Open Access

A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
Automation and Communication Systems for Autonomous Platforms (Special section, pp. 171-218), Zygmunt Kitowski, Paweł Piskur and Stanisław Hożyń (Eds.)

Cite

Alamanda, S. and Boddeti, K. (2021). Relative distance measure arithmetic-based available transfer capability calculation with uncertainty in wind power generation, International Transactions on Electrical Energy Systems 31(11): e13112. Search in Google Scholar

Barth, W. and Nuding, E. (1974). Optimale lösung von intervallgleichungssystemen, Computing 12(2): 117–125. Search in Google Scholar

Boukezzoula, R., Foulloy, L., Coquin, D. and Galichet, S. (2019). Gradual interval arithmetic and fuzzy interval arithmetic, Granular Computing 6(2): 451–471. Search in Google Scholar

Boukezzoula, R., Galichet, S., Foulloy, L. and Elmasry, M. (2014). Extended gradual interval (EGI) arithmetic and its application to gradual weighted averages, Fuzzy Sets and Systems 257: 67–84. Search in Google Scholar

Dubois, D. and Prade, H. (2008). Gradual elements in a fuzzy set, Soft Computing 12: 165–175. Search in Google Scholar

Dymova, L. (2011). Soft Computing in Economics and Finance, Springer Verlag, Berlin/Heidelberg. Search in Google Scholar

Gay, D. (1982). Solving linear interval equations, SIAM Journal on Numerical Analysis 19(4): 858–870. Search in Google Scholar

Kaczorek, T. and Ruszewski, A. (2022). Global stability of discrete-time feedback nonlinear systems with descriptor positive linear parts and interval state matrices, International Journal of Applied Mathematics and Computer Science 32(1): 5–10, DOI: 10.34768/amcs-2022-0001. Search in Google Scholar

Kreinovich, V. (2016). Solving equations (and systems of equations) under uncertainty: How different practical problems lead to different mathematical and computational formulations, Granular Computing 1(3): 171–179. Search in Google Scholar

Lodwick, W. and Dubois, D. (2015). Interval linear systems as a necessary step in fuzzy linear systems, Fuzzy Sets and Systems 281: 227–251. Search in Google Scholar

Lodwick, W. and Thipwiwatpotjana, P. (2017). Flexible and Generalized Uncertainty Optimization: Theory and Methods, Studies in Computational Intelligence, Vol. 696, Springer, Berlin/Heidelberg. Search in Google Scholar

Fortin, J., Dubois, D. and Fargier, H. (2008). Gradual numbers and their application to fuzzy interval analysis, IEEE Transactions on Fuzzy Systems 16(2): 388–402. Search in Google Scholar

Mazandarani, M., Pariz, N. and Kamyad, A. (2018). Granular differentiability of fuzzy-number-valued functions, IEEE Transactions on Fuzzy Systems 26(1): 310–323. Search in Google Scholar

Ngo, V. and Wu, W. (2021). Interval distribution power flow with relative-distance-measure arithmetic, IEEE Transactions on Smart Grid 12(5): 3858–3867. Search in Google Scholar

Piegat, A. and Dobryakova, L. (2020). A decomposition approach to type 2 interval arithmetic, International Journal of Applied Mathematics and Computer Science 30(1): 185–201, DOI: 10.34768/amcs-2020-0015. Search in Google Scholar

Piegat, A. and Landowski, M. (2012). Is the conventional interval-arithmetic correct?, Journal of Theoretical and Applied Computer Science 6(2): 27–44. Search in Google Scholar

Piegat, A. and Landowski, M. (2013). Two interpretations of multidimensional RDM interval arithmetic: Multiplication and division, International Journal of Fuzzy Systems 15(4): 486–496. Search in Google Scholar

Piegat, A. and Pluciński, M. (2015a). Computing with words with the use of inverse RDM models of membership functions, International Journal of Applied Mathematics and Computer Science 25(3): 675–688, DOI: 10.1515/amcs-2015-0049. Search in Google Scholar

Piegat, A. and Pluciński, M. (2015b). Fuzzy number addition with the application of horizontal membership functions, The Scientific World Journal 2015, Article ID: 367214. Search in Google Scholar

Piegat, A. and Pluciński, M. (2017). Fuzzy number division and the multi-granularity phenomenon, Bulletin of the Polish Academy of Sciences: Technical Sciences 65(4): 497–511. Search in Google Scholar

Piegat, A. and Pluciński, M. (2022a). The optimal tolerance solutions of the basic linear equation and the explanation of the Lodwick’s anomaly, Applied Sciences 12(4): 4382. Search in Google Scholar

Piegat, A. and Pluciński, M. (2022b). Realistic optimal tolerant solution of the quadratic interval equation and determining the optimal control decision on the example of plant fertilization, Applied Sciences 12(21): 10725. Search in Google Scholar

Shary, S. (1991). Optimal solution of interval linear algebraic systems, Interval Computations 2: 7–30. Search in Google Scholar

Shary, S. (1992). On controlled solution set of interval algebraic systems, Interval Computations 6(6): 66–75. Search in Google Scholar

Shary, S. (1994). Solving the tolerance problem for interval linear systems, Interval Computations 2: 6–26. Search in Google Scholar

Shary, S. (1995). Solving the linear interval tolerance problem, Mathematics and Computers in Simulation 39(1–2): 53–85. Search in Google Scholar

Siahlooei, E. and Shahzadeh Fazeli, S. (2018). Two iterative methods for solving linear interval systems, Applied Computational Intelligence and Soft Computing 2018, Article ID: 2797038. Search in Google Scholar

Zadeh, L. (1975). The concept of a linguistic variable and its application to approximate reasoning—I, Information Sciences 8(3): 199–249. Search in Google Scholar

eISSN:
2083-8492
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics