Research article

Novel categories of spaces in the frame of fuzzy soft topologies

  • Received: 12 December 2023 Revised: 18 January 2024 Accepted: 29 January 2024 Published: 04 February 2024
  • MSC : 54A40, 54D10

  • In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called $ FS\delta $-separation and $ FS\delta $-regularity axioms by using fuzzy soft $ \delta $-open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the $ FS\delta $-separation and $ FS\delta $-regularity axioms are harmonic and heredity property. Additionally, we examine the connections between $ FS{\delta }^* $-compactness and $ FS\delta $-separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology.

    Citation: Tareq M. Al-shami, Salem Saleh, Alaa M. Abd El-latif, Abdelwaheb Mhemdi. Novel categories of spaces in the frame of fuzzy soft topologies[J]. AIMS Mathematics, 2024, 9(3): 6305-6320. doi: 10.3934/math.2024307

    Related Papers:

  • In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called $ FS\delta $-separation and $ FS\delta $-regularity axioms by using fuzzy soft $ \delta $-open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the $ FS\delta $-separation and $ FS\delta $-regularity axioms are harmonic and heredity property. Additionally, we examine the connections between $ FS{\delta }^* $-compactness and $ FS\delta $-separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology.



    加载中


    [1] A. M. Abd El-latif, Fuzzy soft separation axioms based on fuzzy $\beta$-open soft sets, Ann. Fuzzy Math. Inform., 11 (2016), 223–239.
    [2] A. M. Abd El-latif, Some fuzzy soft topological properties based on fuzzy b-open soft sets, J. Indian Math. Soc., 83 (2016), 251–267. https://www.informaticsjournals.com/index.php/jims/article/view/6608
    [3] J. C. R. Alcantud, The relationship between fuzzy soft and soft topologies, Int. J. Fuzzy Syst., 24 (2022), 1653–1668. https://doi.org/10.1007/s40815-021-01225-4 doi: 10.1007/s40815-021-01225-4
    [4] J. C. R. Alcantud, Complemental fuzzy sets: A semantic justification of q-rung orthopair fuzzy sets, IEEE T. Fuzzy Syst., 31 (2023), 4262–4270, https://doi.org/10.1109/TFUZZ.2023.3280221 doi: 10.1109/TFUZZ.2023.3280221
    [5] B. Ahmad, A. Kharal, On fuzzy soft sets, Adv. Fuzzy Syst., 2009 (2009), 586507. https://doi.org/10.1155/2009/586507 doi: 10.1155/2009/586507
    [6] A. Atay, Disjoint union of fuzzy soft topological spaces, AIMS Math., 8 (2023), 10547–10557. https://doi.org/10.3934/math.2023535 doi: 10.3934/math.2023535
    [7] T. M. Al-shami, Comments on some results related to soft separation axioms, Afr. Mat., 31 (2020), 1105–1119. https://doi.org/10.1007/s13370-020-00783-4 doi: 10.1007/s13370-020-00783-4
    [8] T. M. Al-shami, On soft separation axioms and their applications on decision-making problem, Math. Probl. Eng., 2021 (2021), 8876978. https://doi.org/10.1155/2021/8876978 doi: 10.1155/2021/8876978
    [9] T. M. Al-shami, Soft somewhat open sets: Soft separation axioms and medical application to nutrition, Comput. Appl. Math., 41 (2022), 216. https://doi.org/10.1007/s40314-022-01919-x doi: 10.1007/s40314-022-01919-x
    [10] T. M. Al-shami, (2, 1)-Fuzzy sets: Properties, weighted aggregated operators and their applications to multi-criteria decision-making methods, Complex Intell. Syst., 9 (2023), 1687–1705. https://doi.org/10.1007/s40747-022-00878-4 doi: 10.1007/s40747-022-00878-4
    [11] T. M. Al-shami, J. C. R. Alcantud, A. Mhemdi, New generalization of fuzzy soft sets: $(a, b)$-Fuzzy soft sets, AIMS Math., 8 (2023), 2995–3025. https://doi.org/10.3934/math.2023155 doi: 10.3934/math.2023155
