پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 660 |
| تعداد مقالات | 9,655 |
| تعداد مشاهده مقاله | 68,740,220 |
| تعداد دریافت فایل اصل مقاله | 48,249,546 |
Some frank aggregation operators based on the interval-valued intuitionistic fuzzy numbers | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، Special Issue، اسفند 2021، صفحه 325-342 اصل مقاله (467.72 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23143.2482 | ||
| نویسندگان | ||
| Maryam Oraki* 1؛ Madjid Eshaghi Gordji2؛ Halimeh Ardakani1 | ||
| 1Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| 2Department of Mathematics, Semnan University, Semnan, Iran | ||
| تاریخ دریافت: 26 بهمن 1399، تاریخ بازنگری: 30 فروردین 1400، تاریخ پذیرش: 04 خرداد 1400 | ||
| چکیده | ||
| In this article, we introduce the interval-valued intuitionistic fuzzy set (\textbf{IVIFS}), which are generalized forms of intuitionistic fuzzy set (\textbf{IFS}) and fuzzy set, this is because in intuitionistic fuzzy sets the non-membership function also applies to evaluations, and these sets are useful for modelling ambiguous concepts that abound in real problems. Here we try to look for new methods for more practical solutions in optimization problems for various sciences such as computer science, mathematics, engineering, medicine, psychology, climate and etc. First, with the introduction of t-norm Frank, an action we construct some Frank aggregation operators on interval-valued intuitionistic fuzzy numbers (\textbf{IVIFN}s), including the Frank weighted averaging operator, Frank-ordered weighted averaging operator, Frank hybrid weighted averaging operator, Frank geometric weighted averaging operator, Frank geometric-ordered weighted averaging operator, and Frank geometric hybrid weighted averaging operator. Also, examine some of the characteristics of these operators. In the following, we introduce two multiple attribute group decision-making methods (\textbf{MAGDM}) based on such operators. Finally, we provide illustrative examples of these methods. | ||
| کلیدواژه‌ها | ||
| decision-making sciences؛ aggregation operators؛ nonlinear integrals؛ intuitionistic fuzzy set؛ t-conorm and t-norm Frank | ||
| مراجع | ||
|
[1] S. Abbasbandy and T. Allahviranloo, Numerical solution of fuzzy differential equation by Runge-Kutta method, 11(1) (2004) 117–129. [2] S. Abbasbandy, T. Allahviranloo, O. L´opez-Pouso and J. J. Nieto, ´ Numerical methods for fuzzy differential inclusions, Comput. Math. Appl. 48 (2004) 1633–1641. [3] T. Allahviranloo and M. Barkhordari Ahmadi, Fuzzy Laplace transforms, Soft Comput. 14, Article number: 235 (2010). [4] T. Allahviranloo, S. Abbasbandy, N. Ahmady and E. Ahmady, Improved predictor-corrector method for solving fuzzy initial value problems, Inf. Sci. 179(7) (2009) 945–955. [5] T. Allahviranloo, S. Abbasbandy, O. Sedaghgatfar and P. Darabi, A new method for solving fuzzy integrodifferential equation under generalized differentiability, Neural Comput. Appl. 21 (2012) 191—196. [6] T. Allahviranloo, Z. Gouyandeh, A. Armand and A. Hasanoglu, On fuzzy solutions for heat equation based on generalized Hukuhara differentiability, Fuzzy Sets Syst. 265 (2015) 1–23. [7] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986) 87–96. [8] K. T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets Syst. 33 (1989) 37–46. [9] K. T. Atanassov and G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst. 3 (1989) 343–349. [10] K. T. Atanassov, Operators over interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst. 64 (1994) 159–174. [11] G. Beliakov, A. Pradera and T. Calvo, Aggregation Functions: A Guide For Practitioners, Heidelberg, Germany: Springer, 2007. [12] G. Beliakov, H. Bustince, S. James, T. Calvo and J. Fernandez, Aggregation for Atanassov’s intuitionistic and interval valued fuzzy sets: The median operator, IEEE Trans. Fuzzy Syst. 20(3) (2012) 487–498. [13] Y. J. Cho, Th. M. Rassias and R. Saadat, Fuzzy Operator Theory in Mathematical Analysis, Springer, 2018. [14] G. Deschrijver and E. E Kerre, A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms, Notes Intuitionistic Fuzzy Sets, 8(1) (2002) 19–27. [15] G. Deschrijver, C. Cornelis and E. E. Kerre, On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Trans. Fuzzy Syst. 12(1) (2004) 45–61. [16] R. Ezzatia, T. Allahviranloo, S. Khezerloo and M. Khezerloo, An approach for ranking of fuzzy numbers, Expert Syst. Appl. 39(1) (2012) 690–695. [17] V. L. Gomathi Nayagam, S. Muralikrishnan and G. Sivaraman, Multicriteria decision making method based on interval-valued intuitionistic fuzzy sets, Expert Syst. Appl. 38(3) (2011) 1464–1467. [18] M. Goudarzi, S. M. Vaezpour and R. Saadati, On the intuitionistic fuzzy inner product spaces, Chaos, Sol. Fract. 