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Further research on separated degrees of $M$-fuzzifying convex spaces

Yıl 2025, Cilt: 54 Sayı: 1, 57 - 74, 28.02.2025

Han-liang Huang Zhen-yu Xiu

https://doi.org/10.15672/hujms.1348816

Öz

In this paper, we redefine the concepts of join spaces and product spaces of $M$-fuzzifying convex spaces. Then we further investigate the $S_i$ ($i=0,1,2$) separated degrees of an $M$-fuzzifying convex space in a logical viewpoint. Finally, we study the $S_i$ ($i=0,1,2$) separated degrees of an $M$-fuzzifying convex space from the aspect of convergence structures.

Anahtar Kelimeler

M-fuzzifying convex structure separated degree M-CP degree M-CC degree M-fuzzifying convergence structure

Kaynakça

  • [1] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24, 182-193, 1968.
  • [2] Y.Y. Dong and F.G. Shi, On the disjoint sums of M-fuzzifying convex spaces, Filomat 35 (14), 4675-4690, 2021.
  • [3] J.M. Fang, Stratified L-ordered convergence structures, Fuzzy Sets Syst. 161, 2130- 2149, 2010.
  • [4] Y. Gao and B. Pang, Subcategories of the category of $\top$-convergence spaces, Hacet. J. Math. Stat., in press.
  • [5] U. Höhle and A.P. Šostak, Axiomatic foudations of fixed-basis fuzzy topology, in: U. Höhle, S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Handbook Series 3, Kluwer Academic Publishers, Boston, Dordrecht, London, 123-173, 1999.
  • [6] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985.
  • [7] C. Liang and F. Li, A degree approach to separated axioms in M-fuzzifying convex spaces, J. Intell. Fuzzy Syst. 36, 2885-2893, 2019.
  • [8] C. Liang and F. Li, $S_3$ and $S_4$ separation axioms in M-fuzzifying convex spaces, J. Nonlinear Convex A. 21 (12), 2737-2745, 2020.
  • [9] Y. Maruyama, Lattice-valued fuzzy convex geometry, RIMS Kokyuroku 1641, 22-37, 2009.
  • [10] B. Pang, Convergence structures in M-fuzzifying convex spaces, Quaest. Math. 43 (11), 1541-1561, 2020.
  • [11] B. Pang, Quantale-valued convex structures as lax algebras, Fuzzy Sets Syst. 473, 108737, 2023.
  • [12] B. Pang, Fuzzy convexities via overlap functions, IEEE T. Fuzzy Syst. 31 (4), 1071- 1082, 2023.
  • [13] B. Pang and Z.Y. Xiu, Lattice-valued interval operators and its induced lattice-valued convex structures, IEEE T. Fuzzy Syst. 26 (3), 1525-1534, 2018.
  • [14] M.V. Rosa, On fuzzy topology fuzzy convexity spaces and fuzzy local convexity, Fuzzy Sets Syst. 62, 97-100, 1994.
  • [15] F.G. Shi and E.Q. Li, The restricted hull operator of M-fuzzifying convex structures, J. Intell. Fuzzy Syst. 30, 409-421, 2015.
  • [16] F.G. Shi and Z.Y. Xiu, A new approach to the fuzzification of convex structures, J. Appl. Math. 2014, 249183, 2014.
  • [17] F.G. Shi and Z.Y. Xiu, (L,M)-fuzzy convex structures, J. Nonlinear Sci. Appl. 10 (7), 3655-3669, 2017.
