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Extensions of Intuitionistic Fuzzy Geometric Interaction Operators and Their Application to Cognitive Microcredit Origination

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Abstract

The intuitionistic fuzzy set (IFS), a popular tool to present decision makers’ cognitive information, has received considerable attention from researchers. To extend the interaction operational laws in the computation of cognitive information, this paper focuses on investigating extensions of geometric interaction aggregation operators by means of the t-norm and the corresponding t-conorm under an intuitionistic fuzzy environment. We develop the extending intuitionistic fuzzy-weighted geometric interaction averaging (EIFWGIA) operator, the extending intuitionistic fuzzy-ordered weighted geometric interaction averaging (EIFOWGIA) operator, the intuitionistic fuzzy weighted geometric interaction quasi-arithmetic mean (IFWGIQAM), and the intuitionistic fuzzy-ordered weighted geometric interaction quasi-arithmetic mean (IFOWGIQAM). We investigate the properties of the proposed extensions and apply the extensions to the cognitive microcredit origination problem. For different generator functions h and ϕ, the proposed IFWGIQAM and IFOWGIQAM degenerate into existing intuitionistic fuzzy aggregation operators or extensions, some of which consider situations that in which no interactions exist between membership and non-membership functions, which can be used in more decision situations. The methods developed in this paper can be used to account for several decision situations. The numerical example demonstrates the validity of the proposed approaches by means of comparisons.

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References

  1. Akram M, Dudek WA. Intuitionistic fuzzy hypergraphs with applications. Inf Sci. 2013;218:182–93.

    Google Scholar 

  2. Akram M, Alshehri NO, Dudek WA. Certain types of interval-valued fuzzy graphs. J Appl Math. 2013;2013:11. https://doi.org/10.1155/2013/857070.

    Article  Google Scholar 

  3. Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986;80:87–96.

    Google Scholar 

  4. Atanassov KT. New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets Syst. 1994;61:137–42.

    Google Scholar 

  5. Beliakov G, James S, Mordelová J, Rückschlossová T, Yager RR. Generalized Bonferroni mean operators in multi-criteria aggregation. Fuzzy Sets Syst. 2010;161:2227–42.

    Google Scholar 

  6. Beliakov G, Bustince H, Goswami DP, Mukherjee UK, Pal NR. On averaging operators for Atanassov’s intuitionistic fuzzy sets. Inf Sci. 2011;181:1116–24.

    Google Scholar 

  7. Beliakov G, Pradera A, Calvo T. Aggregation functions: a guide for practitioners, vol. 2. Heidelberg: Springer. p. 007.

  8. Bellman RE, Zadeh LA. Decision-making in a fuzzy environment. Manag Sci. 1970;17:B-141–64.

    Google Scholar 

  9. Calvo T, Mesiar R. Aggregation operators: ordering and bounds. Fuzzy Sets Syst. 2003;139:685–97.

    Google Scholar 

  10. Carneiro J, Conceição L, Martinho D, Marreiros G, Novais P. Including cognitive aspects in multiple criteria decision analysis. Ann Oper Res. 2018;265:269–91.

    Google Scholar 

  11. Chen SM, Tan JM. Handling multi-criteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst. 1994;67:163–72.

    Google Scholar 

  12. Chuu SJ. Interactive group decision-making using a fuzzy linguistic approach for evaluating the flexibility in a supply chain. Eur J Oper Res. 2011;213:279–89.

    Google Scholar 

  13. De SK, Biswas R, Roy AR. Some operations on intuitionistic fuzzy sets. Fuzzy Set and Systems. 2000;114:477–84.

    Google Scholar 

  14. Deschrijver G. The Archimedean property for t-norms in interval-valued fuzzy set theory. Fuzzy Sets Syst. 2006;157:2311–27.

    Google Scholar 

  15. Deschrijver G. Arithmetic operators in interval-valued fuzzy set theory. Inf Sci. 2007;177:2906–24.

    Google Scholar 

  16. Deschrijver G. Generalized arithmetic operators and their relationship to t-norms in interval-valued fuzzy set theory. Fuzzy Sets Syst. 2009;160:3080–102.

    Google Scholar 

  17. Dubois D, Prade H. Fuzzy sets and systems: theory and applications. New York: Academic Press; 1980.

    Google Scholar 

  18. Dymova L, Sevastjinov P. An interpretation of intuitionistic fuzzy sets in terms of evidences theory: decision making aspect. Knowl-Based Syst. 2010;23:772–82.

    Google Scholar 

  19. Flavell JH, Miller PH, Social cognition. (1998) In W. Damon (Ed.), Handbook of child psychology: Vol. 2. Cognition, perception, and language (pp.851–898). Hoboken, NJ, US: John Wiley & Sons Inc.

