# Gram-schmidt Approach for Linear System of Equations with Fuzzy Parameters

Volume 1, Issue 2, pp 80--89
• 1976 Views

### Authors

S. H. Nasseri - Department of Mathematics and Computer Sciences, Mazandaran University, P.O. Box 47415-1468, Babolsar, Iran M. Sohrabi

### Abstract

In this paper, we focus on solving linear system of equations with fuzzy parameters. We employ Dubois and Prades approximate arithmetic operators on LR fuzzy numbers to find a positive fuzzy vector $\tilde{x}$ which satisfies $\tilde{A}\otimes \tilde{x}=\tilde{b}$, where $\tilde{A}$ and $\tilde{b}$ are the fuzzy matrix and vector, respectively. We shall illustrate our method by solving some numerical examples.

### Share and Cite

##### ISRP Style

S. H. Nasseri, M. Sohrabi, Gram-schmidt Approach for Linear System of Equations with Fuzzy Parameters, Journal of Mathematics and Computer Science, 1 (2010), no. 2, 80--89

##### AMA Style

Nasseri S. H., Sohrabi M., Gram-schmidt Approach for Linear System of Equations with Fuzzy Parameters. J Math Comput SCI-JM. (2010); 1(2):80--89

##### Chicago/Turabian Style

Nasseri, S. H., Sohrabi, M.. "Gram-schmidt Approach for Linear System of Equations with Fuzzy Parameters." Journal of Mathematics and Computer Science, 1, no. 2 (2010): 80--89

### Keywords

• Fully fuzzy linear system
• Fuzzy number
• QR-decomposition
• Gram-Schmidt method.

•  93C42
•  93C05
•  03B52
•  15B15

### References

• [1] H. J. Ohlbach, Modelling periodic temporal notions by labelled partitionings of the real numbers, University of Munich, 2004 (2004), 42 pages

• [2] H. J. Ohlbach, Calendrical calculations with time partitionings and fuzzy time intervals, in: Principles and Practice of Semantic Web Reasoning, 2004 (2004), 118--133

• [3] H. J. Ohlbach, Fuzzy time intervals and relations–the FuTIRe library, Institute for Computer Science, Munich (2004)

• [4] H. J. Ohlbach, Relations between fuzzy time intervals, 11th International Symposium on Temporal Representation and Reasoning, 2004 (2004), 44--51

• [5] H. J. Ohlbach, The role of labelled partitionings for modeling periodic temporal notions, 11th International Symposium on Temporal Representation and Reasoning, 2004 (2004), 60--63

• [6] F. Bry, B. Lorenz, H. J. Ohlbach, S. Spranger, On Reasoning on Time and Location on the Web, in: Principles and Practice of Semantic Web Reasoning, 2003 (2003), 69--83

• [7] J. F. Allen, Maintaining knowledge about temporal intervals, Communications of the ACM, 26 (1983), 832--843

• [8] F. Baader, D. Calvanese, D. M. Guinness, D. Nardi, P. P. Schneider, The description logic handbook: Theory, implementation and applications, Cambridge university press, Cambridge (2003)

• [9] B. T. Lee, M. Fischetti, Weaving the Web: the original design and ultimate destiny of the World Wide Web by its inventor, Harper, San Francisco (1999)

• [10] D. R. Cukierman, A Formalization of structured temporal objects and Repetition, Simon Fraser University (PhD thesis), Vancouver (2003)

• [11] D. Dubois, H. Prade, Fundamentals of fuzzy sets, Kluwer Academic Publishers, Boston (2000)

• [12] J. O'Rourke, Computational geometry in C, Cambridge University Press, Cambridge (1998)

• [13] G. Nagypal, B. Motik, A fuzzy model for representing uncertain, subjective and vague temporal knowledge in ontologies, Proceedings of the International Conference on Ontologies, Databases and Applications of Semantics (ODBASE), 2003 (2003), 906--923

• [14] K. U. Schulz, F. Weigel, Systematic and architecture for a resource representing knowledge about named entities, in: Principles and Practice of Semantic Web Reasoning, 2003 (2003), 189--207

• [15] , The ACM Computing Classification System, , (2001),

• [16] N. Dershowitz, E. M. Reingold, Calendrical Calculations, Cambridge University Press, Cambridge (1997)

• [17] H. J. Ohlbach, About real time, calendar systems and temporal notions, in: Advances in Temporal Logic, 2000 (2000), 319--338

• [18] H. J. Ohlbach, Calendar logic, in: Temporal Logic: Mathematical Foundations and Computational Aspects, 2000 (2000), 489--586

• [19] H. J. Ohlbach, D. Gabbay, Calendar logic, Journal of Applied Non-Classical Logics, 8 (1998), 291--323

• [20] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338--353

• [21] J. E. Goodman, J. O’Rourke, Handbook of Discrete and Computational Geometry, CRC Press, Boca Raton (1997)