Weitere Artikel dieser Ausgabe durch Wischen aufrufen
In real decision-making, because of the particularity of human cognition activity, it is difficult to depict the decision information by exact numbers, especially, for complex decision information, how to express and aggregate them is an important work for solving these decision-making problems. In order to express the complex fuzzy information accurately, we proposed the concept of interval-valued linguistic intuitionistic fuzzy numbers (IVLIFNs), where their membership function and non-membership function are represented by interval-valued linguistic terms, and then we developed the operational rules, score function, accuracy function, and comparison method of them. Considering that the Maclaurin symmetric mean (MSM) operator has a good characteristic in dealing with the interrelationships among multi-parameters, and it also is a generalization of arithmetic aggregation operator, Bonferroni mean (BM) operator, and geometric aggregation operator, we further proposed the interval-valued linguistic intuitionistic fuzzy MSM (IVLIFMSM) operator, the weighted interval-valued linguistic intuitionistic fuzzy MSM (WIVLIFMSM) operator, and proved some related properties of them. We gave an illustrative example to demonstrate the steps and the effectiveness of the proposed method by the comparison with existing methods. IVLIFNs can more conveniently express the complex fuzzy information in qualitative environment by considering the cognition of decision-makers, and the proposed method can consider the interrelationship among multiple input arguments, so it can make the decision-making results more reasonable. In a word, the proposed method is more scientific and flexible in solving multiple attribute decision-making (MADM) problems than some existing methods.
Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten
Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:
Abu-Saris R, Hajja M. On Gauss compounding of symmetric weighted arithmetic means. J Math Anal Appl. 2006;322:729–34. CrossRef
Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986;20:87–96. CrossRef
Atanassov KT. More on intuitionistic fuzzy sets. Fuzzy Sets Syst. 1989;33:37–46. CrossRef
Atanassov KT. Operators over interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 1994;64:159–74. CrossRef
Atanassov KT, Gargov G. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 1989;31(3):343–9. CrossRef
Bapat RB. Symmetric function means and permanents. Linear Algebra Appl. 1993;182(101–8. CrossRef
Beliakov G, James S. On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts. Fuzzy Sets Syst. 2013;211(84–9. CrossRef
Bonferroni C. Sulle medie multiple di potenze. Boll Mat Ital. 1950;5:267–70.
Chen SM, Lee LW, Liu HC, Yang SW. Multi-attribute decision making based on interval-valued intuitionistic fuzzy values. Expert Syst Appl. 2012;39:10343–51. CrossRef
Chen ZC, Liu PH. An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. Int J Comput Intell Syst. 2015;8(4):747–60. CrossRef
Delgado M, Herrera F, Herrera-Viedma E, Martinez L. Combining numerical and linguistic information in group decision making. Inf Sci. 1998;107:177–94. CrossRef
Detemple D, Robertson J. On generalized symmetric means of two variables. Univ Beograd Publ Elektrotehn FakSer Mat Fiz. 1979;677(634):236–8.
Farhadinia B, Xu Z. Distance and aggregation-based methodologies for hesitant fuzzy decision making. Cogn Comput. 2017;9(1):81–94. CrossRef
Gao P. On a conjecture on the symmetric means. J Math Anal Appl. 2008;337:416–24 puter and System Sciences 70(1) (2005)73–85. CrossRef
Herrera F, Herrera-Viedma E, Martinez L. A fusion approach for managing multi-granularity linguistic term sets in decision-making. Fuzzy Sets Syst. 2000;114(1):43–58. CrossRef
Herrera F, Herrera-Viedma E. Aggregation operators for linguistic weighted information. IEEE Trans Syst Man Cybern Part A Syst Hum. 1997;27(5):646–56. CrossRef
Liu HZ, Pei DW. HOWA operator and its application to multi-attribute decision making. J Zhejiang Sci Technol Univ. 2012;25:138–42.
Liu PD. Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making. J Comput Syst Sci. 2013;79(1):131–43. CrossRef
Liu PD. The multi-attribute group decision making method based on the interval grey linguistic variables weighted aggregation operator. J Intell Fuzzy Syst. 2013;24(2):405–14.