  • [18] Y. Shi, B. Pang and B. De Baets, Fuzzy structures induced by fuzzy betweenness relations, Fuzzy Sets and Systems 466, 108443, 2023.
  • [19] A.P. Šostak, On a fuzzy topological structure, Rend. Circ. Mat. Palermo (Suppl. Ser. II) 11, 89-103, 1985.
  • [20] M.L.J. Van de Vel, Theory of Convex Structures, North Holland, Amsterdam, 1993.
  • [21] G.J. Wang, Theory of topological molecular lattices, Fuzzy Sets Syst. 47, 351-376, 1992.
  • [22] X.Y. Wu and S.Z. Bai, On M-fuzzifying JHC convex structures and M-fuzzifying Peano interval spaces, J. Intell. Fuzzy Syst. 30, 2447-2458, 2016.
  • [23] X.Y. Wu, E.Q. Li and S.Z. Bai, Geometric properties of M-fuzzifying convex structures, J. Intell. Fuzzy Syst. 32, 4273-4284, 2017.
  • [24] X.Y.Wu, B. Davvaz and S.Z. Bai, On M-fuzzifying convex matroids and M-fuzzifying independent structures, J. Intell. Fuzzy Syst. 33, 269-280, 2017.
  • [25] Z.Y. Xiu and B. Pang, A degree approach to special mappings between M-fuzzifying convex spaces, J. Intell. Fuzzy Syst. 35, 705-716, 2018.
  • [26] Z.Y. Xiu and B. Pang, Base axioms and subbase axioms in M-fuzzifying convex spaces, Iran. J. Fuzzy Syst. 15 (2), 75-87, 2018.
  • [27] Z.Y. Xiu and F.G. Shi, M-fuzzifying interval spaces, Iran. J. Fuzzy Syst. 147 (1), 145-162, 2017.
  • [28] H. Yang and B. Pang, Fuzzy points based betweenness relations in L-convex spaces, Filomat 35 (10), 3521-3532, 2021.
  • [29] W. Yao, Quantitative domains via fuzzy sets: Part I: continuity of fuzzy directed complete posets, Fuzzy Sets Syst. 161, 973-987, 2010.
  • [30] W. Yao, An approach to fuzzy frames via fuzzy posets, Fuzzy Sets Syst. 166, 75-89, 2011.
  • [31] M.S. Ying, A new approach for fuzzy topology (I), Fuzzy Sets Syst. 39, 303-321, 1991.
  • [32] L.A. Zadeh, Fuzzy sets, Inform. Control 8, 238-353, 1965.
  • [33] L. Zhang and B. Pang, A new approach to lattice-valued convergence groups via —- filters, Fuzzy Sets Syst. 455, 198-221, 2023.
  • [34] L. Zhang and B. Pang, Convergence structures in (L,M)-fuzzy convex spaces, Filomat 37, 2859-2877, 2023.
  • [35] L. Zhang and B. Pang, Monoidal closedness of the category of $\top$-semiuniform convergence spaces, Hacet. J. Math. Stat. 51 (5), 1348-1370, 2022.
  • [36] L. Zhang, B. Pang and W. Li, Subcategories of the category of stratified (L,M)- semiuniform convergence tower spaces, Iran. J. Fuzzy Syst. 20 (4), 179-192, 2023.
  • [37] F.F. Zhao and B. Pang, Equivalence among L-closure (interior) operators, L-closure (interior) systems and L-enclosed (internal) relations, Filomat 36 (3), 979-1003, 2022.
  • [38] X.W. Zhou and F.G. Shi, Some separation axioms in L-convex spaces, J. Intell. Fuzzy Syst. 37, 8053-8062, 2019.
  • [39] X.W. Zhou and F.G. Shi, On the sum of L-convex spaces, J. Intell. Fuzzy Syst. 40, 4503-4515, 2021.

