| Title:
|
Convex $(L,M)$-fuzzy remote neighborhood operators (English) |
| Author:
|
Zhao, Hu |
| Author:
|
Jia, Li-Yan |
| Author:
|
Chen, Gui-Xiu |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2024 |
| Pages:
|
150-171 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, two kinds of remote neighborhood operators in $(L, M)$-fuzzy convex spaces are proposed, which are called convex $(L,M)$-fuzzy remote neighborhood operators. It is proved that these two kinds of convex $(L,M)$-fuzzy remote neighborhood operators can be used to characterize $(L, M)$-fuzzy convex structures. In addition, the lattice structures of two kinds of convex $ (L,M) $-fuzzy remote neighborhood operators are also given. (English) |
| Keyword:
|
convex $(L,M)$-fuzzy remote neighborhood operator |
| Keyword:
|
$(L,M)$-fuzzy convex structure |
| Keyword:
|
complete lattice |
| MSC:
|
03E72 |
| MSC:
|
52A01 |
| MSC:
|
54A40 |
| DOI:
|
10.14736/kyb-2024-2-0150 |
| . |
| Date available:
|
2024-06-03T09:37:38Z |
| Last updated:
|
2024-06-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152413 |
| . |
| Reference:
|
[1] Fang, J. M., Yue, Y. L.: $L$-fuzzy closure systems..Fuzzy Sets Syst. 161 (2010), 1242-1252. MR 2603067, |
| Reference:
|
[2] Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislowe, M., Scott, D. S.: Continuous Lattices and Domains..Cambridge University Press, Cambridge 2003. MR 1975381 |
| Reference:
|
[3] Höhle, U., Rodabaugh, S. E.: Mathematics of fuzzy sets. Logic, topology, and measure theory..Handbooks of Fuzzy Sets, 1999. MR 1788902 |
| Reference:
|
[4] Lassak, M.: On metric $B$-convexity for which diameters of any set and its hull are equal..Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 25 (1977), 969-975. MR 0461286 |
| Reference:
|
[5] Maruyama, Y.: Lattice-valued fuzzy convex geometry..RIMS Kokyuroku 1641 (2009), 22-37. |
| Reference:
|
[6] Munkres, J. R.: Topology: A First Course..Prentice-Hall, Englewood Cliffs, NJ 1975. MR 0464128 |
| Reference:
|
[7] Pang, B.: Bases and subbases in $(L,M)$-fuzzy convex spaces-.Comput. Appl. Math. 39 (2020), 41. MR 4059965, |
| Reference:
|
[8] Pang, B.: Hull operators and interval operators in $(L,M)$-fuzzy convex spaces..Fuzzy Sets Syst. 405 (2021), 106-127. MR 4191313, |
| Reference:
|
[9] Pang, B., Shi, F.-G.: Strong inclusion orders between $L$-subsets and its applications in $L$-convex spaces..Quaestion. Math. 41 (2018), 8, 1021-1043. MR 3885942, |
| Reference:
|
[10] Rosa, M. V.: On fuzzy topology fuzzy convexity spaces and fuzzy local convexity..Fuzzy Sets Syst. 62 (1994), 97-100. MR 1259888, |
| Reference:
|
[11] Shi, F. G., Xiu, Z. Y.: A new approach to the fuzzification of convex structures..J. Appl. Math. 2014 (2014), 1-12. MR 3259199, |
| Reference:
|
[12] Shi, F. G., Xiu, Z.-Y.: $(L,M)$-fuzzy convex structures..J. Nonlinear Sci. Appl. 10 (2017), 3655-3669. MR 3680307, |
| Reference:
|
[13] Soltan, V. P.: $d$-convexity in graphs. (Russian).Dokl. Akad. Nauk SSSR 272 (1983), 535-537. MR 0723776 |
| Reference:
|
[14] Šostak, A. P.: On a fuzzy topological structure Rend..Circ. Mat. Palermo 11 (1985), 89-103. MR 0897975 |
| Reference:
|
[15] Vel, M.L.J. Van De: Theory of Convex Structures..North-Holland, Amsterdam 1993. MR 1234493, |
| Reference:
|
[16] Wang, G.-J.: Theory of topological molecular lattices..Fuzzy Sets Syst. 47 (1992), 351-376. MR 1166284, |
| Reference:
|
[17] Xiu, Z. Y., Pang, B.: Base axioms and subbase axioms in $M$-fuzzifying convex spaces..Iran. J. Fuzzy Syst. 15 (2018), 75-87. MR 3840022 |
| Reference:
|
[18] Yang, H., Li, E. Q.: A new approach to interval operators in $L$-convex spaces..J. Nonlinear Convex Anal. 21 (2020), 12, 2705-2714. MR 4194712 |
| Reference:
|
[19] Yang, H., Pang, B.: Fuzzy points based betweenness relations in $L$-convex spaces..Filomat. 35 (2021), 10, 3521-3532. MR 4365455, |
| Reference:
|
[20] Yang, X. F., Li, S. G.: Net-theoretical convergence in $ (L,M) $-fuzzy cotopological spaces..Fuzzy Sets Syst. 204 (2012), 53-65. MR 2950795, |
| Reference:
|
[21] Yue, Y. L., Fang, J. M.: Categories isomorphic to the Kubiak-Šostak extension of TML..Fuzzy Sets Syst. 157 (2006), 832-842. MR 2223563, |
| Reference:
|
[22] Zhao, H., Hu, X., Sayed, O. R., El-Sanousy, E., Sayed, Y. H. Ragheb: Concave $(L,M)$-fuzzy interior operators and $(L,M)$-fuzzy hull operators..Comput. Appl. Math. 40 (2021), 301. MR 4338783, |
| Reference:
|
[23] Zhao, H., Sayed, O. R., El-Sanousy, E., Sayed, Y. H. Ragheb, Chen, G. X.: On separation axioms in $(L, M)$-fuzzy convex structures..J. Intel. Fuzzy Syst. 40 (2021), 5, 8765-8773. MR 4338783, |
| Reference:
|
[24] Zhao, H., Song, Q. L., Sayed, O. R., El-Sanousy, E., Sayed, Y. H.Ragheb, Chen, G. X.: Corrigendum to "On $(L, M)$-fuzzy convex structures"..Filomat. 35 (2021), 5, 1687-1691. MR 4364030, |
| Reference:
|
[25] Zhao, H., Jia, L. Y., Chen, G. X.: Product and coproduct structures of $(L, M)$-fuzzy hull operators..J. Intel. Fuzzy Syst. 44 (2023), 3515-3526. MR 0743509, |
| Reference:
|
[26] Zhao, H., Zhao, Y. J., Zhang, S. Y.: On $(L,N)$-fuzzy betweenness relations..Filomat. 37 (2023), 11, 3559-3573. MR 4573824, |
| Reference:
|
[27] Zhao, H., Hu, X., Chen, G. X.: A new characterization of the product of $(L, M)$-fuzzy convex structures..J. Intel. Fuzzy Syst. 45 (2023), 4535-4545. |
| . |