41(3) (2009) 1105–1112. [19] Z. Gouyandeh, T. Allahviranloo, S. Abbasbandy and A. Armand, A fuzzy solution of heat equation under generalized Hukuhara differentiability by fuzzy Fourier transform, Fuzzy Sets Syst. 309 (2017) 81–97. [20] M. Grabisch, J. L. Marichal, R. Mesiar and E. Pap, Aggregation functions: Means, Info. Sci. 181(1) (2011) 1–22. [21] S. B. Hosseini, R. Saadati and M. Amini, Alexandroff theorem in fuzzy metric spaces, Math. Sci. Res. J. 2004. [22] S. B. Hosseini, D. Oregan and R. Saadati, Some results on intuitionistic fuzzy spaces, Iran. J. Fuzzy Syst. 4(1) (2007) 53–64. [23] P. E. Klement and R. Mesiar, Triangular norms, Tatra Mt. Math. Pupl. 13 (1997) 169–193. [24] P. Liu, Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group, Decision Making, 22(1) (2014) 83–97. [25] X. D. Liu, S. H. Zheng and F. I. Xiong, Entropy and subsethood for general interval-valued intuitionistic fuzzy sets, in Fuzzy Systems and Knowledge Discovery, Fuzzy Syst. Knowledge Disc. 3613 (2005) 42–52. [26] A. Mahmoodirad, T. Allahviranloo and S. Niroomand, A new effective solution method for fully intuitionistic fuzzy transportation problem, Soft Comput. 23 (2019) 4521—4530. [27] P. Melin, G. E. Martinez and R. Svetkov, Choquet and Sugeno integrals and intuitionistic fuzzy integrals as aggregation operators, Notes Intuit. Fuzzy Set. 23(1) (2017) 95–99. [28] E. Pap, Ch. Park and R. Saadati, Additive σ−Random operator inequality and rhom-derivations in fuzzy Banach algebras, U. P. B. Sci. Bull., Series A, 82(2) (2020) 3–14. [29] J. H. Park, Y. B. Park and R. Saadati, Some results in intuitionistic fuzzy metric spaces, J. Comput. Anal. Appl. 10(4) (2008) 441–451. [30] J. Qin and X. Liu, Frank aggregation operators for triangular interval type-2 fuzzy set and its application in multiple attribute group, J. Appl. Math. 2014 (2014), Article ID 923213, 24 pages. [31] R. Saadati and M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. Comput. 17(1) (2005) 475–484. [32] R. Saadati and J. H. Park, Intuitionistic fuzzy Euclidean normed spaces, Commun. Math. Anal. 1(2) (2006) 85–90. [33] R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solit. Fract. 27(2) (2006) 331–344.[34] R. Saadati, Common fixed point theorem in intuitionistic fuzzy metric spaces, Albanian J. Math. 2(4) (2008) 277–282. [35] R. Saadati, M. Vaezpour and Y. J. Cho, Quicksort algorithm: Application of a fixed point theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words, J. Comput. Appl. Math. 228(1) (2009) 219–225. [36] R. Saadati, On the topology of fuzzy metric type spaces, Filomat, 29(1) (2015) 133–141. [37] S. Salahshour and T. Allahviranloo, Application of fuzzy differential transform method for solving fuzzy Volterra integral equations, Appl. Math. Model. 37(3) (2013) 1016–1027. [38] C. Tan and Q. Zhang, Fuzzy multiple attribute decision-making based on interval valued intuitionistic fuzzy sets, Proc. IEEE Int. Conf. Syst, Man, Cybern, vol. 2, Taipei, Taiwan, 2006, pp. 1404-1407. [39] J. Q. Wang, K. J. Li and H. Y. Zhang, Interval-valued intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function, Knowl-Based Syst. 27 (2012) 119–125. [40] W. Wang and X. Liu, Intuitionistic fuzzy information aggregation using Einstein operations, IEEE Trans. Fuzzy Syst. 20(5) (2012) 923–938. [41] W. Z. Wang and X. W. Liu, Intuitionistic fuzzy geometric aggregation operators based on Einstein operations, Int. J. Intell. Syst. 26 (2011) 1049–1075. [42] Z. Wang and J. Xu, A fractional programming method for interval-valued intuitionistic fuzzy multi-attribute decision making, Proc. 49th IEEE Int. Conf. Decision Control, 2010, pp. 636-641. [43] G. W. Wei and W. D. Yi, Induced interval-valued intuitionistic fuzzy OWG operator, Proc. 5th Int. Conf. Fuzzy Syst. Knowl. Discovery, 2008, pp. 605-609. [44] M. M. Xia, Z. S. Xu and B. Zhu, Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm, Knowl. Based Syst. 31 (2012) 78–88. [45] Z. S. Xu and R. R. Yager, Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group, Fuzzy Optim. Decis. Mak. 8 (2009) 123– 139. [46] L. A. Zadeh, Fuzzy sets, Inf. Cont. 8 (1965) 338–356. | ||
|
آمار تعداد مشاهده مقاله: 44,592 تعداد دریافت فایل اصل مقاله: 37,449 |
||