Quotient space of intervals
DOI:
https://doi.org/10.5540/03.2022.009.01.0295Keywords:
Interval space, linear space of intervals, quotient space of intervals.Abstract
This article studies the quotient space of intervals, for this is defined an equivalence relation considering a symmetric difference, is obtained the quotient space of intervals where is defined a specific representative of the equivalence class, and an appropriated norm and metric is defined to proof that this space is a complete metric space.
Downloads
References
Sergey Mironovich Aseev. “Quasilinear operators and their application in the theory of multivalued mappings”. In: Trudy Matematicheskogo Instituta imeni VA Steklova 167 (1985), pp. 25–52.
Y. Chalco-Cano, H. Román-Flores, and M.D. Jiménez-Gamero. “Generalized derivative and π-derivative for set-valued functions”. In: Information Sciences 181.11 (2011), pp. 2177– 2188. doi: 10.1016/j.ins.2011.01.023. url: https://doi.org/10.1016%2Fj.ins.2011. 01.023.
Y. Chalco-Cano et al. “Algebra of generalized Hukuhara differentiable interval-valued functions: review and new properties”. In: Fuzzy Sets and Systems 375 (2019), pp. 53–69. doi: 10.1016/j.fss.2019.04.006. url: https://doi.org/10.1016%2Fj.fss.2019.04.006.
Yurilev Chalco-Cano, Heriberto Román-Flores, and María-Dolores Jiménez-Gamero. “Generalized derivative and π-derivative for set-valued functions”. In: Information Sciences 181.11 (2011), pp. 2177–2188.
Dug Hun Hong and Hae Young Do. “Additive decomposition of fuzzy quantities”. In: Information sciences 88.1-4 (1996), pp. 201–207.
Hans Rådström. “An embedding theorem for spaces of convex sets”. In: Proceedings of the American Mathematical Society 3.1 (1952), pp. 165–169.
Marko Antonio Rojas-Medar et al. “Fuzzy quasilinear spaces and applications”. In: Fuzzy Sets and Systems 152.2 (2005), pp. 173–190.
Luciano Stefanini and Barnabás Bede. “Generalized Hukuhara differentiability of intervalvalued functions and interval differential equations”. In: Nonlinear Analysis: Theory, Methods & Applications 71.3-4 (2009), pp. 1311–1328. doi: 10.1016/j.na.2008.12.005. url: https://doi.org/10.1016%2Fj.na.2008.12.005.
Elder J. Villamizar-Roa, Y. Chalco-Cano, and H. Roman-Flores. “Interval-valued functions in a quotient space”. In: 2015 Annual Conference of the North American Fuzzy Information Processing Society (NAFIPS) held jointly with 2015 5th World Conference on Soft Computing (WConSC). IEEE, 2015. doi: 10.1109/nafips-wconsc.2015.7284182. url: https://doi.org/10.1109%2Fnafips-wconsc.2015.7284182.
