zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Optimality conditions for linear programming problems with fuzzy coefficients. (English) Zbl 1142.90522
Summary: The optimality conditions for linear programming problems with fuzzy coefficients are derived in this paper. Two solution concepts are proposed by considering the orderings on the set of all fuzzy numbers. The solution concepts proposed in this paper will follow from the similar solution concept, called the nondominated solution, in the multiobjective programming problem. Under these settings, the optimality conditions will be naturally elicited.
90C70Fuzzy programming
65K05Mathematical programming (numerical methods)
90C05Linear programming
[1], Fuzzy sets in decision analysis, operations research and statistics (1998)
[2], Fuzzy optimization: recent advances (1994)
[3]Lai, Y. -J.; Hwang, C. -L.: Fuzzy mathematical programming: methods and applications, Lecture notes in economics and mathematical systems 394 (1992) · Zbl 0793.90094
[4]Lai, Y. -J.; Hwang, C. -L.: Fuzzy multiple objective decision making: methods and applications, Lecture notes in economics and mathematical systems 404 (1994) · Zbl 0810.90138
[5], Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty (1990)
[6]Bellman, R. E.; Zadeh, L. A.: Decision making in a fuzzy environment, Management science 17, 141-164 (1970) · Zbl 0224.90032
[7]Buckley, J. J.: Possibilistic linear programming with triangular fuzzy numbers, Fuzzy sets and systems 26, 135-138 (1988) · Zbl 0644.90059 · doi:10.1016/0165-0114(88)90013-9
[8]Buckley, J. J.: Solving possibilistic linear programming problems, Fuzzy sets and systems 31, 329-341 (1989) · Zbl 0671.90049 · doi:10.1016/0165-0114(89)90204-2
[9]Julien, B.: An extension to possibilistic linear programming, Fuzzy sets and systems 64, 195-206 (1994)
[10]Luhandjula, M. K.; Ichihashi, H.; Inuiguchi, M.: Fuzzy and semi-infinite mathematical programming, Information sciences 61, 233-250 (1992) · Zbl 0773.90093 · doi:10.1016/0020-0255(92)90052-A
[11]Herrera, F.; Kovács, M.; Verdegay, J. L.: Optimality for fuzzified mathematical programming problems: A parametric approach, Fuzzy sets and systems 54, 279-285 (1993) · Zbl 0790.90078 · doi:10.1016/0165-0114(93)90373-P
[12]Zimmemmann, H. -J.: Fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems 1, 45-55 (1978) · Zbl 0364.90065 · doi:10.1016/0165-0114(78)90031-3
[13]Zimmermann, H. -J.: Applications of fuzzy set theory to mathematical programming, Information sciences 36, 29-58 (1985) · Zbl 0578.90095 · doi:10.1016/0020-0255(85)90025-8
[14]Inuiguchi, M.; Ichihashi, H.; Kume, Y.: Modality constrained programming problems: A unified approach to fuzzy mathematical programming problems in the setting of possibility theory, Information sciences 67, 93-126 (1993) · Zbl 0770.90078 · doi:10.1016/0020-0255(93)90086-2
[15]Inuiguchi, M.; Tanino, T.; Sakawa, M.: Membership function elicitation in possibilistic programming problems, Fuzzy sets and systems 111, 29-45 (2000) · Zbl 0938.90075 · doi:10.1016/S0165-0114(98)00450-3
[16]Tanaka, H.; Asai, K.: Fuzzy linear programming problems with fuzzy numbers, Fuzzy sets and systems 13, 1-10 (1984) · Zbl 0546.90062 · doi:10.1016/0165-0114(84)90022-8
[17]Lee, E. S.; Li, R. J.: Fuzzy multiple objective programming and compromise programming with Pareto optimum, Fuzzy sets and systems 53, 275-288 (1993) · Zbl 0807.90130 · doi:10.1016/0165-0114(93)90399-3
[18]Li, R. -J.; Lee, E. S.: Fuzzy approaches to multicriteria de novo programs, Journal of mathematical analysis and applications 153, 97-111 (1990)
[19]Li, R. -J.; Lee, E. S.: An exponential membership function for fuzzy multiple objective linear programming, Computers and mathematics with applications 22, No. 12, 55-60 (1991) · Zbl 0749.90088 · doi:10.1016/0898-1221(91)90147-V
[20]W. Rodder, H.-J. Zimmermann, Duality in fuzzy linear programming, in: Internat. Symp. on Extremal Methods and Systems Analysis, University of Texas at Austin, 1977, p. 415–427 · Zbl 0428.90035
[21]Bector, C. R.; Chandra, S.: On duality in linear programming under fuzzy environment, Fuzzy sets and systems 125, 317-325 (2002) · Zbl 1014.90117 · doi:10.1016/S0165-0114(00)00122-6
[22]Bector, C. R.; Chandra, S.; Vijay, V.: Duality in linear programming with fuzzy parameters and matrix games with fuzzy pay-offs, Fuzzy sets and systems 146, 253-269 (2004) · Zbl 1061.90120 · doi:10.1016/S0165-0114(03)00260-4
[23]Bector, C. R.; Chandra, S.; Vidyottama, V.: Matrix games with fuzzy goals and fuzzy linear programming duality, Fuzzy optimization and decision making 3, 255-269 (2004) · Zbl 1079.90183 · doi:10.1023/B:FODM.0000036866.18909.f1
[24]Liu, Y.; Shi, Y.; Liu, Y. -H.: Duality of fuzzy MC2 linear programming: A constructive approach, Journal of mathematical analysis and applications 194, 389-413 (1995) · Zbl 0843.90130 · doi:10.1006/jmaa.1995.1307
[25]Ramík, J.: Duality in fuzzy linear programming: some new concepts and results, Fuzzy optimization and decision making 4, 25-39 (2005) · Zbl 1079.90184 · doi:10.1007/s10700-004-5568-z
[26]Verdegay, J. L.: A dual approach to solve the fuzzy linear programming problems, Fuzzy sets and systems 14, 131-141 (1984) · Zbl 0549.90064 · doi:10.1016/0165-0114(84)90096-4
[27]Wu, H. -C.: Duality theory in fuzzy linear programming problems with fuzzy coefficients, Fuzzy optimization and decision making 2, No. 1, 61-73 (2003)
[28]Zadeh, L. A.: Fuzzy sets, Information and control 8, 338-353 (1965) · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[29]Zadeh, L. A.: The concept of linguistic variable and its application to approximate reasoning I, II and III, Information sciences 8, 199-249 (1975) · Zbl 0397.68071
[30]Horst, R.; Pardalos, P. M.; Thoai, N. V.: Introduction to global optimization, (2000)
[31]Bazarra, M. S.; Sherali, H. D.; Shetty, C. M.: Nonlinear programming, (1993)
[32]Rudin, W.: Principles of mathematical analysis, (1976) · Zbl 0346.26002