    [12] T. M. Al-shami, J. C. R. Alcantud, A. A. Azzam, Two new families of supra-soft topological spaces defined by separation axioms, Mathematics, 10 (2022), 4488. https://doi.org/10.3390/math10234488 doi: 10.3390/math10234488
    [13] T. M. Al-shami, M. E. El-Shafei, On supra soft topological ordered spaces, Arab J. Basic Appl. Sci., 26 (2019), 433–445. https://doi.org/10.1080/25765299.2019.1664101 doi: 10.1080/25765299.2019.1664101
    [14] T. M. Al-shami, H. Z. Ibrahim, A. Mhemdi, Radwan Abu-Gdairi, $n^{th}$ power root fuzzy sets and its topology, Int. J. Fuzzy Log. Inte., 22 (2022), 350–365. http://doi.org/10.5391/IJFIS.2022.22.4.350 doi: 10.5391/IJFIS.2022.22.4.350
    [15] T. M. Al-shami, A. Mhemdi, Generalized frame for orthopair fuzzy sets: $(m, n)$-Fuzzy sets and their applications to multi-criteria decision-making methods, Information, 14 (2023), 56. https://doi.org/10.3390/info14010056 doi: 10.3390/info14010056
    [16] T. M. Al-shami, A. Mhemdi, R. Abu-Gdairi, M. E. El-Shafei, Compactness and connectedness via the class of soft somewhat open sets, AIMS math., 8 (2023), 815–840. https://doi.org/10.3934/math.2023040 doi: 10.3934/math.2023040
    [17] T. M. Al-shami, A. Mhemdi, A. Rawshdeh, H. Al-jarrah, Soft version of compact and Lindelöf spaces using soft somewhere dense set, AIMS Math., 6 (2021), 8064–8077. https://doi.org/10.3934/math.2021468 doi: 10.3934/math.2021468
    [18] S. Atmaca, I. Zorlutuna, On fuzzy soft topological spaces, Ann. Fuzzy Math. Inform., 5 (2013), 377–386.
    [19] A. Aygünoǧlu, H. Aygün, Some notes on soft topological spaces, Neural Comput. Appl., 21 (2012), 113–119. https://doi.org/10.1007/s00521-011-0722-3 doi: 10.1007/s00521-011-0722-3
    [20] N. Çağman, S. Karataş, S. Enginoglu, Soft topology, Comput. Math. Appl., 62 (2011) 351–358. https://doi.org/10.1016/j.camwa.2011.05.016 doi: 10.1016/j.camwa.2011.05.016
    [21] M. E. El-Shafei, T. M. Al-shami, Applications of partial belong and total non-belong relations on soft separation axioms and dec ision-making problem, Comput. Appl. Math., 39 (2020), 138. https://doi.org/10.1007/s40314-020-01161-3 doi: 10.1007/s40314-020-01161-3
    [22] M. E. El-Shafei, M. Abo-Elhamayel, T. M. Al-shami, Partial soft separation axioms and soft compact spaces, Filomat, 32 (2018), 4755–4771. https://doi.org/10.2298/FIL1813755E doi: 10.2298/FIL1813755E
    [23] S. A. El-Sheikh, R. A. Hosny, A. M. Abd El-latif, Characterizations of $b$-soft separation axioms in soft topological spaces, Inf. Sci. Lett., 4 (2015), 125–133. https://doi.org/10.12785/isl/040303 doi: 10.12785/isl/040303
    [24] F. Feng, Y. B. Jun, X. Liu, L. F. Li, An adjustable approach to fuzzy soft set based decision making, J. Comput. Appl. Math., 234 (2010), 10–20. https://doi.org/10.1016/j.cam.2009.11.055 doi: 10.1016/j.cam.2009.11.055
    [25] F. Feng, C. X. Li, B. Davvaz, M. I. Ali, Soft sets combined with fuzzy sets and rough sets: A tentative approach, Soft Comput., 14 (2010), 899–911. https://doi.org/10.1007/s00500-009-0465-6 doi: 10.1007/s00500-009-0465-6
    [26] R. Gao, J. Wu, Filter with its applications in fuzzy soft topological spaces, AIMS Math., 6 (2020), 2359–2368. https://doi.org/10.3934/math.2021143 doi: 10.3934/math.2021143
    [27] H. Z. Ibrahim, T. M. Al-shami, A. Mhemdi, Applications of $n^{th}$ power root fuzzy sets in multicriteria decision making, J. Math., 2023 (2023), 1487724. https://doi.org/10.1155/2023/1487724 doi: 10.1155/2023/1487724
    [28] H.Z.Ibrahim, T. M. Al-shami, M. Arar, M. Hosny, $k^{n}_{m}$-Rung picture fuzzy information in a modern approach to multi-attribute group decision-making, Complex Intell. Syst., 2023. https://doi.org/10.1007/s40747-023-01277-z
