تعداد نشریات | 27 |

تعداد شمارهها | 612 |

تعداد مقالات | 6,232 |

تعداد مشاهده مقاله | 9,353,193 |

تعداد دریافت فایل اصل مقاله | 6,105,038 |

## The distributivity characterization of idempotent null-uninorms over two special aggregation operators | ||

Iranian Journal of Fuzzy Systems | ||

دوره 20، شماره 2، خرداد و تیر 2023، صفحه 103-119 اصل مقاله (231.47 K) | ||

نوع مقاله: Research Paper | ||

شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7559 | ||

نویسندگان | ||

T. H. Zhang^{*} ^{1}؛ F. Qin^{1}؛ J. Wan^{2}؛ Q. M. Hu^{3}
| ||

^{1}School of Mathematics and Statistics, Jiangxi Normal University, 330022 Nanchang, PR China | ||

^{2}School of Literature, Jiangxi Normal University, 330022 Nanchang, PR China | ||

^{3}Networked Supporting Software International S$\&$T Cooperation Base of China, Jiangxi Normal University, 330022 Nanchang, PR China | ||

چکیده | ||

Recently, Zhao et al. \cite{Zhao-2021-25} characterized the distributivity equations of null-uninorms with continuous and Archimedean underlying operators over overlap or grouping functions. Moreover, Liu et al. \cite{Liu-2020-25} studied the distributive laws of continuous t-norms over overlap functions. In this paper, we proceed with the distributivity characterization of idempotent null-uninorms over overlap or grouping functions. In order to do that, we introduce a class of weak overlap and grouping functions with weak coefficients, and obtain the full characterizations of overlap and grouping functions by considering the different values of underlying uninorms' associated functions of idempotent null-uninorms on the interval endpoints and comparing them with the weak coefficients. Obviously, idempotent null-uninorms generalize idempotent uninorms. Thus, the obtained results also generalize the distributivity of idempotent uninorms proposed as future work in | ||

کلیدواژهها | ||

Distributivity equation؛ idempotent null-uninorms؛ associated function؛ idempotent uninorms؛ overlap function؛ grouping function | ||

