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AIMS Mathematics

2023, Volume 8, Issue 9: 21069-21088. doi: 10.3934/math.20231073
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Research article

Applications of picture fuzzy filters: performance evaluation of an employee using clustering algorithm

  • 1.
    Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India
  • 2.
    Department of Computer Science, King Khalid University, Abha-62529, Saudi Arabia
  • Received: 03 May 2023 Revised: 13 June 2023 Accepted: 24 June 2023 Published: 03 July 2023

  • MSC : 03E72, 54A40

  • This article defines the concepts of picture fuzzy filter, picture fuzzy grill, picture fuzzy section, picture fuzzy base, picture fuzzy subbase, picture fuzzy ultrafilter, as well as their fundamental features. Characteristics of the aforementioned concepts are addressed, and equivalence between the picture fuzzy filter and picture fuzzy grills is established. Real-world examples are offered to demonstrate the advantages of picture fuzzy filters in the classification of sets using a clustering technique. Illustration is provided to show the advantages of picture fuzzy sets and the results are compared with intuitionistic fuzzy sets. Clustering technique is applied to the picture fuzzy filter collection reduces the computational process which helps the decision makers to classify the sets with fewer iterations.

    Citation: K. Tamilselvan, V. Visalakshi, Prasanalakshmi Balaji. Applications of picture fuzzy filters: performance evaluation of an employee using clustering algorithm[J]. AIMS Mathematics, 2023, 8(9): 21069-21088. doi: 10.3934/math.20231073

    Related Papers:

  • This article defines the concepts of picture fuzzy filter, picture fuzzy grill, picture fuzzy section, picture fuzzy base, picture fuzzy subbase, picture fuzzy ultrafilter, as well as their fundamental features. Characteristics of the aforementioned concepts are addressed, and equivalence between the picture fuzzy filter and picture fuzzy grills is established. Real-world examples are offered to demonstrate the advantages of picture fuzzy filters in the classification of sets using a clustering technique. Illustration is provided to show the advantages of picture fuzzy sets and the results are compared with intuitionistic fuzzy sets. Clustering technique is applied to the picture fuzzy filter collection reduces the computational process which helps the decision makers to classify the sets with fewer iterations.