    [29] A. Kandil, A. M. El-Etriby, On separation axioms in fuzzy topological spaces, Tamkang J. Math., 18 (1987), 49–59.
    [30] A. Kandil, M. E. El-Shafei, Regularity axioms in fuzzy topological spaces and $FR_i$-proximities, Fuzzy Set. Syst., 27 (1988), 217–231. https://doi.org/10.1016/0165-0114(88)90151-0 doi: 10.1016/0165-0114(88)90151-0
    [31] A. Kandil, O. A. E. Tantawy, Fuzzy soft connected sets in fuzzy soft topological spaces, J. Adv. Math., 12 (2016), 6473–6488. https://doi.org/10.24297/jam.v12i8.136 doi: 10.24297/jam.v12i8.136
    [32] A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, S. S. S. El-Sayed, Fuzzy Soft Hyperconnected spaces, Ann. Fuzzy Math. Inform., 13 (2017), 689–702.
    [33] A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, Sawsan S. El-Sayed, Fuzzy soft topological spaces: Regularity and separation axioms, South Asian J. Math., 8 (2018), 1–10.
    [34] B. Ahmad, A. Kharal, On fuzzy soft sets, Adv. Fuzzy Syst., 2009 (2009), 586507. https://doi.org/10.1155/2009/586507 doi: 10.1155/2020/3807418
    [35] T. M. Al-shami, L. D. R. Kočinac, Nearly soft Menger spaces, J. Math., 2020 (2020), 3807418. https://doi.org/10.1155/2020/3807418 doi: 10.1155/2020/3807418
    [36] T. M. Al-shami, L. D. R. Kočinac, Almost soft Menger and weakly soft Menger spaces, Appl. Comput. Math., 21 (2022), 35–51. https://doi.org/10.30546/1683-6154.21.1.2022.35 doi: 10.30546/1683-6154.21.1.2022.35
    [37] P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, J. Fuzzy Math., 9 (2001), 589–602. doi: 10.30546/1683-6154.21.1.2022.35
    [38] P. K. Maji, R. Biswas, A. R. Roy, A fuzzy soft set theoretic approach to decision making problems, Comput. Math. Appl., 203 (2007), 412–418. https://doi.org/10.1016/j.cam.2006.04.008 doi: 10.1016/j.cam.2006.04.008
    [39] J. Mahanta, P. K. Das, Results on fuzzy soft topological spaces, 2012. https://doi.org/10.48550/arXiv.1203.0634
    [40] S. Mishra, R. Srivastava, On $T_0$ and $T_1$ fuzzy soft topological spaces, Ann. Fuzzy Math. Inform., 10 (2015), 591–605.
    [41] D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5 doi: 10.1016/S0898-1221(99)00056-5
    [42] P. Mukherjee, R. P. Chakraborty, C. Park, On fuzzy soft $\mathrm{\delta}$-open sets and fuzzy soft $\mathrm{\delta }$-continuity, Ann. Fuzzy Math. Inform., 11 (2016), 327–340.
    [43] S. Roy, T. K. Samanta, A note on fuzzy soft topological spaces, Ann. Fuzzy Math. Inform., 3 (2012), 305–311.
    [44] S. Saleh, T. M. Al-shami, A. Mhmedi, On some new types of fuzzy soft compact spaces, J. Math., 2023 (2023), 5065592. https://doi.org/10.1155/2023/5065592 doi: 10.1155/2023/5065592
    [45] S. Saleh, T. M. Al-shami, A. A. Azzam, M. Hosny, Stronger forms of fuzzy pre-Separation and regularity axioms via fuzzy topology, Mathematics, 11 (2023), 4801. https://doi.org/10.3390/math11234801 doi: 10.3390/math11234801
    [46] S. Saleh, A. M. Abd El-latif, A. Al-Salemi, On separation axioms in fuzzy soft topological spaces, S. Asian J. Math., 8 (2018), 92–102.
    [47] S. Saleh, A. Al-Salemi, The R0 and R1 Properties in fuzzy soft topological spaces, J. New Theory, 24 (2018), 50–58.
    [48] M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786–1799. https://doi.org/10.1016/j.camwa.2011.02.006 doi: 10.1016/j.camwa.2011.02.006
    [49] B. Tanay, M. B. Kandemir, Topological structures of fuzzy soft sets, Comput. Math. Appl., 61 (2011), 2952–2957. https://doi.org/10.1016/j.camwa.2011.03.056 doi: 10.1016/j.camwa.2011.03.056
    [50] L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 38–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(820) PDF downloads(76) Cited by(1)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog