Characterization of extension map on fuzzy weakly cut-stable map

Nana Ma; Qingjun Luo; Geni Xu; Nana Ma; Qingjun Luo; Geni Xu

doi:10.3934/math.2022421

AIMS Mathematics

2022, Volume 7, Issue 5: 7507-7518. doi: 10.3934/math.2022421

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Characterization of extension map on fuzzy weakly cut-stable map

School of Statistics, Xi'an University of Finance and Economics, Xi'an 710100, China

Received: 14 April 2021 Revised: 06 December 2021 Accepted: 07 December 2021 Published: 14 February 2022
MSC : 06B35, 08A72, 54C20

In this paper, based on a complete residuated lattice, we propose the definition of fuzzy weakly cut-stable map and prove the extension property of the fuzzy weakly cut-stable map. Following this, it is explored the conditions under which the extension map to be fuzzy order isomorphism.
- quantitative domain,
- fuzzy weakly cut-stable map,
- extension map,
- isomorphism
Citation: Nana Ma, Qingjun Luo, Geni Xu. Characterization of extension map on fuzzy weakly cut-stable map[J]. AIMS Mathematics, 2022, 7(5): 7507-7518. doi: 10.3934/math.2022421

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Abstract

In this paper, based on a complete residuated lattice, we propose the definition of fuzzy weakly cut-stable map and prove the extension property of the fuzzy weakly cut-stable map. Following this, it is explored the conditions under which the extension map to be fuzzy order isomorphism.

References

[1]	G. Giers, K. H. Hofmann K. Keimel, J. D. Lawson, M. Mislove, D. S. Scott, Continuous lattices and domains, Cambridge University Press, 2003.
[2]	A. Bishop, A universal mapping characterization of the completion by cuts, Algebr. Univ., 8 (1978), 349–353. https://doi.org/10.1007/BF02485405 doi: 10.1007/BF02485405
[3]	M. Erne, The Dedekind-MacNeille completion as a reflector, Order, 8 (1991), 159–173. https://doi.org/10.1007/BF00383401 doi: 10.1007/BF00383401
[4]	M. Erne, Ideal completions and compactifications, Appl. Categor. Struct., 9 (2001), 217–243. https://doi.org/10.1023/A:1011260817824 doi: 10.1023/A:1011260817824
[5]	M. Liu, B. Zhao, A non-frame valued cartesian closed category of liminf complete fuzzy orders, Fuzzy Sets Syst., 321 (2017), 50–54. https://doi.org/10.1016/j.fss.2016.07.008 doi: 10.1016/j.fss.2016.07.008
[6]	N. N. Ma, B. Zhao, An equivalent of algebraic $\Omega$-categories, J. Math. Res. Appl., 37 (2017), 148–162.
[7]	H. L. Lai, D. X. Zhang, Closedness of the category of liminf complete fuzzy orders, Fuzzy Sets Syst., 282 (2016), 86–98. https://doi.org/10.1016/j.fss.2014.10.031 doi: 10.1016/j.fss.2014.10.031
[8]	W. Li, H. L. Lai, D. X. Zhang, Yoneda completeness and flat completeness of ordered fuzzy sets, Fuzzy Sets Syst., 313 (2017), 1–24. https://doi.org/10.1016/j.fss.2016.06.009 doi: 10.1016/j.fss.2016.06.009
[9]	K. R. Wagner, Solving recursive domain equations with enriched categories, Pittsburgh: Carnegie Mellon University, School of Computer Science, 1994.
[10]	R. Belohlavek, Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic, 128 (2004), 277–298. https://doi.org/10.1016/j.apal.2003.01.001 doi: 10.1016/j.apal.2003.01.001
[11]	W. X. Xie, Q. Y. Zhang, L. Fan, The Dedekind-MacNeille completions for fuzzy posets, Fuzzy Sets Syst., 160 (2009), 2292–2316. https://doi.org/10.1016/j.fss.2008.12.002 doi: 10.1016/j.fss.2008.12.002
[12]	K. Y. Wang, B. Zhao, Join-completions of $L$-ordered sets, Fuzzy Sets Syst., 199 (2012), 92–107. https://doi.org/10.1016/j.fss.2011.12.011 doi: 10.1016/j.fss.2011.12.011
[13]	N. N. Ma, B. Zhao, Fuzzy cut-stable maps and its extension property, J. Intell. Fuzzy Syst., 30 (2016), 2213–2221. https://doi.org/10.3233/IFS-151990 doi: 10.3233/IFS-151990
[14]	R. Halas, J. Lihova, On weakly cut-stable maps, Inform. Sci., 180 (2010), 971–983. https://doi.org/10.1016/j.ins.2009.11.025 doi: 10.1016/j.ins.2009.11.025
[15]	R. Belohlavek, Some properties of residuated lattices, Czech. Math. J., 53 (2003), 161–171. https://doi.org/10.1023/A:1022935811257 doi: 10.1023/A:1022935811257
[16]	Q. Y. Zhang, W. X. Xie, L. Fan, Fuzzy complete lattices, Fuzzy Sets Syst., 160 (2009), 2275–2291. https://doi.org/10.1016/j.fss.2008.12.001 doi: 10.1016/j.fss.2008.12.001
[17]	N. N. Ma, B. Zhao, Some results on fuzzy $Z_{L}$-continuous $($algebraic$)$ poset, Soft Comput., 22 (2018), 4549–4559. https://doi.org/10.1007/s00500-017-2924-9 doi: 10.1007/s00500-017-2924-9
[18]	U. Hohle, S. E. Rodabaugh, Mathematical of fuzzy sets: Logic, topology, and measure theory, Kluwer Academic Publishers, Boston/Dordrecht/London, 1999.

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