Skip to main content
SpringerLink
Log in

Medical diagnostic process based on modified composite relation on pythagorean fuzzy multi-sets

  • Original Paper
  • Published:
Granular Computing Aims and scope Submit manuscript

Abstract

Pythagorean fuzzy multiset (PFMS) is a generalized Pythagorean fuzzy set (PFS) with a higher degree of accuracy. It is characterized by the capacity to handle imprecisions because of its inbuilt ability to allow repetitions of the orthodox parameters of PFSs. Max–min–max composite relation on PFMSs has been studied and proven to be resourceful. However, max–min–max approach used maximum and minimum values of the parameters of PFMS only without considering the average values. This paper proposes a modified version of the max–min–max composite relation on PFMSs to enhance reliable output by incorporating the average values of the PFMSs’ parameters. Some numerical examples are given to juxtapose the correctness of the max–min–max composite relation on PFMSs with that of the modified version to ascertain reliability/superiority of the modified version. To demonstrate the applicability of the proposed composite relation on PFMSs, an illustration of medical diagnosis is considered assuming there are some patients whose symptoms are represented in Pythagorean fuzzy multi-values. To determine the diagnosis of the patients, the max–min–max composite relation and its modified version are deployed to find the correlation between each of the patients with some suspected diseases.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Atanassov KT (1983) Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia

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

    Article  MATH  Google Scholar 

  • Atanassov KT (1999) Intuitionistic fuzzy sets: theory and applications. Physica-Verlag, Heidelberg

    Book  MATH  Google Scholar 

  • 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 

  • Chen SM, Cheng SH, Chiou CH (2016) Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Inf Fusion 27:215–227

    Article  Google Scholar 

  • Chen SM, Cheng SH, Lan TC (2016a) Multicriteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values. Inf Sci 367–368:279–295

    Article  Google Scholar 

  • Cheng SH, Chen SM, Lan TC (2016b) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343–344:15–40

    Article  MathSciNet  MATH  Google Scholar 

  • Das S, Kar MB, Kar S (2013) Group multi-criteria decision making using intuitionistic multi-fuzzy sets. J Uncertain Anal Appl. https://doi.org/10.1186/2195-5468-1-10

    Article  Google Scholar 

  • De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Set Syst 117(2):209–213

    Article  MATH  Google Scholar 

  • Ejegwa PA (2015) Mathematical techniques to transform intuitionistic fuzzy multisets to fuzzy sets. J Inf Comput Sci 10(2):169–172

    Google Scholar 

  • Ejegwa PA (2016) Some operations on intuitionistic fuzzy multisets. J Fuzzy Math 24(4):761–768

    MATH  Google Scholar 

  • Ejegwa PA (2019a) Improved composite relation for Pythagorean fuzzy sets and its application to medical diagnosis. Granul Comput 5(2):277–286

    Article  Google Scholar 

  • Ejegwa PA (2019b) Pythagorean fuzzy set and its application in career placements based on academic performance using max–min–max composition. Complex Intell Syst 5:165–175

    Article  Google Scholar 

  • Ejegwa PA (2019c) Modified Zhang and Xu’s distance measure of Pythagorean fuzzy sets and its application to pattern recognition problems. Neural Comput Appl 32(14):10199–10208

    Article  Google Scholar 

  • Ejegwa PA (2019d) Personnel appointments: a Pythagorean fuzzy sets approach using similarity measure. J Inf Comput Sci 14(2):94–102

    Google Scholar 

  • Ejegwa PA (2019e) Modal operators on Pythagorean fuzzy sets and some of their properties. J Fuzzy Math 27(4):939–956

    Google Scholar 

  • Ejegwa PA (2020a) New similarity measures for Pythagorean fuzzy sets with applications. Int J Fuzzy Comput Model 3(1):75–94

    Article  MathSciNet  Google Scholar 

  • Ejegwa PA (2020b) Generalized triparametric correlation coefficient for Pythagorean fuzzy sets with application to MCDM problems. Granul Comput. https://doi.org/10.1007/s41066-020-00215-5

    Article  Google Scholar 

  • Ejegwa PA (2020c) Pythagorean fuzzy multiset and its application to course placements. Open J Discrete Appl Math 3(1):55–74

    Article  MathSciNet  Google Scholar 

  • Ejegwa PA, Awolola JA (2013) Some algebraic structures of intuitionistic fuzzy multisets. Int J Sci Technol 2(5):373–376

    Google Scholar 

  • Ejegwa PA, Awolola JA (2019) Novel distance measures for Pythagorean fuzzy sets with applications to pattern recognition problems. Granul Comput. https://doi.org/10.1007/s41066-019-00176-4

    Article  Google Scholar 

  • Ejegwa PA, Onyeke IC (2020) Medical diagnostic analysis on some selected patients based on modified Thao et al.’s correlation coefficient of intuitionistic fuzzy sets via an algorithmic approach. J Fuzzy Exten Appl 1(2):130–141

    Google Scholar 

  • Garg H (2018a) Some methods for strategic decision-making problems with immediate probabilities in Pythagorean fuzzy environment. Int J Intell Syst 33(4):687–712

    Article  Google Scholar 

  • Garg H (2018b) A new exponential operational laws and their aggregation operators of interval-valued Pythagorean fuzzy information. Int J Intell Syst 33(3):653–683

    Article  Google Scholar 

  • Garg H, Kumar K (2018) An advance study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making. Soft Comput 22(15):4959–4970

    Article  MATH  Google Scholar 

  • Jana C, Pal M (2019a) Assessment of enterprise performance based on picture fuzzy Hamacher aggregation operators. Symmetry 11(1):75. https://doi.org/10.3390/sym11010075

    Article  MATH  Google Scholar 

  • Jana C, Pal M (2019b) A robust single-Valued neutrosophic soft aggregation operators in multi-criteria decision-making. Symmetry 11(1):110. https://doi.org/10.3390/sym11010110

    Article  Google Scholar 

  • Jana C, Pal M, Wang JQ (2019) Bipolar fuzzy Dombi aggregation operators and its application in multiple attribute decision-making process. J Amb Intell Human Comput 10(9):3533–3549

    Article  Google Scholar 

  • Jana C, Senapati T, Pal M (2019a) Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision-making. Int J Intell Syst 34(9):2019–2038

    Article  Google Scholar 

  • Jana C, Senapati T, Pal M, Yager RR (2019b) Picture fuzzy Dombi aggregation operators: application to MADM process. Appl Soft Comput 74(1):99–109

    Article  Google Scholar 

  • Jana C, Pal M, Karaaslan F, Wang JQ (2020a) Trapezoidal neutrosophic aggregation operators and its application in multiple attribute decision-making process. Sci Iran 27(3):1655–1673

    Google Scholar 

  • Jana C, Pal M, Wang JQ (2020b) Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making. Soft Comput 24:3631–3646

    Article  MATH  Google Scholar 

  • Khan MSA, Abdullah S, Ali A, Amin F (2019) Pythagorean fuzzy prioritized aggregation operators and their application to multiattribute group decision making. Granul Comput 4:249–263

    Article  Google Scholar 

  • Liu P, Chen SM, Wang Y (2020) Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators. Inf Sci 512:830–854

    Article  MathSciNet  MATH  Google Scholar 

  • Rahman K, Abdullah S (2019) Generalized interval-valued Pythagorean fuzzy aggregation operators and their application to group decision making. Granul Comput 4:15–25

    Article  MATH  Google Scholar 

  • Rajarajeswari P, Uma N (2013) Hausdroff similarity measures for intuitionistic fuzzy multisets and its application in medical diagnosis. Int J Math Arch 4(10):106–111

    Google Scholar 

  • Rajarajeswari P, Uma N (2014) Normalized Hamming measure for intuitionistic fuzzy multisets and its application in medical diagnosis. Int J Math Trends Technol 5(3):219–225

    Article  Google Scholar 

  • Shinoj TK, Sunil JJ (2012) Intuitionistic fuzzy multisets and its application in medical diagnosis. Int J Math Comput Sci 6:34–38

    Google Scholar 

  • Shinoj TK, Sunil JJ (2013) Accuracy in collaborative robotics: an intuitionistic fuzzy multiset approach. Glob J Sci Front Res Math Decis Sci 13:21–28

    Google Scholar 

  • Szmidt E, Kacprzyk J (2001) Intuitionistic fuzzy sets in some medical applications. Note IFS 7(4):58–64

    MATH  Google Scholar 

  • Ulucay V, Deli I, Sahin M (2019) Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems. Complex Intell Syst 5:65–78

    Article  Google Scholar 

  • Yager RR (2013) Pythagorean membership grades in multicriteria decision making. Technical Report MII-3301 Machine Intelligence Institute, Iona College, New Rochelle, NY

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:38–353

    Article  Google Scholar 

  • Zeng S, Chen SM, Kuo LW (2019) Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method. Inf Sci 488:76–92

    Article  Google Scholar 

  • Zhang X (2016) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31:593–661

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics/Statistics/Computer Science, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria

    P. A. Ejegwa

  2. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, 721102, India

    C. Jana & M. Pal

Authors
  1. P. A. Ejegwa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Jana
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Jana.

Ethics declarations

Conflict of interest

The author declares that there is no conflict of interest toward the publication of this manuscript.

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

Ejegwa, P.A., Jana, C. & Pal, M. Medical diagnostic process based on modified composite relation on pythagorean fuzzy multi-sets. Granul. Comput. 7, 15–23 (2022). https://doi.org/10.1007/s41066-020-00248-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41066-020-00248-w

Keywords

Search

Navigation