رتبه بندی اعداد Z با استفاده از روش خوشه بندی بهینه
سعید جعفری
1
(
گروه مهندسی برق، دانشگاه آزاد اسلامی واحد بوشهر
)
مجتبی نجفی
2
(
گروه مهندسی برق، دانشگاه آزاد اسلامی واحد بوشهر
)
نقی مودبی پیرکلاهچاهی
3
(
گروه مهندسی برق، دانشگاه آزاد اسلامی واحد بوشهر
)
نجمه چراغی شیرازی
4
(
گروه مهندسی برق، دانشگاه آزاد اسلامی واحد بوشهر
)
کلید واژه: عددkz, خوشه بندی k-means, فازی, امکانی-احتمالاتی, عددz,
چکیده مقاله :
استفاده از مفاهیم جدید در انجام محاسبات توسط کلمات زبان طبیعی به منظور مدلسازی عدم قطعیت ها، در سال های اخیر مورد توجه قرار گرفته است. در این راستا مفهوم عدد Z توسط دکتر زاده در سال 2011مطرح گردید. در این مفهوم عدم قطعیت داده ها، بصورت یک جفت اعداد فازی (A, B) معرفی می گردد. هدف از عدد Z مدلسازی جملات غیردقیق زبان طبیعی می باشد، به طوری که اولین عامل عدد Z نشان دهنده امکان رخداد و عامل دوم نشان‌دهنده احتمال رخداد عامل اول می باشد. با این حال، عدد Z مشکلات پیچیده و هزینه محاسباتی بالایی دارند. در عدد Z به منظور تشکیل مولفه اول و دوم جفت اعداد فازی (A, B)، کارشناسان ممکن است راه حل های نامناسبی در دیتاهای با تعداد بالا ارائه دهند که این عامل باعث می گردد، نتایج نهایی به درستی محاسبه نگردد، این ضعف در تصمیم گیری های گروهی در زمان استفاده از عدد Z بیشتر نمایان می گردد. به منظور رفع این چالش، نویسندگان گروه بندی هدفمند مجموع دیتاها را پیشنهاد می نمایند. در این راه حل ، گروه بندی دیتاها بر اساس خوشه بندی (k-means) صورت می پذیرد و در ادامه مولفه های اول و دوم عدد Z به صورت هدفمند تشکیل می گردد. به منظور نشان دادن اثر بخشی روش پیشنهادی، اقدام به محاسبه عدم قطعیت قیمت لحظه ای برق در بازار PJM می نماییم. در پایان نتایج بدست آمده توسط روش پیشنهادی با نتایج بدست آمده روش فازی، عدد Z و دیتای واقعی مقایسه گردیده است.
چکیده انگلیسی :
The use of new concepts in performing calculations by natural language words in order to model uncertainties has been considered in recent years. In this regard, the concept of Z-number was proposed by Dr. Zadeh in 2011. In this concept, data uncertainty is introduced as a pair of fuzzy numbers (A, B). The purpose of Z number is to model imprecise natural language sentences, so that the first factor of Z-number indicates the possibility of occurrence and the second factor indicates the probability of occurrence of the first factor. However, Z-numbers have complex problems and high computational cost. In the Z-number in order to form the first and second components of the pair of fuzzy numbers (A, B), experts may provide inappropriate solutions in high number of data, which causes the final results to not be calculated correctly, this weakness in Group decisions are more visible when using the Z-number. In order to solve this challenge, the authors suggest the purposeful grouping of all data. In this solution, data grouping is done based on clustering (k-means) and then the first and second components of the Z-number are formed purposefully. In order to show the effectiveness of the proposed method, we calculate the uncertainty of the current price of electricity in the PJM market. At the end, the results obtained by the proposed method have been compared with the results obtained by the fuzzy method, Z-number and real data.
[1] A. L. Zadeh, "Fuzzy sets," Information and control, vol. 8, no. 3, pp. 338-353, 1965, doi: 10.1016/S0019-9958(65)90241-X.
[2] A. P. Dempster, "A generalization of Bayesian inference," Journal of the Royal Statistical Society, Series B (Methodological) , vol. 30, no. 2, pp. 205-232, doi: 10.1111/j.2517-6161.1968.tb00722.x.
[3] G. Shafer, “A mathematical theory of evidence turns 40,” International Journal of Approximate Reasoning, vol. 79, pp. 7-25, 2016, doi: 10.1016/j.ijar.2016.07.009.
[4] M. J. Mendel and J.R. Bob, "Type-2 fuzzy sets made simple," IEEE Transactions on fuzzy systems, vol. 10, no. 2, pp. 117-127, 2002, doi: 10.1109/91.995115.
[5] G. Ulutagay and V. Kreinovich, “Density-Based Fuzzy Clustering as a First Step to Learning Rules: Challenges and Solutions,” in Advance Trends in Soft Computing: Proceedings of WCSC , 2013, San Antonio, Texas, USA , pp. 357-372, doi: 10.1007/978-3-319-03674-8.