  20. Garg H, Arora R. Dual hesitant fuzzy soft aggregation operators and their application in decision-making. Cogn Comput. 2018;10:769–89.

    Google Scholar 

  21. Gau WL, Buehrer DJ. Vague sets. IEEE Trans Syst Man Cybern. 1993;23:610–4.

    Google Scholar 

  22. He YD, He Z. Extensions of Atanassov’s intuitionistic fuzzy interaction Bonferroni means and their application to multiple attribute decision making. IEEE Trans Fuzzy Syst. 2016;24:558–73.

    Google Scholar 

  23. He YD, Chen HY, Zhou LG, Liu JP, Tao ZF. Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making. Inf Sci. 2014;259:142–59.

    Google Scholar 

  24. He YD, Chen HY, Zhou LG, Han B, Zhao QY, Liu JP. Generalized intuitionistic fuzzy geometric interaction operators and their application to decision making. Expert Syst Appl. 2014;41:2484–95.

    Google Scholar 

  25. Hong DH, Choi CH. Multicriteria fuzzy decision-making problems based on vague set thoery. Fuzzy Sets Syst. 2000;114:103–13.

    Google Scholar 

  26. Jiménez JMM, Vargas LG. Cognitive multiple criteria decision making and the legacy of the analytic hierarchy process. Estudios de Economía Aplicada. 2018;36:67–80.

    Google Scholar 

  27. Klement EP, Mesiar R, editors. Logical, algebraic, analytic, and probabilistic aspects of triangular norms. New York: Elsevier; 2005.

    Google Scholar 

  28. Kolesárová A. Limit properties of quasi-arithmetic means. Fuzzy Sets Syst. 2001;124:65–71.

    Google Scholar 

  29. Li DF. TOPSIS-based nonlinear-programming methodology for multi-attribute decision making with interval-valued intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst. 2010;18:299–311.

    Google Scholar 

  30. Li X, Chen X. D-intuitionistic hesitant fuzzy sets and their application in multiple attribute decision making. Cogn Comput. 2018;10:496–505.

    Google Scholar 

  31. Li J, Wang JQ. Multi-criteria outranking methods with hesitant probabilistic fuzzy sets. Cogn Comput. 2017;9:611–25.

    Google Scholar 

  32. Liu XW. An orness measure for quasi-arithmetic means. IEEE Trans Fuzzy Syst. 2006;14:837–48.

    Google Scholar 

  33. Liu PD, Li HG. Interval-valued intuitionistic fuzzy power Bonferroni aggregation operators and their application to group decision making. Cogn Comput. 2017;9:494–512.

    Google Scholar 

  34. Liu PD, Shi LL. Some neutrosophic uncertain linguistic number Heronian mean operators and their application to multi-attribute group decision making. Neural Comput & Applic. 2017;28:1079–93.

    Google Scholar 

  35. Liu PD, Tang GL. Multi-criteria group decision-making based on interval neutrosophic uncertain linguistic variables and Choquet integral. Cogn Comput. 2016;8:1036–56.

    Google Scholar 

  36. Liu PD, Wang P. Some improved linguistic intuitionistic fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Inf Technol Decis Mak. 2017;16:817–50.

    Google Scholar 

  37. Liu PD, Zhang XH. A novel picture fuzzy linguistic aggregation operator and its application to group decision-making. Cogn Comput. 2018;10:242–59.

    Google Scholar 

  38. Liu F, Zhang WG, Wang ZX. A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making. Eur J Oper Res. 2012;218:747–54.

    Google Scholar 

  39. Liu PD, Zhang L, Liu X, Wang P. Multi-valued Neutrosophic number Bonferroni mean operators and their application in multiple attribute group decision making. Int J Inf Technol Decis Mak. 2016;15:1181–210.

    Google Scholar 

  40. Liu PD, Chen SM, Liu J. Some intuitionistic fuzzy interaction partitioned Bonferroni mean operators and their application to multi-attribute group decision making. Inf Sci. 2017;411:98–121.

    Google Scholar 

  41. Meng FY, Chen XH. Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cogn Comput. 2015;7:445–63.

    Google Scholar 

  42. Meng FY, Wang C, Chen XH. Linguistic interval hesitant fuzzy sets and their application in decision making. Cogn Comput. 2016;8:52–68.

    Google Scholar 

  43. Merigó JM, Gil-Lafuente AM. The induced generalized OWA operator. Inf Sci. 2009;179:729–41.

    Google Scholar 

  44. Merigó JM, Gil-Lafuente AM. Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making. Inf Sci. 2013;236:1–16.

    Google Scholar 

  45. Peng HG, Wang JQ. Outranking decision-making method with Z-number cognitive information. Cogn Comput. 2018;10:752–68.

