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)
Solving a class of fuzzy linear programs by using semi-infinite programming techniques. (English) Zbl 1061.90122
Summary: This paper deals with a class of Fuzzy Linear Programming problems characterized by the fact that the coefficients in the constraints are modeled as LR-fuzzy numbers with different shapes. Solving such problems is usually more complicated than finding a solution when all the fuzzy coefficients have the same shape. We propose a primal semi-infinite algorithm as a valuable tool for solving this class of Fuzzy Linear programs and, we illustrate it by means of several examples.

MSC:
90C70Fuzzy programming
90C34Semi-infinite programming
WorldCat.org
Full Text: DOI
References:
[1] Anderson, E. J.; Lewis, A. S.: An extension of the simplex algorithm for semi-infinite linear programming. Math. programming 44, 247-269 (1989) · Zbl 0682.90058
[2] Carlsson, C.; Korhonen, P.: A parametric approach to fuzzy linear programming. Fuzzy sets and systems 20, 17-30 (1986) · Zbl 0603.90093
[3] Chanas, S.: On the interval approximation of a fuzzy number. Fuzzy sets and systems 122, 353-359 (2001) · Zbl 1010.03523
[4] Chang, P. T.; Lee, E. S.: Fuzzy arithmetics and comparison of fuzzy numbers. Fuzzy optimization: recent advances, 69-82 (1994) · Zbl 0925.90384
[5] M. Delgado, J. Kacprzyk, J.-L. Verdegay, M.A. Vila (Eds.), Fuzzy Optimization: Recent Advances, Physica-Verlag, Wursburg, 1994. · Zbl 0812.00011
[6] Dubois, D.; Kerre, E.; Mesiar, R.; Prade, H.: Fuzzy interval analysis. Fundamentals of fuzzy sets, 483-581 (2000) · Zbl 0988.26020
[7] Dubois, D.; Prade, H.: Systems of linear fuzzy constraints. Fuzzy sets and systems 3, 37-48 (1980) · Zbl 0425.94029
[8] D. Dubois, H. Prade, Fuzzy numbers: an overview, in: J. Bezdek (Ed.), Analysis of Fuzzy Information, vol. 2, CRC-Press, Boca Raton, FL, 1988, pp. 3--39. · Zbl 0663.94028
[9] D. Dubois, H. Prade (Eds.), Fundamentals of Fuzzy Sets, Kluwer Academic, Dordrecht, 2000. · Zbl 1018.03045
[10] Fang, S. C.; Hu, C. F.; Wang, H. F.; Wu, S. Y.: Linear programming with fuzzy coefficients in constraints. Comput. math. Appl. 37, 63-76 (1999) · Zbl 0931.90069
[11] Goberna, M. A.; Lopez, M. A.: Linear semi-infinite optimization. (1998) · Zbl 0635.90059
[12] Hettich, R.; Kortanek, K. O.: Semi-infinite programmingtheory, methods and applications. SIAM rev. 35, 380-429 (1993) · Zbl 0784.90090
[13] Inuiguchi, M.; Ichihashi, H.; Tanaka, H.: Fuzzy programming--a survey of recent developments. Stochastic versus fuzzy approaches to multi objective mathematical programming under uncertainty, 45-68 (1990) · Zbl 0728.90091
[14] Klir, G. J.; Folger, T. A.: Fuzzy sets, uncertainty and information. (1988) · Zbl 0675.94025
[15] Kolesárová, A.: Triangular norm-based additions of similar fuzzy numbers and preserving of similarity. Busefal 69, 43-54 (1997) · Zbl 0920.04009
[16] Lai, Y. J.; Hwang, C. L.: Fuzzy mathematical programming: theory and applications. (1992) · Zbl 0793.90094
[17] León, T.; Sanmatı\acute{}as, S.; Vercher, E.: A multi-local optimization algorithm. Top 6, 1-18 (1998) · Zbl 0910.90258
[18] León, T.; Sanmatı\acute{}as, S.; Vercher, E.: On the numerical treatment of linearly constrained semi-infinite problems. Eur. J. Oper. res. 121, 78-91 (2000)
[19] T. León, E. Vercher, New descent rules for solving the linear semi-infinite programming problem, Oper. Res. Lett. (1994) 105--114. · Zbl 0810.90123
[20] Pedrycz, W.: Why triangular membership functions?. Fuzzy sets and systems 64, 21-30 (1994)
[21] Ramik, J.; Rimanek, J.: Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy sets and systems 16, 123-138 (1985)
[22] Reemtsen, R.; Görner, S.: Numerical methods for semi-infinite programming: a survey. Semi-infinite programming, 195-275 (1998) · Zbl 0908.90255
[23] Rommelfanger, H.; Slowinski, R.: Fuzzy linear programming with single or multiple objective functions. Fuzzy sets in decision analysis, operations research and statistics, 179-213 (1998)
[24] Romelfanger, H.: Inequality relations in fuzzy constraints and its use in linear fuzzy optimization. The interface between artificial intelligence and operational research in fuzzy environment, 195-211 (1989)
[25] Sakawa, M.: Fuzzy nonlinear programming with single or single or multiple objective functions. Fuzzy sets in decision analysis, operations research and statistics, 215-248 (1998) · Zbl 0927.90106
[26] Tanaka, H.; Guo, P.: Possibilistic data analysis for operations research. (1999) · Zbl 0931.91011
[27] Tanaka, H.; Ichihashi, H.; Asai, K.: A formulation of fuzzy linear programming problems based on comparison of fuzzy numbers. Control cybernet. 13, 186-194 (1984) · Zbl 0551.90062
[28] Zimmermann, H. -J.: Fuzzy set theory and its applications. (1996) · Zbl 0845.04006