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Group Decision and Negotiation

, Volume 28, Issue 5, pp 991–1050 | Cite as

Exponential, Logarithmic and Compensative Generalized Aggregation Operators Under Complex Intuitionistic Fuzzy Environment

  • Harish GargEmail author
  • Dimple Rani
Article
  • 33 Downloads

Abstract

This manuscript presents some new exponential, logarithmic and compensative exponential of logarithmic operational laws based on t-norm and co-norm for complex intuitionistic fuzzy (CIF) numbers. The prevailing extensions of fuzzy set theory handle the uncertain data by representing the satisfaction and dissatisfaction degrees as real values and can deal with only one-dimensional problems due to which some important information may be lost in some situations. A modification to these, CIF sets are characterized by complex-valued degrees of satisfaction and dissatisfaction and handle two dimensional data simultaneously in one set using additional terms, called phase terms, which generally give information related with periodicity. Motivated by the characteristics of CIF model, we present some new operational laws and compensative operators namely generalized CIF compensative weighted averaging and generalized CIF compensative weighted geometric. Some properties related to proposed operators are discussed. In light of the developed operators, a group decision-making method is put forward in which weights are determined objectively and is illustrated with the aid of an example. The reliability of the presented decision-making method is explored by comparing it with several prevailing studies. The influence of the parameters used in exponential and logarithmic operations on CIF numbers is also discussed.

Keywords

Exponential, Logarithm operational laws Multi-criteria decision-making Complex intuitionistic fuzzy set Compensative generalized aggregation operators 

