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# Application of Geometric Approach for Fuzzy Linear Systems to a Fuzzy Input-Output Analysis

Nizami Gasilov1, Sahin Emrah Amrahov2 , Afet Golayoglu Fatullayev ˇ 1, Halil Ibrahim Karaka¸s1, Ömer Akın3

Ankara University, Computer Engineering Department, Ankara, Turkey
TOBB ETU, Ankara, Turkey

Computer Modeling in Engineering & Sciences 2012, 88(2), 93-106. https://doi.org/10.3970/cmes.2012.088.093

## Abstract

Uncertainties in some parameters of problems of Leontief input-output analysis lead naturally to fuzzy linear systems. In this work, we consider input-output model, where the technology matrix is crisp and the vector of final outputs is fuzzy. The model is expressed by a fuzzy linear system with crisp matrix and with fuzzy right-hand side vector. We apply a geometric method for solving the system. The method finds the solution in the form of a fuzzy set of vectors. The solution set is shown to be a parallelepiped in coordinate space and is expressed by an explicit formula. The features of the proposed method are illustrated by examples.

## Keywords

APA Style
Gasilov, N., , S.E.A., , A.G.F.ˇ., Karaka¸s, H.I., Akın, Ö. (2012). Application of geometric approach for fuzzy linear systems to a fuzzy input-output analysis. Computer Modeling in Engineering & Sciences, 88(2), 93-106. https://doi.org/10.3970/cmes.2012.088.093
Vancouver Style
Gasilov N, SEA, AGFˇ, Karaka¸s HI, Akın Ö. Application of geometric approach for fuzzy linear systems to a fuzzy input-output analysis. Comput Model Eng Sci. 2012;88(2):93-106 https://doi.org/10.3970/cmes.2012.088.093
IEEE Style
N. Gasilov, S.E.A. , A.G.F.ˇ. , H.I. Karaka¸s, and Ö. Akın "Application of Geometric Approach for Fuzzy Linear Systems to a Fuzzy Input-Output Analysis," Comput. Model. Eng. Sci., vol. 88, no. 2, pp. 93-106. 2012. https://doi.org/10.3970/cmes.2012.088.093

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