Abstract
Integer Programming problems in which they exists some lack of precision of a vague nature in their formulation are considered. It is also provided a classification of this kind of problems, and a description for each of them is carried out. In particular, we focuse on the fuzzy boolean case for which a solution method is shown.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bellman, R.E. and Zadeh, L.A. (1970): Decision Making in a Fuzzy Environment. Man. Sci. 17 (B), 4, 141–164.
Delgado, M., J.L. Verdegay and M.A. Vila (1989): A General Model for Fuzzy Linear Programming. Fuzzy Sets and Systems 29, 21–29.
Fabian, C. and M. Stoica (1984): Fuzzy Integer Programming. In Fuzzy Sets and Decision Analysis. H.J. Zimmermann, L. A. Zadeh and B. R. Gaines (Eds). North-Holland, 123-131.
Gal, T. (1979): Postoptimal Analyses, Parametric Programming and Related Topics. McGraw Hill.
Garfinkel, R.S and Nemhauser, G.L. (1972): Integer Programming. Wiley Interscience.
Geoffrion, A. M. and R. Nauss (1977): Parametric and Postoptimality Analysis in Integer Linear Programming. Management Science 23, 453–466.
Marsten, R.E. and Morin, T.L. (1977): Parametric Integer Programming: The Right-Hand-Side Case. Annals of Discrete Math. 1, 375–390.
Nauss, R. M. (1979): Parametric Integer Programming. University of Missouri Press.
Negoita, C.V. and D.A. Ralescu (1975): Applications of Fuzzy Sets to Systems Analysis. Birkhauser.
Orlovski, S.A. (1977): On Programming with Fuzzy Constraint Sets. Kybernetes 6, 197–201.
Taha, H.A. (1975): Integer Programming. Theory, Applications and Computations. Academic Press.
Verdegay, J.L. (1982): Fuzzy Mathematical Programming. In Fuzzy Information and Decision Processes. M.M. Gupta and E. Sanchez (Eds). North-Holland, 231-237.
Yager, R.R. (1988): A Mathematical Programming Approach to Inference with the Capability of Implementing Default Rules. Int. J. of Man-Machine Studies 29, 685–714.
Zadeh, L.A. (1978): Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1, 3–28.
Zadeh, L. A. (1979): Calculus of Fuzzy Restrictions. In Fuzzy Sets and their Applications to Cognitive and Decision Processes. L.A. Zadeh, K.S. Fu, K. Tanaka and M. Shimura, (Eds.), Academic Pres, 1-40.
Zimmermann, H.J. and M.A. Pollatschek (1984): Fuzzy 0-1 Linear Programs. In Fuzzy Sets and Decision Analysis. H. J. Zimmermann, L.A. Zadeh and B. R. Gaines (Eds). North-Holland, 133-145.
Zimmermann, H.J. (1987): Fuzzy Sets, Decision Making and Expert Systems. Kluwer Academic Publishers.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Herrera, F., Verdegay, J.L. (1991). Approaching Fuzzy Integer Linear Programming Problems. In: Fedrizzi, M., Kacprzyk, J., Roubens, M. (eds) Interactive Fuzzy Optimization. Lecture Notes in Economics and Mathematical Systems, vol 368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45700-5_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-45700-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54577-4
Online ISBN: 978-3-642-45700-5
eBook Packages: Springer Book Archive