Algorithms for clustering fuzzy soft sets based on their energies
DOI:
https://doi.org/10.22105/scfa.vi.34Keywords:
Fuzzy soft set, Energy, Singular valuesAbstract
In this paper, we continue the study of fuzzy soft sets and their applications. Besides the significance of energy and $\lambda$-energy of fuzzy soft sets for developing decision-making algorithms, these energies are also crucial for forming data clustering algorithms. The main result of this work is the development of data clustering algorithms based on the energies of fuzzy soft sets.
References
C. C. Aggarwal, Linear Algebra and Optimization for Machine Learning, Springer
Nature Switzerland AG, ISBN 978-3-030-40343-0, 2020.
M. I. Ali, F. Feng, X. Y. Liu, W. K. Min, M. Shabir, On some new operations
in soft set theory, Computers and Mathematics with Applications 57 (9) (2009)
–1553.
N. C¸ a˘gman, S. Enginoglu, Soft set theory and uni-int decision making, Eur. J.
Oper. Res. 207 (2010) 848–855.
N. C¸ a˘gman, F. Citak, S. Enginoglu, Fuzzy parametrized fuzzy soft set theory and
its applications, Turk. j. Fuzzy Syst. 1 (1) (2010) 21–35.
N. C¸ a˘gman, S. Enginoglu, F. Citak, Fuzzy Soft Set Theory and Its Applications,
Iranian Journal of Fuzzy Systems 8 (3) (2011) 137–147.
F. Fang, J. B. Jun, X. Liu, L. Li, An adjustable approach to fuzzy soft set based
decision making, Journal of Computational and Applied Mathematics 234 (2010)
–20.
I. Gutman, The energy of a graph, Ber. Math.Statist. Sekt. Forschungsz. Graz
(1978) 1–22.
I. Gutman, D. Kiani, M. Mirzakhah, B. Zhou, On incidence energy of a graph,
Linear Algebra Appl. 431 (2009) 1223–1233.
M. Jooyandeh, D. Kiani, M. Mirzakhah, Incidence energy of a graph, MATCH
Commun. Math. Comput. Chem. 62 (2009) 561–572.
Z. Liu, K. Qin, Z. Pei, A method for fuzzy soft sets in decision-making based on
an ideal solution, Symmetry 9 (10) (2017), 246.
P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics
with Applications 45 (2003) 555–562.
P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9 (3) (2001)
–602.
D. Molodtsov, Soft set theory-first results, Computers and Mathematics with
Applications 37 (1999) 19–31.
Lj. Mudri´c-Staniˇskovski, Lj. Djurovi´c, N. Stojanovi´c, Energy of a fuzzy soft
set and its application in decision-making, Iranian Journal of Fuzzy Systems,
DOI:10.22111/ijfs.2024.46797.8243
V. Nikiforov, The energy of graphs and matrices, J. Math. Anal. Appl. 326 (2007)
–1475.
V. Nikiforov, Beyond graph energy: Norms of graphs and matrices, Linear Algebra
Appl. 506 (2016) 82–138.
K. Rezaei, H. Rezaei, New distance and similarity measures for hesitant fuzzy
soft sets, Iranian Journal of Fuzzy Systems 16 (6) (2019) 159–176.
A. Sezgin, S. Ahmad, A. Mehmood, A New Operation on Soft Sets: Extended
Difference of Soft Sets, Journal of New Theory 27 (2019) 33–42.
A. Sezgin, A. O. Atagun, On operations of soft sets, Comput. Math. Appl. 61
(2011) 1457–1467.
N. Stojanovi´c, M. Boriˇci´c Joksimovi´c, Soft Outer Measure and Soft Premeasure,
Filomat 36 (6) (2022) 2129–2141.
N. Stojanovi´c, A new operation on soft sets: extended symmetric difference of soft
sets, Vojnotehniˇcki glasnik/Military Technical Courier 69 (4) (2021) 779–791.
L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965) 338–353.
J. Zhang, J. Li, New results on the incidence energy of graphs, MATCH Commun.
Math. Comput. Chem. 68 (2012) 777–803.
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