SpringerLink
Log in

Novel aggregation operators and ranking method for complex intuitionistic fuzzy sets and their applications to decision-making process

  • Published:
Artificial Intelligence Review Aims and scope Submit manuscript

Abstract

Complex intuitionistic fuzzy set (CIFS) is a distinctive intuitionistic fuzzy set (IFS) in which the membership degrees are determined on the unit disc of the complex plane and can more clearly express the imprecision and ambiguity in the data. The prevailing studies on IFS deal with the data over the subset of a real number and hence there is a sacrifice of some information during the method under certain conditions. As an alteration to these, CIFS characterized with supplementary terms in membership degrees called as phase terms and hence examine two-dimensional data concurrently in a single set. To get full utilization of these assets, in this paper, the aim of the practice is classified into two turns: (i) to define the possibility degree measure to order the numbers, and (ii) to define some novel operational laws and aggregation operators (AOs) to aggregate the various choices over CIFS environment. The beneficial features of the proposed weighted averaging and geometric AOs are addressed. Finally, a decision-making approach is extended for the multicriteria decision-making problem with complex intuitionistic fuzzy information, in which weights are managed objectively. A practical illustration is furnished to address the availability and advantages of the proposed method by comparison with some existing methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ali M, Smarandache F (2017) Complex neutrosophic set. Neural Comput Appl 28(7):1817–1834

    Article  Google Scholar 

  • Alkouri A, Salleh A (2012) Complex intuitionistic fuzzy sets. In: 2nd international conference on fundamental and applied sciences 2012, vol 1482, pp 464–470

  • Alkouri AUM, Salleh AR (2013) Complex Atanassov’s intuitionistic fuzzy relation. Abstr Appl Anal Article ID 287382, 18 pages

  • Arora R, Garg H (2019) Group decision-making method based on prioritized linguistic intuitionistic fuzzy aggregation operators and its fundamental properties. Comput Appl Math 8(2):1–36. https://doi.org/10.1007/s40314-019-0764-1

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  MATH  Google Scholar 

  • Blanco-Mesa F, Merigó JM, Gil-Lafuente AM (2017) Fuzzy decision making: a bibliometric-based review. J Intell Fuzzy Syst 32(3):2033–2050

    Article  Google Scholar 

  • Blanco-Mesa F, León-Castro E, Merigó JM (2019) A bibliometric analysis of aggregation operators. Appl Soft Comput 81.https://doi.org/10.1016/j.asoc.2019.105488

  • 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):133–149

    Article  MATH  Google Scholar 

  • Dammak F, Baccour L, Alimi AM (2016) An exhaustive study of possibility measures of interval-valued intuitionistic fuzzy sets and application to multicriteria decision making. Adv Fuzzy Syst 2016, Article ID 9185706, 10 pages

  • Dick S, Yager RR, Yazdanbakhsh O (2016) On pythagorean and complex fuzzy set operations. IEEE Trans Fuzzy Syst 24(5):1009–1021

    Article  Google Scholar 

  • Fan CL, Song Y, Fu Q, Lei L, Wang X (2018) New operators for aggregating intuitionistic fuzzy information with their application in decision making. IEEE Access 6:27214–27238

    Article  Google Scholar 

  • Garg H (2016) Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making. Comput Ind Eng 101:53–69

    Article  Google Scholar 

  • Garg H (2017) Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng Appl Artif Intell 60:164–174

    Article  Google Scholar 

  • 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 1–30. https://doi.org/10.1007/s10462-018-9668-5

  • Garg H, Kumar K (2019a) Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision-making. Granul Comput 4(2):237–247

    Article  Google Scholar 

  • Garg H, Kumar K (2019b) Linguistic interval-valued atanassov intuitionistic fuzzy sets and their applications to group decision-making problems. IEEE Trans Fuzzy Syst 1–10. https://doi.org/10.1109/TFUZZ.2019.2897961

  • Garg H, Kumar K (2019c) 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

  • Garg H, Rani D (2019a) A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making. Appl Intell 49(2):496–512

    Article  Google Scholar 

  • Garg H, Rani D (2019b) New generalized Bonferroni mean aggregation operators of complex intuitionistic fuzzy information based on Archimedean t-norm and t-conorm. J Exp Theor Artif Intell 1–29. https://doi.org/10.1080/0952813X.2019.1620871

  • Garg H, Rani D (2019c) Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process. Arab J Sci Eng 44(3):2679–2698

    Article  Google Scholar 

  • Garg H, Rani D (2019d) Some results on information measures for complex intuitionistic fuzzy sets. Int J Intell Syst 34(10):2319–2363. https://doi.org/10.1002/int.22127

    Article  Google Scholar 

  • Garg H, Rani D (2019e) Complex interval- valued intuitionistic fuzzy sets and their aggregation operators. Fundam Inform 164(1):61–101

    Article  MathSciNet  MATH  Google Scholar 

  • Gou XJ, Xu ZS, Lei Q (2016) New operational laws and aggregation method of intuitionistic fuzzy information. J Intell Fuzzy Syst 30:129–141

    Article  MATH  Google Scholar 

  • 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. Information Sciences 259:142–159

