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)
An interactive satisficing method based on alternative tolerance for fuzzy multiple objective optimization. (English) Zbl 1205.90262
Summary: An interactive satisficing method based on alternative tolerance is proposed for fuzzy multiple objective optimization. The new tolerances of the dissatisficing objectives are generated using an auxiliary programming problem. According to the alternative tolerant limits, either the membership functions are changed, or the objective constraints are added. The lexicographic two-phase programming is implemented to find the final solution. The results of the dissatisficing objectives are iteratively improved. The presented method not only acquires the efficient or weak efficient solution of all the objectives, but also satisfies the progressive preference of decision maker. Numerical examples show its power.
MSC:
90C29Multi-objective programming; goal programming
90C70Fuzzy programming
References:
[1]Chankong, V.; Haimes, Y. V.: Multiobjective decision making: theory and methodology, (1983) · Zbl 0622.90002
[2]Lai, Y. J.; Hwang, C. L.: Fuzzy multiple objective decision making: methods and applications, (1994)
[3]Steuer, R. E.: Multiple criteria optimization: theory, computation, and application, (1985)
[4]Tamiz, M.: Multi-objective programming and goal programming: theories and applications, (1996)
[5]Urli, B.; Nadeau, R.: PROMISE/scenarios: an interactive method for multiobjective stochastic linear programming under partial uncertainty, Eur. J. Oper. res. 155, 361-372 (2004) · Zbl 1045.90060 · doi:10.1016/S0377-2217(02)00859-7
[6]Abo-Sinna, M. A.; Abou-El-Enie, T. H. M.: An interactive algorithm for large scale multiple objective programming problems with fuzzy parameters through TOPSIS approach, Appl. math. Comput. 177, 515-527 (2006) · Zbl 1096.65051 · doi:10.1016/j.amc.2005.11.030
[7]Abo-Sinna, M. A.; Amer, A. H.; El Sayed, H. H.: An interactive algorithm for decomposing the parametric space in fuzzy multiobjective dynamic programming problem, Appl. math. Comput. 177, 684-699 (2006) · Zbl 1089.65044 · doi:10.1016/j.amc.2005.04.107
[8]Aghezzaf, B.; Ouaderhman, T.: An interactive interior point algorithm for multiobjective linear programming problems, Oper. res. Lett. 29, 163-170 (2001) · Zbl 0993.90081 · doi:10.1016/S0167-6377(01)00089-X
[9]Yang, J. B.; Li, D.: Normal vector identification and interactive tradeoff analysis using minimax formulation in multiobjective optimization, IEEE trans. Syst. man cybernet. A: syst. Humans 32, No. 3, 305-319 (2002)
[10]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, Manage. sci. 19, No. 4, 357-368 (1972) · Zbl 0247.90069 · doi:10.1287/mnsc.19.4.357
[11]Benayoun, R.; De Montagolfier, J.; Tergny, J.; Larichev, O.: Linear programming with multiple objective functions: step method (STEM), Math. program. 1, No. 3, 366-375 (1971) · Zbl 0242.90026 · doi:10.1007/BF01584098
[12]A.P. Wierzbicki, The use of reference objectives in multiobjective optimization, Multiple Criteria Decision Making Theory and Application, in: Fandel, Gal (Eds.), Springer-Verlag, New York, 1980, pp. 468 – 486. · Zbl 0435.90098
[13]Liu, B.: Theory and practice of uncertain programming, (2002)
[14]Bellman, R. E.; Zadeh, L. A.: Decision-making in a fuzzy environment, Manage. sci. 17, B141-B164 (1970) · Zbl 0224.90032
[15]Hannan, E.: Linear programming with multiple fuzzy goals, Fuzzy sets syst. 6, 235-248 (1981) · Zbl 0465.90080 · doi:10.1016/0165-0114(81)90002-6
[16]Tiwari, R. N.; Dharmar, S.; Rao, J. R.: Fuzzy goal programming – an additive model, Fuzzy sets syst. 24, 27-34 (1987) · Zbl 0627.90073 · doi:10.1016/0165-0114(87)90111-4
[17]Li, S. Y.; Yang, Y. P.; Teng, C. J.: Fuzzy goal programming with multiple priorities via generalized varying-domain optimization method, IEEE trans. Fuzzy syst. 12, No. 5, 596-605 (2004)
[18]Tanaka, H.; Okuda, T.; Asai, K.: On fuzzy mathematical programming, J. cybernet. 3, 37-46 (1974) · Zbl 0297.90098 · doi:10.1080/01969727308545912
[19]Zimmermann, H. J.: Fuzzy programming and linear programming with several objective functions, Fuzzy sets syst. 1, 45-55 (1978) · Zbl 0364.90065 · doi:10.1016/0165-0114(78)90031-3
[20]Sakawa, M.: Interactive multiobjective decision making by sequential proxy optimization technique: SPOT, Eur. J. Oper. res. 9, No. 4, 386-396 (1982) · Zbl 0477.90074 · doi:10.1016/0377-2217(82)90183-7
[21]Sakawa, M.; Yano, H.; Yumine, T.: An interactive fuzzy satisficing method for multiobjective linear-programming problems and its application, IEEE trans. Syst. man cybernet. 17, No. 4, 654-661 (1987) · Zbl 0634.90081
[22]Sakawa, M.; Kosuke, K.; Hideki, K.: An interactive fuzzy satisficing method for multiobjective linear programming problems with random variable coefficients through a probability maximization model, Fuzzy sets syst. 146, 205-220 (2004) · Zbl 1061.90124 · doi:10.1016/j.fss.2004.04.003
[23]Mohan, C.; Nguyen, H. T.: Reference direction interactive method for solving multiobjective fuzzy programming problems, Eur. J. Oper. res. 107, 599-613 (1998) · Zbl 0968.90072 · doi:10.1016/S0377-2217(97)00161-6
[24]Werners, B.: An interactive fuzzy programming system, Fuzzy sets syst. 23, 131-147 (1987) · Zbl 0634.90076 · doi:10.1016/0165-0114(87)90105-9
[25]Werners, B.: Interactive multiple objective programming subject to flexible constraints, Eur. J. Oper. res. 31, 342-349 (1987) · Zbl 0636.90085 · doi:10.1016/0377-2217(87)90043-9
[26]Wang, X. M.; Qin, Z. L.; Hu, Y. D.: An interactive algorithm for multicriteria decision making: the attainable reference point method, IEEE trans. Syst. man cybernet. A: syst. Humans 31, No. 3, 194-198 (2001)
[27]Lee, E. S.; Li, R. J.: Fuzzy multiple objective programming and compromise programming with Pareto optimum, Fuzzy sets syst. 53, 275-288 (1993) · Zbl 0807.90130 · doi:10.1016/0165-0114(93)90399-3