    Google Scholar 

  46. Pires P, Mendes L, Mendes J, Rodrigues R, Pereira A. Integrated e-healthcare system for elderly support. Cogn Comput. 2016;8:1–17.

    Google Scholar 

  47. Rezaei J, Ortt R. Multi-criteria supplier segmentation using a fuzzy preference relation based AHP. Eur J Oper Res. 2013;225:75–84.

    Google Scholar 

  48. Rodriguez RM, Martinez L, Herrera F. Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst. 2012;20:109–19.

    Google Scholar 

  49. Saaty TL. The analytic hierarchy process. New York: McGraw-Hill; 1980.

    Google Scholar 

  50. Sedikides C, Guinote A. How status shapes social cognition: introduction to the special issue, “the status of status: vistas from social cognition”. Soc Cogn. 2018;36:1–3.

    Google Scholar 

  51. Tao ZF, Han B, Chen HY. On intuitionistic fuzzy copula aggregation operators in multiple-attribute decision making. Cogn Comput. 2018;10:610–24.

    Google Scholar 

  52. Tian ZP, Wang J, Wang JQ, Zhang HY. A likelihood-based qualitative flexible approach with hesitant fuzzy linguistic information. Cogn Comput. 2016;8:670–83.

    CAS  Google Scholar 

  53. TorraV, Narukawa Y, Modeling decisions: information fusion and aggregation operators, Spring, 2007.

  54. Wan SP, Li DF. Atanassov’s intuitionistic fuzzy programming method for heterogeneous multi-attribute group decision making with Atanassov’s intuitionistic fuzzy truth degrees. IEEE Trans Fuzzy Syst. 2014;22:300–12.

    Google Scholar 

  55. Wang XZ, Dong CR. Improving generalization of fuzzy if-then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst. 2009;17:556–67.

    Google Scholar 

  56. Wang WZ, Liu XW. Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Trans Fuzzy Syst. 2012;20:923–38.

    Google Scholar 

  57. Xia MM, Chen J. Multi-criteria group decision making based on bilateral agreements. Eur J Oper Res. 2015;240:756–64.

    Google Scholar 

  58. Xia MM, Xu ZS, Chen J. Algorithms for improving consistence or consensus of reciprocal [0,1]-valued preference relations. Fuzzy Sets Syst. 2013;216:108–33.

    Google Scholar 

  59. Xu ZS. An overview of methods for determining OWA weights. Int J Intell Syst. 2005;20:843–65.

    Google Scholar 

  60. Xu ZS, Hu H. Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Mak. 2010;9:267–80.

    Google Scholar 

  61. Xu ZS, Intuitionistic fuzzy aggregation operations. IEEE Trans Fuzzy Syst. 2007;15:1179–87.

  62. Xu ZS, Yager RR. Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst. 2006;35:417–33.

    Google Scholar 

  63. Yager RR. On ordered weighted averaging aggregation operators in multi- criteria decision making. IEEE Trans Syst Man Cybern. 1988;18:183–90.

    Google Scholar 

  64. Yager RR. The power average operator. IEEE Trans Syst Man Cybern-Part A: Syst Humans. 2001;31:724–31.

    Google Scholar 

  65. Ye J. Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets. Appl Math Model. 2010;34:3864–70.

    Google Scholar 

  66. Zadeh LA. Fuzzy set. Inf Control. 1965;8:338–53.

    Google Scholar 

  67. Zhai JH, Xu HY, Wang XZ. Dynamic ensemble extreme learning machine based on sample entropy. Soft Comput. 2012;16:1493–502.

    Google Scholar 

  68. Zhang ZM. Generalized Atanassov’s intuitionistic fuzzy power geometric operators and their application to multiple attribute group decision making. Information Fusion. 2013;14:460–86.

    Google Scholar 

  69. Zhang HY, Ji P, Wang JQ, Chen XH. A neutrosophic normal cloud and its application in decision-making. Cogn Comput. 2016;8:649–69.

    CAS  Google Scholar 

  70. Zhao H, Xu ZS, Ni MF, Liu SS. Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst. 2010;25:1–30.

    CAS  Google Scholar 

  71. Zhu B, Xu ZS. Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans Fuzzy Syst. 2014;22:35–45.

    Google Scholar 

  72. Zhu B, Xu ZS. Analytic hierarchy process-hesitant group decision making. Eur J Oper Res. 2014;239:794–801.

    Google Scholar 

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  1. College of Management and Economics, Tianjin University, Tianjin, 300072, China

    Lin Zhang & Yingdong He

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Zhang, L., He, Y. Extensions of Intuitionistic Fuzzy Geometric Interaction Operators and Their Application to Cognitive Microcredit Origination. Cogn Comput 11, 748–760 (2019). https://doi.org/10.1007/s12559-019-09659-7

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