (1962) · Zbl 0118.14904 [6] Duffin, R. J., Dual programs and minimum cost, SIAM J. Appl. Math., 10, 119-123 (1962) · Zbl 0106.13905 [7] Duffin, R. J.; Peterson, E. L.; Zener, C., Geometric Programming: Theory and Applications (1967), John Wiley & Sons: John Wiley & Sons New York · Zbl 0171.17601 [8] Verdegay, J. L., A dual approach to solve the fuzzy linear programming problem, Fuzzy Sets and Systems, 14, 131-140 (1984) · Zbl 0549.90064 [9] Wu, F.; Yan, Y. Y., Geometric programming, Math. in Practice and Theory, 1-2 (1982) [10] Zadeh, L. A., Fuzzy sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606 [11] Zener, C., A mathematical aid in optimizing engineering design, (Proc. Nat. Acad. Sci. U.S.A., 47 (1961)), 537-539 · Zbl 0094.36701 [12] Zimmermann, H.-J., Description and optimization of fuzzy systems, Internat. J. General Systems, 2, 209-215 (1976) · Zbl 0338.90055 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.