Is an interval the right result of arithmetic operations on intervals?

Bader, F. and Nipkow, T. (1998). Term Rewriting and All That, Cambridge University Press, Cambridge.10.1017/CBO9781139172752Search in Google Scholar

Birkhoff, G. (1967). Lattice Theory, Vol. XXV, Colloquium Publications, American Mathematical Society, Providence, RI.Search in Google Scholar

Chalco-Cano, Y., Lodwick, W. and Bede, B. (2014). Single level constraint interval arithmetic, Fuzzy Sets and Systems257: 146–168.10.1016/j.fss.2014.06.017Search in Google Scholar

Dabala, K. (2009). Research of possibilities of interval arithmetic application to induction motors efficiency determination, Zeszyty Problemowe: Maszyny Elektryczne (84): 39–44.Search in Google Scholar

Dymova, L. (2011). Soft Computing in Economics and Finance, Springer, Berlin/Heidelberg.10.1007/978-3-642-17719-4Open DOISearch in Google Scholar

Figuiredo, L. and Stolfi, J. (2004). Affine arithmetic: Concepts and applications, Numerical Algorithms37(1): 147–158.10.1023/B:NUMA.0000049462.70970.b6Open DOISearch in Google Scholar

Hanss, M. (2005). Applied Fuzzy Arithmetic, Springer, Berlin/Heidelberg.Search in Google Scholar

Hayes, B. (2003). A lucid interval, American Scientist91(6): 484–488.10.1511/2003.6.484Open DOISearch in Google Scholar

Kaucher, E. (1980). Interval analysis in the extended interval space IR, Computing Supplement2: 33–49.10.1007/978-3-7091-8577-3_3Search in Google Scholar

Kovalerchuk, B. and Kreinovich, V. (2016). Comparisons of applied tasks with intervals, fuzzy sets and probability approaches, Proceedings of the 2016 IEEE International Conference on Fuzzy Systems (FUZZ), Vancouver, Canada, pp. 1478–1483.Search in Google Scholar

Leontief, W. (1949). The Structure of the American Economy, 1919–1935, Oxford University Press, London.Search in Google Scholar

Leontief, W. (1966). Input-Output Economics, Oxford University Press, New York, NY.Search in Google Scholar

Lodwick, W. (1999). Constrained interval arithmetic, Technical Report CCM, University of Colorado at Denver, Denver, CO.Search in Google Scholar

Lodwick, W. and Dubois, D. (2015). Interval linear systems as a necessary step in fuzzy linear systems, Fuzzy Sets and Systems281: 227–251.10.1016/j.fss.2015.03.018Search in Google Scholar

Lyashko, M. (2005). The optimal solution of an interval systems of linear algebraic equations, Reliable Computing11(2): 227–251.10.1007/s11155-005-3032-6Open DOISearch in Google Scholar

Mazarhuiya, F., Mahanta, A. and Baruah, H. (2011). Solution of fuzzy equation a+x = b using method of superimposition, Applied Mathematics2(8): 1039–1045.10.4236/am.2011.28144Open DOISearch in Google Scholar

Moore, R. (1996). Interval Analysis, Prentice Hall, Englewood Cliffs, NJ.Search in Google Scholar

Moore, R., Baker, K. and Cloud, M. (2009). Introduction to Interval Analysis, SIAM, Philadelphia, PA.10.1137/1.9780898717716Search in Google Scholar

Moore, R. and Young, C. (1959). Interval analysis I, Technical Report LMSD285875, Lockheed Missiles and Space Division, Sunnyvale, CA.Search in Google Scholar

Neumaier, A. (1990). Interval Methods for Systems of Equations, Cambridge University Press, Cambridge.10.1017/CBO9780511526473Search in Google Scholar

Pedrycz, W., Skowron, A. and Kreinovich, V. (2008). Handbook of Granular Computing, John Wiley&Sons, Chichester.10.1002/9780470724163Search in Google Scholar

Piegat, A. and Landowski, M. (2012). Is the conventional interval arithmetic correct?, Journal of Theoretical and Applied Computer Science6(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 Systems15(4): 488–496.Search in Google Scholar

Piegat, A. and Pluciński, M. (2015). Computing with words with the use of inverse RDM models of membership functions, International Journal of Applied Mathematics and Computer Science25(3): 675–688, DOI: 10.1515/amcs-2015-0049.10.1515/amcs-2015-0049Open DOISearch in Google Scholar

Piegat, A. and Plucinski, M. (2017). Fuzzy number division and the multi-granularity phenomenon, Bulletin of the Polish Academy of Sciences: Technical Sciences65(4): 497–511.10.1515/bpasts-2017-0055Search in Google Scholar

Piegat, A. and Tomaszewska, K. (2013). Decision making under uncertainty using info-gap theory and a new multidimensional RDM interval arithmetic, Przegląd Elektrotechniczny89(8): 71–76.Search in Google Scholar

Pilarek, M. (2010). Solving systems of linear equations using the interval extended zero method and multimedia extensions, Scientific Research of the Institute of Mathematics and Computer Science9(2): 203–212.Search in Google Scholar

Popova, E. (1998). Algebraic solutions to a class of interval equations, Journal of Universal Computer Science4(1): 48–67.Search in Google Scholar

Sevastjanov, P. and Dymova, L. (2009). A new method for solving internal and fuzzy equations: Linear case, Information Sciences179: 925–937.10.1016/j.ins.2008.11.031Search in Google Scholar

Shary, S. (1996). Algebraic approach to the interval linear static identification, tolerance and control problems, or one more application of Kaucher arithmetic, Reliable Computing2(1): 3–33.10.1007/BF02388185Open DOISearch in Google Scholar

Shary, S. (2002). A new technique in systems analysis under interval uncertainty and ambiguity, Reliable Computing8: 321–418.10.1023/A:1020505620702Search in Google Scholar

Sunaga, T. (1958). Theory of an interval algebra and its application to numerical analysis, RAAG Memoirs2: 547–564.Search in Google Scholar

Warmus, M. (1956). Calculus of approximations, Bulletin de l’Académie Polonaise des Sciences Cl. III4(5): 253–259.Search in Google Scholar