    Article  MathSciNet  MATH  Google Scholar 

  • Huang JY (2014) Intuitionistic fuzzy Hamacher aggregation operator and their application to multiple attribute decision making. J Intell Fuzzy Syst 27:505–513

    Article  MathSciNet  MATH  Google Scholar 

  • Kaur G, Garg H (2018) Cubic intuitionistic fuzzy aggregation operators. Int J Uncertain Quantif 8(5):405–427

    Article  MathSciNet  Google Scholar 

  • 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):2775–2794

    Article  Google Scholar 

  • Klir GJ, Yuan B (2005) Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall of India Private Limited, New Delhi

    MATH  Google Scholar 

  • Kumar T, Bajaj RK (2014) On complex intuitionistic fuzzy soft sets with distance measures and entropies. J Math Article ID 972198, 12 pages

  • Kumar K, Garg H (2018a) Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making. Appl Intell 48(8):2112–2119

    Article  Google Scholar 

  • Kumar K, Garg H (2018b) TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math 37(2):1319–1329

    Article  MathSciNet  MATH  Google Scholar 

  • Liu P (2014) Some hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Trans Fuzzy Syst 22(1):83–97

    Article  Google Scholar 

  • Liu P, Liu J (2018) Some q-rung orthopair fuzzy bonferroni mean operators and their application to multi-attribute group decision making. Int J Intell Syst 33(2):315–347

    Article  Google Scholar 

  • Liu P, Tang G (2018) Some intuitionistic fuzzy Prioritized interactive Einstein Choquet operators and their application in decision making. IEEE Access 6:72357–72371

    Article  Google Scholar 

  • Liu P, Wang P (2018) Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33(2):259–280

    Article  Google Scholar 

  • Liu P, Wang P (2019) Multiple-attribute decision-making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers. IEEE Trans Fuzzy Syst 27(5):834–848

    Article  Google Scholar 

  • Liu P, Chen S-M, Wang P (2019) Multiple-attribute group decision-making based on q-rung orthopair fuzzy power maclaurin symmetric mean operators. IEEE Trans Syst Man Cybern Syst 99:1–16. https://doi.org/10.1109/TSMC.2018.2852948

    Article  Google Scholar 

  • Peng XD, Garg H (2018) Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure. Comput Ind Eng 119:439–452

    Article  Google Scholar 

  • Peng X, Dai J, Garg H (2018) Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function. Int J Intell Syst 33(11):2255–2282

    Article  Google Scholar 

  • Quran AA, Hassan N (2018) The complex neutrosophic soft expert set and its application in decision making. J Intell Fuzzy Syst 34:569–582

    Article  Google Scholar 

  • Ramot D, Milo R, Fiedman M, Kandel A (2002) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10(2):171–186

    Article  Google Scholar 

  • Ramot D, Friedman M, Langholz G, Kandel A (2003) Complex fuzzy logic. IEEE Trans Fuzzy Syst 11(4):450–461

    Article  Google Scholar 

  • 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):423–439

    Article  MathSciNet  Google Scholar 

  • Rani D, Garg H (2018) Complex intuitionistic fuzzy power aggregation operators and their applications in multi-criteria decision-making. Expert Syst 35(6):e12325. https://doi.org/10.1111/exsy.12325

    Article  Google Scholar 

  • Singh S, Garg H (2018) Symmetric triangular interval type-2 intuitionistic fuzzy sets with their applications in multi criteria decision making. Symmetry 10(9):401. https://doi.org/10.3390/sym10090401

    Article  MATH  Google Scholar 

  • Wan SP, Dong J (2014) A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making. J Comput Syst Sci 80(1):237–256

    Article  MathSciNet  MATH  Google Scholar 

  • Wang W, Liu X (2012) Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Trans Fuzzy Syst 20(5):923–938

    Article  Google Scholar 

  • Wang X, Triantaphyllou E (2008) Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Omega Int J Manag Sci 36:45–63

    Article  Google Scholar 

  • Wei CP, Tang X (2010) Possibility degree method for ranking intuitionistic fuzzy numbers. In: 3rd IEEE/WIC/ACM international conference on web intelligence and intelligent agent technology (WI-IAT ’10), pp 142–145

  • Xu Z-S, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J General Syst 35:417–433

    Article  MathSciNet  MATH  Google Scholar 

  • Yazdanbakhsh O, Dick S (2018) A systematic review of complex fuzzy sets and logic. Fuzzy Sets Syst 338:1–22

    Article  MathSciNet  MATH  Google Scholar 

  • Ye J (2017) Intuitionistic fuzzy hybrid arithmetic and geometric aggregation operators for the decision-making of mechanical design schemes. Appl Intell 47:743–751

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zhou W, Xu Z (2017) Extreme intuitionistic fuzzy weighted aggregation operators and their applications in optimism and pessimism decision-making processes. J Intell Fuzzy Syst 32:1129–1138

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab, 147004, India

    Harish Garg & Dimple Rani

Authors
  1. Harish Garg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dimple Rani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Harish Garg.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Garg, H., Rani, D. Novel aggregation operators and ranking method for complex intuitionistic fuzzy sets and their applications to decision-making process. Artif Intell Rev 53, 3595–3620 (2020). https://doi.org/10.1007/s10462-019-09772-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10462-019-09772-x

Keywords

Search

Navigation