Yıl 2025, Cilt: 54 Sayı: 1, 57 - 74, 28.02.2025

Han-liang Huang Zhen-yu Xiu

https://doi.org/10.15672/hujms.1348816

Öz

Kaynakça

  • [1] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24, 182-193, 1968.
  • [2] Y.Y. Dong and F.G. Shi, On the disjoint sums of M-fuzzifying convex spaces, Filomat 35 (14), 4675-4690, 2021.
  • [3] J.M. Fang, Stratified L-ordered convergence structures, Fuzzy Sets Syst. 161, 2130- 2149, 2010.
  • [4] Y. Gao and B. Pang, Subcategories of the category of $\top$-convergence spaces, Hacet. J. Math. Stat., in press.
  • [5] U. Höhle and A.P. Šostak, Axiomatic foudations of fixed-basis fuzzy topology, in: U. Höhle, S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Handbook Series 3, Kluwer Academic Publishers, Boston, Dordrecht, London, 123-173, 1999.
  • [6] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985.
  • [7] C. Liang and F. Li, A degree approach to separated axioms in M-fuzzifying convex spaces, J. Intell. Fuzzy Syst. 36, 2885-2893, 2019.
  • [8] C. Liang and F. Li, $S_3$ and $S_4$ separation axioms in M-fuzzifying convex spaces, J. Nonlinear Convex A. 21 (12), 2737-2745, 2020.
  • [9] Y. Maruyama, Lattice-valued fuzzy convex geometry, RIMS Kokyuroku 1641, 22-37, 2009.
  • [10] B. Pang, Convergence structures in M-fuzzifying convex spaces, Quaest. Math. 43 (11), 1541-1561, 2020.
  • [11] B. Pang, Quantale-valued convex structures as lax algebras, Fuzzy Sets Syst. 473, 108737, 2023.
  • [12] B. Pang, Fuzzy convexities via overlap functions, IEEE T. Fuzzy Syst. 31 (4), 1071- 1082, 2023.
  • [13] B. Pang and Z.Y. Xiu, Lattice-valued interval operators and its induced lattice-valued convex structures, IEEE T. Fuzzy Syst. 26 (3), 1525-1534, 2018.
  • [14] M.V. Rosa, On fuzzy topology fuzzy convexity spaces and fuzzy local convexity, Fuzzy Sets Syst. 62, 97-100, 1994.
  • [15] F.G. Shi and E.Q. Li, The restricted hull operator of M-fuzzifying convex structures, J. Intell. Fuzzy Syst. 30, 409-421, 2015.
  • [16] F.G. Shi and Z.Y. Xiu, A new approach to the fuzzification of convex structures, J. Appl. Math. 2014, 249183, 2014.
  • [17] F.G. Shi and Z.Y. Xiu, (L,M)-fuzzy convex structures, J. Nonlinear Sci. Appl. 10 (7), 3655-3669, 2017.
  • [18] Y. Shi, B. Pang and B. De Baets, Fuzzy structures induced by fuzzy betweenness relations, Fuzzy Sets and Systems 466, 108443, 2023.
  • [19] A.P. Šostak, On a fuzzy topological structure, Rend. Circ. Mat. Palermo (Suppl. Ser. II) 11, 89-103, 1985.
  • [20] M.L.J. Van de Vel, Theory of Convex Structures, North Holland, Amsterdam, 1993.
  • [21] G.J. Wang, Theory of topological molecular lattices, Fuzzy Sets Syst. 47, 351-376, 1992.
  • [22] X.Y. Wu and S.Z. Bai, On M-fuzzifying JHC convex structures and M-fuzzifying Peano interval spaces, J. Intell. Fuzzy Syst. 30, 2447-2458, 2016.
  • [23] X.Y. Wu, E.Q. Li and S.Z. Bai, Geometric properties of M-fuzzifying convex structures, J. Intell. Fuzzy Syst. 32, 4273-4284, 2017.
  • [24] X.Y.Wu, B. Davvaz and S.Z. Bai, On M-fuzzifying convex matroids and M-fuzzifying independent structures, J. Intell. Fuzzy Syst. 33, 269-280, 2017.
  • [25] Z.Y. Xiu and B. Pang, A degree approach to special mappings between M-fuzzifying convex spaces, J. Intell. Fuzzy Syst. 35, 705-716, 2018.
  • [26] Z.Y. Xiu and B. Pang, Base axioms and subbase axioms in M-fuzzifying convex spaces, Iran. J. Fuzzy Syst. 15 (2), 75-87, 2018.
  • [27] Z.Y. Xiu and F.G. Shi, M-fuzzifying interval spaces, Iran. J. Fuzzy Syst. 147 (1), 145-162, 2017.
  • [28] H. Yang and B. Pang, Fuzzy points based betweenness relations in L-convex spaces, Filomat 35 (10), 3521-3532, 2021.
  • [29] W. Yao, Quantitative domains via fuzzy sets: Part I: continuity of fuzzy directed complete posets, Fuzzy Sets Syst. 161, 973-987, 2010.
  • [30] W. Yao, An approach to fuzzy frames via fuzzy posets, Fuzzy Sets Syst. 166, 75-89, 2011.
  • [31] M.S. Ying, A new approach for fuzzy topology (I), Fuzzy Sets Syst. 39, 303-321, 1991.
  • [32] L.A. Zadeh, Fuzzy sets, Inform. Control 8, 238-353, 1965.
  • [33] L. Zhang and B. Pang, A new approach to lattice-valued convergence groups via —- filters, Fuzzy Sets Syst. 455, 198-221, 2023.
  • [34] L. Zhang and B. Pang, Convergence structures in (L,M)-fuzzy convex spaces, Filomat 37, 2859-2877, 2023.
  • [35] L. Zhang and B. Pang, Monoidal closedness of the category of $\top$-semiuniform convergence spaces, Hacet. J. Math. Stat. 51 (5), 1348-1370, 2022.
  • [36] L. Zhang, B. Pang and W. Li, Subcategories of the category of stratified (L,M)- semiuniform convergence tower spaces, Iran. J. Fuzzy Syst. 20 (4), 179-192, 2023.
  • [37] F.F. Zhao and B. Pang, Equivalence among L-closure (interior) operators, L-closure (interior) systems and L-enclosed (internal) relations, Filomat 36 (3), 979-1003, 2022.
  • [38] X.W. Zhou and F.G. Shi, Some separation axioms in L-convex spaces, J. Intell. Fuzzy Syst. 37, 8053-8062, 2019.
  • [39] X.W. Zhou and F.G. Shi, On the sum of L-convex spaces, J. Intell. Fuzzy Syst. 40, 4503-4515, 2021.
Toplam 39 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Topoloji
Bölüm Matematik
Yazarlar