[6] Y. Wang et al., "Pairwise constraints-based semi-supervised fuzzy clustering with multi-manifold regularization," Information Sciences, vol. 638, p. 118994, 2023, doi: 10.1016/j.ins.2023.118994.
[7] L. Guo et al., "Pixel and region level information fusion in membership regularized fuzzy clustering for image segmentation," Information Fusion , vol. 92, pp. 479-497, 2023, doi: 10.1016/j.inffus.2022.12.008.
[8] F. Xiao, "A multiple-criteria decision-making method based on D numbers and belief entropy," International Journal of Fuzzy Systems , vol. 21, no. 4, pp. 1144-1153, 2019, doi: 10.1007/s40815-019-00620-2.
[9] J. Pérez-Ortega et al., "POFCM: A Parallel Fuzzy Clustering Algorithm for Large Datasets," Mathematics , vol. 11, no. 8, 2023, doi: 10.3390/math11081920.
[10] L. Wang, C. Guonan and C. Xinye, "Fuzzy clustering optimal k selection method based on multi-objective optimization," Soft Computing, vol. 27, no. 3, pp. 1289-1301, 2023, doi: 10.1007/s00500-022-07727-z.
[11] Y. Tian, L. Liu, X. Mi and B. Kang, “ZSLF: A new soft likelihood function based on Z-numbers and its application in expert decision system,” IEEE Trans. Fuzzy Syst., vol. 29, no. 8, pp. 2283–2295, Aug. 2021, doi: 10.1109/TFUZZ.2020.2997328.
[12] R. Cerqueti and R. Mattera, "Fuzzy clustering of time series with time-varying memory," International Journal of Approximate Reasoning, vol. 153, pp. 193-218, 2023, doi: 10.1016/j.ijar.2022.11.021.
[13] A. R. Rajeswari et al., "A trust-based secure neuro fuzzy clustering technique for mobile ad hoc networks," Electronics , vol. 12, no. 274, 2023, doi: 10.3390/electronics12020274.
[14] R. Cheng, B. Kang and J. Zhang, "An Improved Method of Converting Z-number into Classical Fuzzy Number," 33rd Chinese Control and Decision Conference (CCDC), Kunming, China, 2021, pp. 3823-3828, doi: 10.1109/CCDC52312.2021.9601658.
[15] A. R. Aliev, A. V. Alizadeh and O. H. Huseynov, "The arithmetic of discrete Z-numbers," Information Sciences, vol. 290 , pp. 134-155, 2015, doi: 10.1016/j.ins.2014.08.024.
[16] F. Liu et al., "Evaluating Internet hospitals by a linguistic Z-number-based gained and lost dominance score method considering different risk preferences of experts," Information Sciences, vol. 630, pp. 647-668, 2023, doi: 10.1016/j.ins.2023.02.061.
[17] F. Teng et al., "Probabilistic linguistic Z number decision-making method for multiple attribute group decision-making problems with heterogeneous relationships and incomplete probability information," International Journal of Fuzzy Systems, vol. 24, no. 1, pp. 1-22, 2022, doi: 10.1007/s40815-021-01161-3.
[18] R. Jafari, W. Yu and X. Li, "Numerical solution of fuzzy equations with Z-numbers using neural networks," Intelligent Automation & Soft Computing, pp. 1-7, 2017, doi: 10.1080/10798587.2017.1327154.
[19] S. Massanet, J. V. Riera and J. Torrens, "A new vision of Zadeh’s Z-numbers," International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Cham: Springer International Publishing, vol. 47, 2016, doi: 10.1007/978-3-319-40581-0_47.
[20] A. R. Aliev et al., "Z‐number‐based linear programming." International Journal of Intelligent Systems , vol. 30, no. 5, pp. 563-589, 2015, doi: 10.1002/int.21709.
[21] D. Wu et al., "A new medical diagnosis method based on Z-numbers," Applied Intelligence , vol. 48, pp. 854-867, 2018, doi: 10.1007/s10489-017-1002-4.
[22] R. Cheng, J. Zhang and B. Kang, "Ranking of Z-Numbers Based on the Developed Golden Rule Representative Value," in IEEE Transactions on Fuzzy Systems, vol. 30, no. 12, pp. 5196-5210, Dec. 2022, doi: 10.1109/TFUZZ.2022.3170208.
[23] A. R. Aliev et al., "Eigensolutions of partially reliable decision preferences described by matrices of Z-numbers," International Journal of Information Technology & Decision Making, vol. 19, no. 06, pp. 1429-1450, 2020, doi: 10.1142/S0219622020010063.
[24] R. Banerjee and K. P. Sankar, "A machine-mind architecture and Z*-numbers for real-world comprehension," Pattern Recognition and Big Data, pp. 805-842, 2017, doi: 10.1142/9789813144552_0026.
[25] Q. Liu et al., "On the negation of discrete z-numbers," Information Sciences, vol. 537, pp. 18-29, 2020, doi: 10.1016/j.ins.2020.05.106.
[26] https://hourlypricing.comed.com/live-prices/?date=20230310.