The existence of fuzzy Dedekind completion of Archimedean fuzzy Riesz space
Tóm tắt
The fuzzy Riesz space is an attempt to study vector spaces with fuzzy ordering to model scenarios of more vague nature. The aim of this paper is to prove the existence of fuzzy Dedekind completion, whereas to achieve this goal, other related concepts like fuzzy order convergence, fuzzy positive operators, and their related results are also explored to enrich the theory of fuzzy Riesz spaces.
Tài liệu tham khảo
Abramovich Y, Sirotkin G (2005) On order convergence of nets. Positivity 9(3):287–292
Ajmal N, Thomas KV (1994) Fuzzy lattices. Inf Sci 79:271–291
Aliprantis CD, Burkinshaw O (2003) Locally solid Riesz spaces with applications to economics, 2nd edn. Mathematical Surveys and Monographs, vol 105. American Mathematical Society, Providence
Aliprintis CD, Burkinshaw O (2006) Positive operator. Spriger, Dordrecht
Beg I (1997) \({\sigma }\)-complete fuzzy Riesz spaces. Results Math 31:292–299
Beg I (1998) Extenssion of fuzzy positive linear operator. J Fuzzy Math 6:849–855
Beg I, Islam M (1994) Fuzzy Riesz spaces. J Fuzzy Math 2:211–241
Beg I, Islam M (1995) Fuzzy ordered linear spaces. J Fuzzy Math 3:659–670
Beg I, Islam M (1997) Fuzzy Archimedean spaces. J Fuzzy Math 5:413–423
Bodenhofer U (2003) Representations and constructions of similarity-based fuzzy orderings. Fuzzy Sets Syst 137:113–137
Chon I (2009) Partial order relations and fuzzy lattices. Korean J Math 17(4):361–374
Davvaz B, Kazanci O (2011) A new kind of fuzzy sublattice (ideal, filter) of a lattice. Int J Fuzzy Syst 13(1):55–63
Gao N, Triostsky VG, Xanthos F (2017) UO-convergence and its applications to Cesaro mean in Banach lattices. Isr J Math 220:649–689
Hong L (2015) Fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections. Analele Universitatii de Vest din Timisoara: Seria Matematica-Informatica 1:77–108
Iqbal M, Malik MGA, Bashir Y, Bashir Z (2019) The unbounded fuzzy order convergence in fuzzy Riesz spaces. Symmetry 11:971
Luxemburg WAJ, Zaanen AC (1971) Riesz spaces, I. North-Holland, Amsterdam
Park C, Movahednia E, Mosadegh SMSM, Mursaleen M (2018) Riesz fuzzy normed spaces and stability of a lattice preserving functional equation. J Comput Anal Appl 24(3):569–579
Venugopalan P (1992) Fuzzy ordered sets. Fuzzy Sets Syst 46:221–226
Walt JH (2011) The order convergence structure. Indag Math 21:138–155
Xie W, Zhang Q, Fan L (2009) The Dedekind–MacNeille completions for fuzzy posets. Fuzzy Sets Syst 160:2292–2316
Yang W (2014) Fuzzy weak regular, strong and preassociative filters in residuated lattices. Fuzzy Inf Eng 6:223–233
Yuan B, Wu W (1990) Fuzzy ideals on a distributive lattice. Fuzzy Sets Syst 35:231–240
Zaanen AC (1997) Introduction to operator theory in Riesz spaces. Springer, New York
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zadeh LA (1971) Similarity relations and fuzzy ordering. Inf Sci 8:177–200