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    [1] T. Al-shami, H. Ibrahim, A. Azzam, A. El-Maghrabi, SR-fuzzy sets and their weighted aggregated operators in application to decision-making, J. Funct. Space., 2022 (2022), 3653225. http://dx.doi.org/10.1155/2022/3653225 doi: 10.1155/2022/3653225
    [2] T. 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. http://dx.doi.org/10.3390/info14010056 doi: 10.3390/info14010056
    [3] T. 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. http://dx.doi.org/10.1007/s40747-022-00878-4 doi: 10.1007/s40747-022-00878-4
    [4] T. Al-shami, J. Alcantud, A. Mhemdi, New generalization of fuzzy soft sets: (a, b)-fuzzy soft sets, AIMS Mathematics, 8 (2023), 2995–3025. http://dx.doi.org/10.3934/math.2023155 doi: 10.3934/math.2023155
    [5] Z. Ameen, T. Al-shami, A. Azzam, A. Mhemdi, A novel fuzzy structure: infra-fuzzy topological spaces, J. Funct. Space., 2022 (2022), 9778069. http://dx.doi.org/10.1155/2022/9778069 doi: 10.1155/2022/9778069
    [6] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87–96. http://dx.doi.org/10.1016/S0165-0114(86)80034-3
    [7] K. Atanassov, G. Gargov, Elements of intuitionistic fuzzy logic-Part I, Fuzzy Set. Syst., 95 (1998), 39–52. http://dx.doi.org/10.1016/S0165-0114(96)00326-0 doi: 10.1016/S0165-0114(96)00326-0
    [8] C. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182–190. http://dx.doi.org/10.1016/0022-247X(68)90057-7
    [9] D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Set. Syst., 88 (1997), 81–89. http://dx.doi.org/10.1016/S0165-0114(96)00076-0 doi: 10.1016/S0165-0114(96)00076-0
    [10] B. Cuong, Picture fuzzy sets, Journal of Computer Science and Cybernetics, 30 (2014), 409–420. http://dx.doi.org/10.15625/1813-9663/30/4/5032
    [11] B. Cuong, V. Kerinovich, Picture fuzzy sets-a new concept for computational intelligence problems, Proceedings of Third World Congress on Information and Communication Technologies (WICT 2013), 2013, 1–6. http://dx.doi.org/10.1109/WICT.2013.7113099
    [12] P. Dutta, Medical diagnosis based on distance measures between picture fuzzy sets, International Journal of Fuzzy System Applications, 7 (2018), 15–36. http://dx.doi.org/10.4018/IJFSA.2018100102 doi: 10.4018/IJFSA.2018100102
    [13] T. Gerstenkorn, J. Mańko, Correlation of intuitionistic fuzzy sets, Fuzzy Set. Syst., 44 (1991), 39–43. http://dx.doi.org/10.1016/0165-0114(91)90031-K doi: 10.1016/0165-0114(91)90031-K
    [14] G. Klir, B. Yuan, Fuzzy sets and fuzzy logic: theory and applications, New Jersey: Prentice-Hall Inc, 1995.
    [15] O. Montiel, J. Camacho, R. Sepulveda, O. Castillo, Fuzzy system to control the movement of a wheeled mobile robot, In: Soft computing for intelligent control and mobile robotics, Berlin: Springer, 2010,445–463. http://dx.doi.org/10.1007/978-3-642-15534-5_27
    [16] O. Montiel, R. Sepulveda, O. Castillo, A. Basturk, High performance fuzzy systems for real world problems, Adv. Fuzzy Syst., 2012 (2012), 316187. http://dx.doi.org/10.1155/2012/316187 doi: 10.1155/2012/316187
    [17] J. Peng, J. Wang, H. Zhang, T. Sun, X. Chen, OWA aggregation over a continuous fuzzy argument with applications in fuzzy multi-criteria decision-making, J. Intell. Fuzzy Syst., 27 (2014), 1407–1417. http://dx.doi.org/10.3233/IFS-131107 doi: 10.3233/IFS-131107
    [18] J. Peters, Associated near sets of distance functions in pattern analysis, In: Multi-disciplinary trends in artificial intelligence, Berlin: Springer, 2011, 1–13. http://dx.doi.org/10.1007/978-3-642-25725-4_1
    [19] A. Razaq, I. Masmali, H. Garg, U. Shuaib, Picture fuzzy topological spaces and associated continuous functions, AIMS Mathematics, 7 (2022), 14840–14861. http://dx.doi.org/10.3934/math.2022814 doi: 10.3934/math.2022814
    [20] M. Sanchez, O. Castillo, J. Castro, P. Melin, Fuzzy granular gravitational clustering algorithm for multivariate data, Inform. Sci., 279 (2014), 498–511. http://dx.doi.org/10.1016/j.ins.2014.04.005 doi: 10.1016/j.ins.2014.04.005
    [21] P. Singh, Correlation coefficients for picture fuzzy sets, J. Intell. Fuzzy Syst., 28 (2015), 591–604. http://dx.doi.org/10.3233/IFS-141338 doi: 10.3233/IFS-141338
    [22] P. Smets, The degree of belief in a fuzzy event, Inform. Sci., 25 (1981), 1–19. http://dx.doi.org/10.1016/0020-0255(81)90008-6 doi: 10.1016/0020-0255(81)90008-6
    [23] M. Sugeno, An introductory survey of fuzzy control, Inform. Sci., 36 (1985), 59–83. http://dx.doi.org/10.1016/0020-0255(85)90026-X doi: 10.1016/0020-0255(85)90026-X
    [24] N. Thao, N. Dinh, Rough picture fuzzy set and picture fuzzy topologies, Journal of Computer Science and Cybernetics, 31 (2015), 245–253. http://dx.doi.org/10.15625/1813-9663/31/3/5046 doi: 10.15625/1813-9663/31/3/5046
    [25] P. Thong, L. Son, Picture fuzzy clustering: a new computational intelligence method, Soft Comput., 20 (2016), 3549–3562. http://dx.doi.org/10.1007/s00500-015-1712-7 doi: 10.1007/s00500-015-1712-7
    [26] C. Tian, J. Peng, S. Zhang, W. Zhang, J. Wang, Weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems, Comput. Ind. Eng., 137 (2019), 106037. http://dx.doi.org/10.1016/j.cie.2019.106037 doi: 10.1016/j.cie.2019.106037
    [27] C. Tian, J. Peng, S. Zhang, J. Wang, M. Goh, A sustainability evaluation framework for WET-PPP projects based on a picture fuzzy similarity-based VIKOR method, J. Clean. Prod., 289 (2021), 125130. http://dx.doi.org/10.1016/j.jclepro.2020.125130 doi: 10.1016/j.jclepro.2020.125130
    [28] V. Visalakshi, M. Uma, E. Roja, On soft fuzzy $C$-structure compactification, Kochi Journal of Mathematics, 8 (2013), 119–133.
    [29] Z. Wang, Z. Xu, S. Liu, J. Tang, A netting clustering analysis method under intuitionistic fuzzy environment, Appl. Soft Comput., 11 (2011), 5558–5564. http://dx.doi.org/10.1016/j.asoc.2011.05.004 doi: 10.1016/j.asoc.2011.05.004
    [30] Z. Xu, J. Chen, J. Wu, Clustering algorithm for intuitionistic fuzzy sets, Inform. Sci., 178 (2008), 3775–3790. http://dx.doi.org/10.1016/j.ins.2008.06.008 doi: 10.1016/j.ins.2008.06.008
    [31] T. Yogalakshmi, O. Castillo, On intuitionistic fuzzy $C$-ends, In: Advances in algebra and analysis, Cham: Birkhäuser, 2018,177–184. https://dx.doi.org/10.1007/978-3-030-01120-8_21
    [32] L. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
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