تحلیلی بر اعداد فازی دوقطبی

نوع مقاله : مروری

نویسندگان

گروه ریاضی و آمار، دانشکده علوم پایه، دانشگاه گنبد کاووس، گنبد کاووس، ایران

چکیده

 در این مقاله به معرفی و مرور مجموعه ها و انواع مختلف اعداد فازی دوقطبی خواهیم
پرداخت و سپس با تعریف جمع و ضرب اسکالر برای اعداد فازی دوقطبی مثلثی، به معرفی
یک رتبه بندی جدید مبتنی بر مرکز ثقل برای این دسته از اعداد می پردازیم و با بیان چند قضیه
و گزاره، ویژگی های روش جدید را اثبات خواهیم کرد. در پایان مثال های عددی و مقایسه ای را
ارائه می کنیم
 

کلیدواژه‌ها

موضوعات


[1] Akram, M., Ali, M. and Allahviranloo, T. (2020). Certain methods to solve bipolar fuzzy linear system of equations. Computational and Applied Mathematics, 39(3), 213.
 
[2] Akram, M., Allahviranloo, T., Pedrycz, W. and Ali, M. (2021). Methods for solving LR­bipolar fuzzy linear systems. Soft Computing, 25(1), 85­108.
 
[3] Akram, M. and Arshad, M. (2019). A novel trapezoidal bipolar fuzzy TOPSIS method for group decision­making. Group Decision and Negotiation, 28, 565­584.
 
[4] Akram, M., Muhammad, G. and Allahviranloo, T. (2019). Bipolar fuzzy linear system of equations. Computational and Applied Mathematics, 38, 1­29.
 
[5] Akram, M., Shumaiza and Rodríguez Alcantud, J. C. (2023). Extended PROMETHEE Method with Bipolar Fuzzy Sets Multi­criteria Decision Making Methods with Bipolar Fuzzy Sets (pp. 151­175): Springer.
 
[6] Akram, M., Shumaiza and Rodríguez Alcantud, J. C. (2023). TOPSIS and ELECTRE I Methodologies: Bipolar Fuzzy Formulations Multi­criteria Decision Making Methods with Bipolar Fuzzy Sets (pp. 1­34): Springer.
 
[7] Akram, M., Shumaiza and Rodríguez Alcantud, J. C. (2023). VIKOR Method with Trapezoidal Bipolar Fuzzy Sets Multi­criteria Decision Making Methods with Bipolar Fuzzy Sets (pp. 67­91): Springer.
 
[8] Alolaiyan, H., Mateen, M. H., Pamucar, D., Mahmmod, M. K. and Arslan, F. (2021). A certain structure of bipolar fuzzy subrings. Symmetry, 13(8), 1397.
 
[9] Ashraf, S., Abdullah, S., Aslam, M., Qiyas, M. and Kutbi, M. A. (2019). Spherical fuzzy sets and its representation of spherical fuzzy t­norms and t­conorms. Journal of Intelligent Fuzzy Systems, 36(6), 6089­6102.
 
[10] Atanassov, K. T. and Atanassov, K. T. (1999). Intuitionistic fuzzy sets: Springer.
 
[11] Babakordi, F. (2022). Market Equilibrium Point Analysis by a Fuzzy Approach. Journal of Operational Research In Its Applications (Applied Mathematics)­Lahijan Azad University, 19(3), 17­28.
 
[12] Babakordi, F. (2023). An Efficient Method for Solving the Fuzzy AH1N1/09 Influenza Model Using the Fuzzy Atangana­Baleanu­Caputo Fractional Derivative. Fuzzy Optimization and Modeling Journal, 4(1), 57­70.
 
[13] Babakordi, F. (2023). An Efficient Method for Solving the Fuzzy AH1N1/09 Influenza Model Using the Fuzzy Atangana­Baleanu­Caputo Fractional Derivative. Fuzzy Optimization and Modeling Journal, 4(1), 57­70.
 
[14] Babakordi, F. and Taghi­Nezhad, N. (2021). Introducing hesitant fuzzy equations and determining market equilibrium price. Control and Cybernetics, 50.
 
[15] Ghanbari, R., Ghorbani­Moghadam, K. and Mahdavi­Amiri, N. (2018). A Direct Method to Compare Bipolar LR Fuzzy Numbers. Advances in Fuzzy Systems.
 
[16] Ghanbari, R., Ghorbani­Moghadam, K. and Mahdavi­Amiri, N. (2019). Duality in bipolar fuzzy number linear programming problem. Fuzzy Information and Engineering, 11(2), 175­185.
 
[17] Gong, S. and Hua, G. (2023). Bipolar interval­valued fuzzy set in graph and hypergraph settings. Journal of Intelligent Fuzzy Systems, 44(2), 1755­1767.
 
[18] Han, Y., Shi, P. and Chen, S. (2015). Bipolar­valued rough fuzzy set and its applications to the decision information system. IEEE Transactions on Fuzzy Systems, 23(6), 2358­2370.
 
[19] Jana, C., Pal, M. and Wang, J. (2019). A robust aggregation operator for multi­criteria decisionmaking method with bipolar fuzzy soft environment. Iranian Journal of Fuzzy Systems, 16(6), 1­16.
 
[20] Jeevaraj, S. (2021). Ranking of Trapezoidal Bipolar Fuzzy Numbers Based on a New Improved Score Function Fuzzy Systems and Data Mining VII (pp. 41­53): IOS Press.
 
[21] Krishnaveni, J., Rajalakshmi, B. and Santhanaathiveeralakshmi, V. (2022). Fuzzy bipolar sets in rank­ordering system. Paper presented at the AIP Conference Proceedings.
 