Liu PD. Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Trans Fuzzy Syst. 2014;22(1):83–97. CrossRef
Liu PD, Chen YB, Chu YC. Intuitionistic uncertain linguistic weighted Bonferroni OWA operator and its application to multiple attribute decision making. Cybern Syst. 2014;45(5):418–38. CrossRef
Liu PD, Li Y. Multiple attribute group decision making methods based on trapezoidal fuzzy two-dimension linguistic power generalized aggregation operators. Soft Comput. 2016;20(7):2689–704. CrossRef
Liu PD, Li HG. Multiple attribute decision making method based on some normal neutrosophic Bonferroni mean operators. Neural Comput & Applic. 2017;28(1):179–94. CrossRef
Liu PD, Liu ZM, Zhang X. Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making. Appl Math Comput. 2014;230:570–86.
Liu PD, Qin XY. Power average operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision making. J Intell Fuzzy Syst. 2017;01:1029–43. CrossRef
Liu PD, Tang GL. Multi-criteria group decision-making based on interval neutrosophic uncertain linguistic variables and Choquet integral. Cogn Comput. 2016;8(6):1036–56. CrossRef
Liu PD, Wang YM. Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators. Appl Soft Comput. 2014;17(90–104. CrossRef
Liu PD, Wang YM. Multiple attribute decision-making method based on single valued Neutrosophic normalized weighted Bonferroni mean. Neural Comput & Applic. 2014;25(7–8):2001–10. CrossRef
Maclaurin C. A second letter to Martin Folkes, Esq; concerning the roots of equations, with demonstration of other rules of algebra. Philos Trans R Soc Lond Ser A. 1729;36:59–96. CrossRef
Pecaric J, Wen JJ, Wang WL, Lu T. A generalization of Maclaurin’s inequalities and its applications. Math Inequal Appl. 2005;8:583–98.
Qin JD, Liu XW. An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J Intell Fuzzy Syst. 2014;27:2177–90.
Qin JD, Liu XW. Approaches to uncertain linguistic multiple attribute decision making based on dual Maclaurin symmetric mean. J Intell Fuzzy Syst. 2015;29:171–86. CrossRef
Qin JD, Liu XW. Hesitant fuzzy Maclaurin symmetric mean operators and its application to multiple-attribute decision making. Int J Fuzzy Syst. 2015;17(4):509–20. CrossRef
Tian Z, Wang J, Wang JQ, Zhang HY. A likelihood-based qualitative flexible approach with hesitant fuzzy linguistic information. Cogn Comput. 2016;8(4):670–83. CrossRef
Wang JQ, Kuang JJ, Wang J, et al. An extended outranking approach to rough stochastic multi-criteria decision-making problems. Cogn Comput. 2016;8(6):1144–60. CrossRef
Wang WZ, Liu XW. Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Trans Fuzzy Syst. 2012;20(5):923–38. CrossRef
Xu ZS. A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci. 2004;166:19–30. CrossRef
Xu ZS. Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf Sci. 2004;168:171–84. CrossRef
Xu ZS. Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst. 2007;15(6):1179–87. CrossRef
Xu ZS, Yager RR. Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst. 2006;35:417–33. CrossRef
Yao YY. Three-way decisions and cognitive computing. Cogn Comput. 2016;8(4):543–54. CrossRef
Yu DJ. Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator. Int J Intell Syst. 2012;27:635–61. CrossRef
Zadeh LA. Fuzzy sets. Inf Control. 1965;8:338–56. CrossRef
Zadeh LA. The concept of a linguistic variable and its applications to approximate reasoning. Inf Sci. 1975;8(3):199–249. CrossRef
Zhao H, Xu ZS, Ni MF, Liu S. Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst. 2010;25:1–30. CrossRef
Zhao N, Xu Z, Liu F. Group decision making with dual hesitant fuzzy preference relations. Cogn Comput. 2016;8(6):1119–43. CrossRef
- A New Decision-Making Method Based on Interval-Valued Linguistic Intuitionistic Fuzzy Information
- Springer US
Print ISSN: 1866-9956
Elektronische ISSN: 1866-9964
Neuer Inhalt/© ITandMEDIA, Best Practices für die Mitarbeiter-Partizipation in der Produktentwicklung/© astrosystem | stock.adobe.com