zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Interactive fuzzy decision making for multiobjective nonlinear programming using augmented minimax problems. (English) Zbl 0629.90054
An interactive fuzzy decision-making method for solving multiobjective nonlinear programming problems is presented. The decision maker (DM) has fuzzy goals for each of the objectives which are quantified by eliciting corresponding membership functions through the interaction with DM. The DM specifies his reference membership values and the augmented minimax problem is solved for this case. The DM analyses the solution and responds by updating his reference membership values etc. In this way the compromise or satisfying solution for the DM can be derived. It is a Pareto-optimal solution.
Reviewer: F.V.Burshtein

MSC:
90B50Management decision making, including multiple objectives
90C31Sensitivity, stability, parametric optimization
90C30Nonlinear programming
WorldCat.org
Full Text: DOI
References:
[1] Bellman, R. E.; Zadeh, L. A.: Decision making in a fuzzy environment. Management sci. 17, 141-164 (1970) · Zbl 0224.90032
[2] Charnes, A.; Cooper, W. W.: Goal programming and multiple objective optimizations. European J. Oper. res. 1, 39-54 (1977) · Zbl 0375.90079
[3] Choo, E. U.; Atkins, D. R.: Proper efficiency in nonconvex multicriteria programming. Math. oper. Res. 8, 467-470 (1983) · Zbl 0523.90083
[4] Geoffrion, A. M.: Proper efficiency the theory of vector maximization. J. math. Anal. appl. 22, 618-630 (1968) · Zbl 0181.22806
[5] Geoffrion, A. M.; Dyer, J. S.; Feinberg, A.: An interactive approach for multicriterion optimization with an application to the operation of an Academic department. Management sci. 19, 357-368 (1972) · Zbl 0247.90069
[6] Haimes, Y. Y.; Hall, W. A.; Freedman, H. T.: Multiobjective optimization in water resources systems: the surrogate worth trade-off method. (1975)
[7] Haimes, Y. Y.; Chankong, V.: Kuhn-Tucker multipliers as trade-offs in multiobjective decision-making analysis. Automatica 15, 59-72 (1979) · Zbl 0406.90065
[8] Hannan, E. L.: Linear programming with multiple fuzzy goals. Fuzzy sets and systems 6, 235-248 (1981) · Zbl 0465.90080
[9] Ignizio, J. P.: Generalized goal programming: an overview. Comput. & oper. Res. 10, 277-289 (1983)
[10] Lasdon, L. S.; Fox, R. L.; Ratner, M. W.: Nonlinear optimization using the generalized reduced gradient method. Rev. francaise automat. Inform. rech. Opér. 3, 73-103 (1974) · Zbl 0329.90060
[11] Lasdon, L. S.; Waren, A. D.; Ratner, M. W.: GRG2 user’s guide, technical memorandum. (1980)
[12] Leberling, H.: On finding compromise solution in multicriteria problems using the fuzzy MIN-operator. Fuzzy sets and systems 6, 105-118 (1981) · Zbl 0465.90081
[13] Luhandjula, M. K.: Compensatory operators in fuzzy linear programming with multiple objectives. Fuzzy sets and systems 8, 245-252 (1982) · Zbl 0492.90076
[14] Sakawa, M.: Interactive multiobjective decision making by the sequential proxy optimization technique: SPOT. European J. Oper. res. 9, 386-396 (1982) · Zbl 0477.90074
[15] Sakawa, M.; Mon, N.: Interactive multiobjective decision-making for nonconvex problems based on the weighted tchebycheff norm. Large scale systems 5, 69-82 (1983) · Zbl 0533.90080
[16] Sakawa, M.: Interactive computer programs for fuzzy linear programming with multiple objectives. Internat. J. Man-machine stud. 18, 489-503 (1983) · Zbl 0513.90079
[17] Sakawa, M.; Yumine, T.: Interactive fuzzy decision-making for multiobjective linear fractional programming problems. Large scale systems 5, 105-114 (1983) · Zbl 0533.90085
[18] Sakawa, M.; Yumine, T.; Nango, Y.: Interactive fuzzy decision making for multiobjective nonlinear programming problems. Trans. inst. Elec. commun. Eng. Japan 66-a, 1243-1250 (1983) · Zbl 0533.90085
[19] Steuer, R. E.; Choo, E. U.: An interactive weighted tchebycheff procedure for multiple objective programming. Math. programming 26, 326-344 (1983) · Zbl 0506.90075
[20] Wierzbicki, A. P.: The use of reference objectives in multiobjective optimization -- theoretical implications and practical experiences. Working paper WP-79-66 (1979)
[21] Yano, H.; Sakawa, M.: Trade-off rates in the weighted tchebycheff norm method. Trans. S.I.C.E. 21, 248-255 (1985) · Zbl 0656.90089
[22] Zimmermann, H. -J.: Fuzzy programming linear programming with several objective functions. Fuzzy sets and systems 1, 45-55 (1978) · Zbl 0364.90065
[23] Zimmermann, H. -J.: Fuzzy mathematical programming. Comput. & oper. Res. 10, 291-298 (1983)
[24] Zimmermann, H. -J.; Gaines, B. R.; Zadeh, L. A.: Fuzzy sets and decision analysis, TIMS studies in the management sciences 12. (1984) · Zbl 0534.00023
[25] Zionts, S.; Wallenius, J.: An interactive programming method for solving the multiple criteria problem. Management sci. 22, 652-663 (1976) · Zbl 0318.90053