Han-liang Huang 0000-0003-3402-4433

Zhen-yu Xiu 0000-0002-5231-9182

Erken Görünüm Tarihi 14 Nisan 2024
Yayımlanma Tarihi 28 Şubat 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 54 Sayı: 1

Kaynak Göster

APA Huang, H.-l., & Xiu, Z.-y. (2025). Further research on separated degrees of $M$-fuzzifying convex spaces. Hacettepe Journal of Mathematics and Statistics, 54(1), 57-74. https://doi.org/10.15672/hujms.1348816
AMA Huang Hl, Xiu Zy. Further research on separated degrees of $M$-fuzzifying convex spaces. Hacettepe Journal of Mathematics and Statistics. Şubat 2025;54(1):57-74. doi:10.15672/hujms.1348816
Chicago Huang, Han-liang, ve Zhen-yu Xiu. “Further Research on Separated Degrees of $M$-Fuzzifying Convex Spaces”. Hacettepe Journal of Mathematics and Statistics 54, sy. 1 (Şubat 2025): 57-74. https://doi.org/10.15672/hujms.1348816.
EndNote Huang H-l, Xiu Z-y (01 Şubat 2025) Further research on separated degrees of $M$-fuzzifying convex spaces. Hacettepe Journal of Mathematics and Statistics 54 1 57–74.
IEEE H.-l. Huang ve Z.-y. Xiu, “Further research on separated degrees of $M$-fuzzifying convex spaces”, Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 1, ss. 57–74, 2025, doi: 10.15672/hujms.1348816.
ISNAD Huang, Han-liang - Xiu, Zhen-yu. “Further Research on Separated Degrees of $M$-Fuzzifying Convex Spaces”. Hacettepe Journal of Mathematics and Statistics 54/1 (Şubat 2025), 57-74. https://doi.org/10.15672/hujms.1348816.
JAMA Huang H-l, Xiu Z-y. Further research on separated degrees of $M$-fuzzifying convex spaces. Hacettepe Journal of Mathematics and Statistics. 2025;54:57–74.
MLA Huang, Han-liang ve Zhen-yu Xiu. “Further Research on Separated Degrees of $M$-Fuzzifying Convex Spaces”. Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 1, 2025, ss. 57-74, doi:10.15672/hujms.1348816.
Vancouver Huang H-l, Xiu Z-y. Further research on separated degrees of $M$-fuzzifying convex spaces. Hacettepe Journal of Mathematics and Statistics. 2025;54(1):57-74.

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