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)
Measuring the satisfaction of constraints in fuzzy linear programming. (English) Zbl 1015.90098
Summary: The paper proposes a new kind of method for solving fuzzy linear programming problems based on the satisfaction (or fulfillment) degree of the constraints. Using a new ranking method of fuzzy numbers, the fulfillment of the constraints can be measured. Then the properties of the ranking index are discussed. With this ranking index, the decision maker can make the constraints tight or loose based on his optimistic or pessimistic attitude and get the optimal solution from the fuzzy constraint space. The corresponding value of objective distribution function can be obtained. A numerical example illustrates the merits of the approach.

90C70Fuzzy programming
68T20AI problem solving (heuristics, search strategies, etc.)
90C08Special problems of linear programming
Full Text: DOI
[1] Baas, S. M.; Kwakernaak, H.: Rating and ranking of multiple aspect alternatives using fuzzy sets. Automatica 13, 47-58 (1977) · Zbl 0363.90010
[2] Baoding, L.; Kakuzo, I.: Chance constrained programming with fuzzy parameters. Fuzzy sets and systems 94, 227-237 (1998) · Zbl 0923.90141
[3] Bellmann, R. E.; Zadeh, L. A.: Decision making in fuzzy environment. Management sci. 17, 141-164 (1970)
[4] Buckley, J. J.: Joint solution to fuzzy programming problems. Fuzzy sets and systems 72, 215-220 (1995) · Zbl 0845.90127
[5] Buckley, J. J.; Feuring, T.: Evolutionary algorithms to fuzzy problemsfuzzy linear programming. Fuzzy sets and systems 109, 35-53 (2000) · Zbl 0956.90064
[6] Buckley, J. J.; Feuring, T.; Hayashi, Y.: Neural net solutions to fuzzy linear programming. Fuzzy sets and systems 106, 99-111 (1999) · Zbl 0957.90132
[7] Cheng, C. H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy sets and systems 95, 307-317 (1998) · Zbl 0929.91009
[8] Dubois, D.: Linear programming with fuzzy data. The analysis of fuzzy information, 241-263 (1987)
[9] Dubois, D.; Prade, H.: Ranking fuzzy numbers in the setting of possibility theory. Inform. sci. 30, 183-224 (1983) · Zbl 0569.94031
[10] Fang, S. C.; Hu, C. F.: Linear programming with fuzzy coefficients in constraints. Comput. math. Appl. 37, 63-76 (1999) · Zbl 0931.90069
[11] Fortemps, P.: Job shop scheduling with imprecise durationsa fuzzy approach. IEEE trans. Fuzzy systems 5, 557-569 (1997)
[12] Fortemps, P.; Roubens, M.: Ranking and defuzzification methods based on area compensation. Fuzzy sets and systems 82, 319-330 (1996) · Zbl 0886.94025
[13] Ichihashi, H.; Tanaka, H.: Formulation and analysis of fuzzy linear programming problem with interval coefficients. J. Japan indust. Management assoc 40, 320-329 (1988)
[14] Julien, B.: A extension to possiblistic linear programming. Fuzzy sets and systems 64, 195-206 (1994)
[15] Liou, T. S.; Wang, M. J.: Ranking fuzzy numbers with integral value. Fuzzy sets and systems 50, 247-255 (1992) · Zbl 1229.03043
[16] Lushu, L.; Zhaohan, S.: A new approach to fuzzy multiple objective programming. J. fuzzy math. 4, No. 2, 355-361 (1996) · Zbl 0857.90138
[17] Maleki, H. R>; Tata, M.; Mashinchi, M.: Linear programming with fuzzy variables. Fuzzy sets and systems 109, 21-33 (2000) · Zbl 0956.90068
[18] Nakahara, Y.: User oriented ranking criteria and its application to fuzzy mathematical programming problems. Fuzzy sets and systems 94, 275-286 (1998) · Zbl 0919.90146
[19] Nakahara, Y.; Sasak, M.; Gen, M.: On the linear programming problems with interval coefficients. Internat J. Comput. indust. Eng. 23, 301-304 (1997)
[20] Ramik, J.; Remelfanger, A.: A single and multivalued order on fuzzy numbers and its use in linear programming with fuzzy coefficients. Fuzzy sets and systems 57, 203-208 (1993)
[21] Ramik, J. R.; Rommelfanger, H.: Fuzzy mathematical programming based on some new inequality relations. Fuzzy sets and systems 81, 77-87 (1996) · Zbl 0877.90085
[22] Rommelfanger, H.: Fuzzy linear programming and application. European J. Oper. res. 92, 512-527 (1996) · Zbl 0914.90265
[23] Saade, J. J.; Schwarzlander, H.: Ordering fuzzy sets over the real linea approach based on decision making under uncertainty. Fuzzy sets and systems 50, 237-246 (1992)
[24] Tanaka, H.; Ichihashi, H.: A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers. Control cybernet. 13, 185-194 (1984) · Zbl 0551.90062
[25] Tong, S.: Interval number and fuzzy number linear programming. Fuzzy sets and systems 66, 301-306 (1994)
[26] Tseng, T.; Klein, C. M.: New algorithm for the ranking procedure in fuzzy decision making. IEEE trans. Systems man cybernet. 19, 1289-1296 (1989)
[27] Yuan, Y.: Criteria for evaluating fuzzy ranking methods. Fuzzy sets and systems 44, 139-157 (1991) · Zbl 0747.90003