مراجع | ||

[1] P. Akella, Structure of n-uninorms, Fuzzy Sets and Systems, 158 (2007), 1631-1651.
[2] B. C. Bedregal, H. Bustince, E. Palmeira, G. Dimuro, J. Fernandez, Generalized interval-valued owa operators with interval weights derived from interval-valued overlap functions, International Journal of Approximate Reasoning, 90 (2017), 1-16. [3] B. C. Bedregal, G. P. Dimuro, H. Bustince, E. Barrenechea, New results on overlap and grouping functions, Information Sciences, 249 (2013), 148-170. [4] G. Beliakov, H. Bustince, T. Calvo. A practical guide to averaging functions, Springer, Berlin, New York, 2016.
[5] G. Beliakov, A. Pradera, T. Calvo. Aggregation functions: A guide for practitioners, Springer, Berlin, 2007.
[6] P. Benvenuti, R. Mesiar, Pseudo-arithmetical operations as a basis for the general measure and integration theory, Information Sciences, 160 (2004), 1-11. [7] H. Bustince, J. Fernandez, R. Mesiar, J. Montero, R. Orduna, Overlap functions, Nonlinear Analysis, Theory, Methods and Applications, 72 (2010), 1488-1499. [8] H. Bustince, M. Pagola, R. Mesiar, E. H¨ullermeier, E. Herrera, Grouping, overlaps, and generalized bientropic functions for fuzzy modeling of pairwise comparisons, IEEE Transactions on Fuzzy Systems, 20 (2012), 405-415. [9] H. Bustince, M. Pagola, R. Mesiar, J. Montero, R. Orduna, Overlap index, overlap functions and migrativity, In: Proceedings of IFSA/EUSFLAT Conference, 2009, 300-305. [10] T. Calvo, B. De Baets, J. Fodor, The functional equations of Frank and Alsina for uninorms and nullnorms, Fuzzy Sets and Systems, 120 (2001), 385-394. [11] B. De Baets, Idempotent uninorms, European Journal of Operational Research, 118 (1999), 631-642.
[12] G. P. Dimuro, B. Bedregal, Archimedean overlap functions: The ordinal sum and the cancellation, idempotency and limiting properties, Fuzzy Sets and Systems, 252 (2014), 39-54. [13] G. P. Dimuro, B. Bedregal, On residual implications derived form overlap functions, Information Sciences, 312 (2015), 78-88. [14] G. P. Dimuro, B. Bedregal, On the laws of contraposition for residual implications derived from grouping functions, In: 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Istanbul, (2015), 1-7. [15] G. P. Dimuro, B. Bedregal, H. Bustince, M. J. Asiain, R. Mesiar, On additive generators of overlap functions, Fuzzy Sets and Systems, 287 (2016), 76-96. [16] G. P. Dimuro, B. Bedregal, R. H. N. Santiago, On (G,N)-implications derived grouping functions, Information Sciences, 279 (2014), 1-17. [17] P. Dryga´s, D. Ruiz-Aguilera, J. Torrens, A characterization of a class of uninorms with continuous underlying operators, Fuzzy Sets and Systems, 287 (2016), 137-153. [18] D. Dubois, E. Pap, H. Prade, Hybrid probabilistic-possibilistic mixtures and utility functions, in preferences and decisions under incomplete knowledge, Studies in Fuzziness and Soft Computing, 51, Springer-Verlag, (2000), 51-73. [19] M. Elkano, M. Galar, J. A. Sanz, A. Fernandez, et.al., Enhancing multi-class classification in FARC-HD fuzzy classifier: On the synergy between n-dimensional overlap functions and decomposion strategies, IEEE Transactions on Fuzzy Systems, 23 (2015), 1562-1580.
[20] M. Elkano, M. Galar, J. A. Sanz, P. F. Schiavo, et al., Consensus via penalty functions for decision making in ensembles in fuzzy rulebased classification systems, Applied Soft Computing, 67 (2018), 728-740. [21] J. C. Fodor, M. Roubens, Fuzzy preference modelling and multicriteria decision support, Kluwer Academic Publishers, Dordrecht, 1994.
[22] J. C. Fodor, R. R. Yager, A. Rybalov, Structure of uninorms, International Journal of Uncertainty Fuzziness Knowledge-Based Systems, 5(4) (1997), 411-427.
[23] M. Grabisch, J. Marichal, R. Mesiar, E. Pap, Aggregations functions, Cambridge University Press, 2009.
[24] D. G´omez, J. T. Rodr´ıguez, J. Y´a¯nez, J. Montero, A new modularity measure for fuzzy community detection problems based on overlap and grouping functions, International Journal of Approximate Reasoning, 74 (2016), 88-107. [25] M. Gonz´alez-Hidalgo, S. Massanet, A. Mir, D. Ruiz-Aguilera, On the choice of the pair conjunction-implication into the fuzzy morphological edge detector, IEEE Transactions on Fuzzy Systems, 23(4) (2015), 872-884. [26] D. Joˇci´c, I. Stajner-Papuga, ˇ Some implications of the restricted distributivity of aggregation operators with absorbing elements for utility theory, Fuzzy Sets and Systems, 291 (2016), 54-65. [27] A. Jurio, H. Bustince, M. Pagola, A. Pradera, R. Yager, Some properties of overlap and grouping functions and their application to image thresholding, Fuzzy Sets and Systems, 229 (2013), 69-90. [28] M. Kalina, O. Sta˘sov´a, Idempotent uninorms and nullnorms on bounded posets, Iranian Journal of Fuzzy Systems, 18(5) (2021), 53-68. [29] E. P. Klement, R. Mesiar, E. Pap, Triangular norms, Kluwer Academic Publishers, Dordrecht, 2000.