[22] Kutlu Gündoğdu, F. and Kahraman, C. (2019). Spherical fuzzy sets and spherical fuzzy TOPSIS method. Journal of Intelligent Fuzzy Systems, 36(1), 337­352.
 
[23] Lu, M. and Busemeyer, J. R. (2014). Do traditional chinese theories of Yi Jing (’Yin­Yang’and Chinese medicine go beyond western concepts of mind and matter. Mind and Matter, 12(1), 37­59.
 
[24] Mandal, W. A. (2021). Bipolar pythagorean fuzzy sets and their application in Multiattribute decision making problems. Annals of Data Science, 1­33.
 
[25] Mehmood, M. A., Akram, M., Alharbi, M. G. and Bashir, S. (2021). Optimization of LR­type fully bipolar fuzzy linear programming problems. Mathematical Problems in Engineering, 2021, 1­36.
 
[26] Mehmood, M. A., Akram, M., Alharbi, M. G. and Bashir, S. (2021). Solution of fully bipolar fuzzy linear programming models. Mathematical Problems in Engineering 2021, 1­31.
 
[27] Princy, R. and Mohana, K. (2019). Spherical bipolar fuzzy sets and its application in multi criteria decision making problem. Journal of New Theory(32), 58­70.
 
[28] Singh, P. K. (2022). Bipolar fuzzy concepts reduction using granular­based weighted entropy. Soft Computing, 26(19), 9859­9871.
 
[29] Sriram, S. and Sivaranjani, K. (2023). Operations on Bipolar Pythagorean Fuzzy Matrix. Paper presented at the 2023 Third International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT).
 
[30] Taghi­Nezhad, N. and Babakordi, F. (2023). Fully hesitant parametric fuzzy equation. Soft Computing, 1­12.
 
[31] Taghi­nezhad, N., Naseri, H., Khalili Goodarzi, F. and Taleshian Jelodar, F. (2015). Reactive Scheduling Presentation for an Open Shop problem Focused on jobs’ due Dates. Journal of Production and Operations Management, 6(2), 95­112.
 
[32] Taghi­Nezhad, N. A. (2019). The p­median problem in fuzzy environment: proving fuzzy vertex optimality theorem and its application. Soft Computing, 23(22), 11399­11407.
 
[33] Taghi­Nezhad, N. A. (2022). A revisit of the proposed model for solving fuzzy linear fractional programming problem. International Journal of Mathematics in Operational Research, 23(2), 215­231.
 
[34] Taghi­Nezhad, N. A. (2023). Fuzzy Linear Fractional Programming for Container Transportation Optimization. Iranian Journal of Marine Science and Technology.
 
[35] Taleshian, F., Fathali, J. and Allah Taghi­Nezhad, N. (2022). Finding the absolute and vertex center of a fuzzy tree. Transportation Letters, 14(6), 591­599.
 
[36] Taleshian, F., Fathali, J. and Taghi­Nezhad, N. A. (2018). Fuzzy majority algorithms for the 1­median and 2­median problems on a fuzzy tree. Fuzzy Information and Engineering, 10(2), 1­24.
 
[37] Wang, Y.­M., Yang, J.­B., Xu, D.­L. and Chin, K.­S. (2006). On the centroids of fuzzy numbers. Fuzzy Sets and Systems, 157(7), 919­926. doi:https://doi.org/10.1016/j.fss.2005.11.006
 
[38] Yager, R. R. (2013). Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), 958­965.
 
[39] Yiarayong, P. (2021). A new approach of bipolar valued fuzzy set theory applied on semigroups. International Journal of Intelligent Systems, 36(8), 4415­4438.
 
[40] Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338 ­ 353.
 
[41] Zhang, W.­R. (1998). (Yin)(Yang) bipolar fuzzy sets. Paper presented at the 1998 IEEE international conference on fuzzy systems proceedings. IEEE world congress on computational intelligence (Cat. No. 98CH36228).
 
[42] Zhang, W.­R. (2013). Bipolar quantum logic gates and quantum cellular combinatorics–a logical extension to quantum entanglement. Journal of Quantum Information Science, 3(2), 93.
 
[43] Zhang, W.­R. (2016). G­CPT Symmetry of Quantum Emergence and Submergence–An Information Conservational Multiagent Cellular Automata Unification of CPTSymmetry and CP Violation for Equilibrium­Based Many­World Causal Analysis of Quantum Coherence and Decoherence. Journal of Quantum Information Science, 6(2), 62.
 
[44] Zhang, W.­R., Pandurangi, A. K., Peace, K. E., Zhang, Y.­Q. and Zhao, Z. (2011). MentalSquares: a generic bipolar support vector machine for psychiatric disorder classification, diagnostic analysis and neurobiological data mining. International journal of data mining and bioinformatics, 5(5), 532­557.
 
[45] Zhang, W.­R. and Peace, K. E. (2014). Causality is logically definable—toward an equilibriumbased computing paradigm of quantum agents and quantum intelligence (QAQI)(Survey and research). Journal of Quantum Information Science, 4, 227­268.
 
[46] Zhang, W.­R., Zhang, J. H., Shi, Y. and Chen, S.­S. (2009). Bipolar linear algebra and YinYangN­element cellular networks for equilibrium­based biosystem simulation and regulation. Journal of Biological Systems, 17(04), 547­576.
 
[47] Zhang, W.­R. and Zhang, L. (2004). YinYang bipolar logic and bipolar fuzzy logic. Information sciences, 165(3­4), 265­287.
 
[48] Zhang, X. and Xu, Z. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29(12), 1061­1078.