Notes

References

  1. Ali M, Smarandache F (2017) Complex neutrosophic set. Neural Comput Appl 28(7):1817–1834CrossRefGoogle Scholar
  2. Alkouri A, Salleh A (2012) Complex intuitionistic fuzzy sets, Vol. 1482, 2012, Ch. 2nd international conference on fundamental and applied sciences, pp 464–470Google Scholar
  3. Alkouri AUM, Salleh AR (2013a) Complex Atanassov’s intuitionistic fuzzy relation. Abstract Appl Anal Article ID 287382Google Scholar
  4. Alkouri AUM, Salleh AR (2013b) Some operations on complex atanassov’s intuitionistic fuzzy sets. AIP Conf Proc 1571(1):987–993CrossRefGoogle Scholar
  5. Arora R, Garg H (2019) Group decision-making method based on prioritized linguistic intuitionistic fuzzy aggregation operators and its fundamental properties. Comput Appl Math 38(2):1–36.  https://doi.org/10.1007/s40314-019-0764-1 CrossRefGoogle Scholar
  6. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRefGoogle Scholar
  7. Chen SM, Chang CH (2016) Fuzzy multiattribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators. Inf Sci 352–353:133–149CrossRefGoogle Scholar
  8. Dick S, Yager RR, Yazdanbakhsh O (2016) On Pythagorean and complex fuzzy set operations. IEEE Trans Fuzzy Syst 24(5):1009–1021CrossRefGoogle Scholar
  9. Garg H (2016a) Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making. Comput Ind Eng 101:53–69CrossRefGoogle Scholar
  10. Garg H (2016b) Some series of intuitionistic fuzzy interactive averaging aggregation operators. SpringerPlus 5(1):999.  https://doi.org/10.1186/s40064-016-2591-9 CrossRefGoogle Scholar
  11. Garg H (2017) Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng Appl Artif Intell 60:164–174CrossRefGoogle Scholar
  12. Garg H (2018) New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making. Int J Intell Syst 33(3):653–683CrossRefGoogle Scholar
  13. Garg H (2019) Intuitionistic fuzzy hamacher aggregation operators with entropy weight and their applications to multi-criteria decision-making problems. Iran J Sci Technol Trans Electr Eng 43(3):597–613CrossRefGoogle Scholar
  14. Garg H, Arora R (2019) Generalized intuitionistic fuzzy soft power aggregation operator based on t-norm and their application in multi criteria decision-making. Int J Intell Syst 34(2):215–246CrossRefGoogle Scholar
  15. Garg H, Kumar K (2018) A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. Artif Intell Rev.  https://doi.org/10.1007/s10462-018-9668-5 Google Scholar
  16. Garg H, Kumar K (2019a) Linguistic interval-valued atanassov intuitionistic fuzzy sets and their applications to group decision-making problems. IEEE Trans Fuzzy Syst.  https://doi.org/10.1109/TFUZZ.2019.2897961 Google Scholar
  17. Garg H, Kumar K (2019b) A novel possibility measure to interval-valued intuitionistic fuzzy set using connection number of set pair analysis and their applications. Neural Comput Appl.  https://doi.org/10.1007/s00521-019-04291-w Google Scholar
  18. Garg H, Rani D (2019a) Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process. Arab J Sci Eng 44(3):2679–2698CrossRefGoogle Scholar
  19. Garg H, Rani D (2019b) Robust averaging-geometric aggregation operators for complex intuitionistic fuzzy sets and their applications to MCDM process. Arab J Sci Eng.  https://doi.org/10.1007/s13369-019-03925-4 Google Scholar
  20. Garg H, Rani D (2019c) A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making. Appl Intell 49(2):496–512CrossRefGoogle Scholar
  21. Garg H, Rani D (2019d) Some results on information measures for complex intuitionistic fuzzy sets. Int J Intell Syst.  https://doi.org/10.1002/int.22127 Google Scholar
  22. Garg H, Rani D (2019e) Complex interval-valued intuitionistic fuzzy sets and their aggregation operators. Fundam Inform 164(1):61–101CrossRefGoogle Scholar
  23. Garg H, Rani D (2019f) New generalized Bonferroni mean aggregation operators of complex intuitionistic fuzzy information based on Archimedean t-norm and t-conorm. J Exp Theor Artif Intelli.  https://doi.org/10.1080/0952813X.2019.1620871 Google Scholar
  24. Gou XJ, Xu ZS, Lei Q (2016a) New operational laws and aggregation method of intuitionistic fuzzy information. J Intell Fuzzy Syst 30:129–141CrossRefGoogle Scholar
  25. Gou XJ, Xu ZS, Liao HC (2016b) Exponential operations of interval-valued intuitionistic fuzzy numbers. J Mach Learn Cybern 7(3):501–518CrossRefGoogle Scholar
  26. Goyal M, Yadav D, Tripathi A (2016) Intuitionistic fuzzy genetic weighted averaging operator and its application for multiple attribute decision making in E-learning. Indian J Sci Technol 9(1):1–15CrossRefGoogle Scholar
  27. He Y, Chen H, Zhau L, Liu J, Tao Z (2014) Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making. Inf Sci 259:142–159CrossRefGoogle Scholar
  28. Huang JY (2014) Intuitionistic fuzzy Hamacher aggregation operator and their application to multiple attribute decision making. J Intell Fuzzy Syst 27:505–513Google Scholar
  29. Kaur G, Garg H (2018) Cubic intuitionistic fuzzy aggregation operators. Int J Uncert Quantif 8(5):405–427CrossRefGoogle Scholar
  30. Kaur G, Garg H (2019) Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process. Arab J Sci Eng 44(3):2775–2794CrossRefGoogle Scholar
  31. Klir GJ, Yuan B (2005) Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall of India Private Limited, New DelhiGoogle Scholar
  32. Kumar T, Bajaj RK (2014) On complex intuitionistic fuzzy soft sets with distance measures and entropies. J Math Article ID 972198Google Scholar
  33. Li Z, Wei F (2017) The logarithmic operational laws of intuitionistic fuzzy sets and intuitionistic fuzzy numbers. J Intell Fuzzy Syst 33:3241–3253CrossRefGoogle Scholar
  34. Luo X, Xu Z, Gou X (2018) Exponential operational laws and new aggregation operators of intuitionistic fuzzy information based on archimedean t-conorm and t-norm. Int J Mach Learn Cybern 9(8):1261–1269CrossRefGoogle Scholar
  35. Ramot D, Milo R, Fiedman M, Kandel A (2002) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10(2):171–186CrossRefGoogle Scholar
  36. Ramot D, Friedman M, Langholz G, Kandel A (2003) Complex fuzzy logic. IEEE Trans Fuzzy Syst 11(4):450–461CrossRefGoogle Scholar
  37. Rani D, Garg H (2017) Distance measures between the complex intuitionistic fuzzy sets and its applications to the decision-making process. Int J Uncertain Quantif 7(5):423–439CrossRefGoogle Scholar
  38. Rani D, Garg H (2018) Complex intuitionistic fuzzy power aggregation operators and their applications in multi-criteria decision-making. Exp Syst 35(6):e12325.  https://doi.org/10.1111/exsy.12325 CrossRefGoogle Scholar
  39. Thirunavukarasu P, Suresh R, Ashokkumar V (2017) Theory of complex fuzzy soft set and its applications. Int J Innov Res Sci Technol 3(10):13–18Google Scholar
  40. Wang WZ, Liu XW (2011) Intuitionistic fuzzy geometric aggregation operators based on Einstein operations. Int J Intell Syst 26:1049–1075CrossRefGoogle Scholar
  41. Wang W, Liu X (2012) Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Trans Fuzzy Syst 20(5):923–938CrossRefGoogle Scholar
  42. Xia MM, Xu ZS, Zhu B (2012) Some issues on intuitionistic fuzzy aggregation operators based on archimedean t-conorm and t-norm. Knowl Based Syst 31:78–88CrossRefGoogle Scholar
  43. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187CrossRefGoogle Scholar
  44. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433CrossRefGoogle Scholar
  45. Yazdanbakhsh O, Dick S (2018) A systematic review of complex fuzzy sets and logic. Fuzzy Sets Syst 338:1–22CrossRefGoogle Scholar
  46. Ye J (2017) Intuitionistic fuzzy hybrid arithmetic and geometric aggregation operators for the decision-making of mechanical design schemes. Appl Intell 47:743–751CrossRefGoogle Scholar
  47. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of MathematicsThapar Institute of Engineering and Technology (Deemed University)PatialaIndia

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