[30] E. P. Klement, R. Mesiar, E. Pap, Integration with respect to decomposable measures, based on a conditionally distributive semiring on the unit interval, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 8 (2000), 701-717. [31] G. J. Klir, B. Yuan, Fuzzy sets and fuzzy logic: Theory and application, Prentice-Hall, Inc. Upper Saddle River, New Jersey, 1995. [32] W. H. Li, F. Qin, New results on the migrativity properties for overlap (grouping) functions, Iranian Journal of Fuzzy Systems, 18(3) (2021), 111-128. [33] H. W. Liu, Distributivity and conditional distributivity of semi-uninorms over continuous t-conorms and t-norms, Fuzzy Sets and Systems, 268 (2015), 27-43. [34] H. Liu, B. Zhao, New results on the distributive laws of uninorms over overlap and grouping functions, IEEE Transactions on Fuzzy Systems, 29 (2021), 1927-1941. [35] M. Mas, G. Mayor, J. Torrens, The modularity condition for uninorms and t-operators, Fuzzy Sets and Systems, 126 (2002), 207-218.
[36] M. Mas, M. Monserrat, D. Ruiz-Aguilera, J. Torrens, Migrative uninorms and nullnorms over t-norms and tconorms, Fuzzy Sets and Systems, 261 (2015), 20-32.
[37] E. Pap, Decomposable measures and nonlinear equations, Fuzzy Sets and Systems, 92 (1997), 205-221.
[38] J. Qiao, On distributive laws of uninorms over overlap and grouping functions, IEEE Transactions on Fuzzy Systems, 27(12) (2019), 2279-2292. [39] J. Qiao, B. Q. Hu, On the migrativity of uninorms and nullnorms over overlap and grouping functions, Fuzzy Sets and Systems, 346 (2018), 1-54. [40] J. Qiao, B. Q. Hu, The distributivity laws of fuzzy implications over overlap and grouping functions, Information Sciences, 438 (2018), 107-126. [41] J. Qiao, B. Q. Hu, On homogeneous, quasi-homogeneous and pseudo-homogeneous overlap and grouping functions, Fuzzy Sets and Systems, 357 (2019), 58-90. [42] E. Rak, Distributivity equation for nullnorms, Journal of Electrical Engineering, 56 (2005), 53-55.
[43] E. Rak, The distributivity property of increasing binary operations, Fuzzy Sets and Systems, 232 (2013), 110-119.
[44] D. Ruiz, J. Torrens, Distributive idempotent uninorms, International Journal of Uncertainty Fuzziness KnowledgeBased Systems, 4 (2003), 413-428.
[45] Y. Su, J. V. Riera, D. Ruiz-Aguilera, J. Torrens, The modularity condition for uninorms revisited, Fuzzy Sets and Systems, 357 (2019), 27-46. [46] Y. Su, W. Zong, H. W. Liu, P. Xue, On distributivity equations for semi-t-operators over uninorms, Fuzzy Sets and Systems, 287 (2016), 172-183. [47] W. Sander, J. Siedekum, Multiplication, distributivity and fuzzy integral I, Kybernetika, 41 (2005), 397-422.
[48] W. Sander, J. Siedekum, Multiplication, distributivity and fuzzy integral II, Kybernetika, 41 (2005), 469-496.
[49] F. Sun, X. P. Wang, X. B. Qu, Uni-nullnorms and null-uninorms, Journal of Intelligent and Fuzzy Systems, 32 (2017), 1969-1981. [50] Y. M. Wang, H. W. Liu, The modularity condition for overlap and grouping functions, Fuzzy Sets and Systems, 372 (2019), 97-110.
[51] L. Yang, F. Qin, The novel method of constructing fuzzy implications by ordinal sum, Journal of Jiangxi Normal University (Natural Science), 42(3) (2018), 254-259. [52] H. P. Zhang, Y. Ouyang, B. De Baets, Construction of uni-nullnorms and null-uninorms on a bounded lattice, Fuzzy Sets and Systems, 403 (2021), 78-87. [53] T. H. Zhang, F. Qin, W. H. Li, On the distributivity equations between uni-nullnorms and overlap (grouping) functions, Fuzzy Sets and Systems, 403 (2021), 56-77. [54] T. H. Zhang, F. Qin, H. W. Liu, Y. M. Wang, Modularity conditions between overlap (grouping) function and uni-nullnorm or null-uninorm, Fuzzy Sets and Systems, 414 (2021), 94-114. [55] Y. Zhao, K. Li, On the distributivity equations between null-uninorms and overlap (grouping) functions, Fuzzy Sets and Systems, 433 (2022), 122-139. [56] H. J. Zhou, X. X. Yan, Migrativity properties of overlap functions over uninorms, Fuzzy Sets and Systems, 403 (2021), 10-37. | ||

آمار تعداد مشاهده مقاله: 68 تعداد دریافت فایل اصل مقاله: 135 |