Skip to main content
SpringerLink
Log in

Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

ELECTRE is a family of multi-criteria decision analysis techniques which has the ability to provide as much as possible precise and suitable set of actions or alternatives to the underlying problem by eliminating the alternatives which are outranked by others. Group decision making is an effective process to provide the most appropriate solution to real-world decision-making scenarios by considering and merging the expert opinions of multiple individuals on problem. The purpose of this research study is to extend the ELECTRE I method to Pythagorean fuzzy ELECTRE I (PF-ELECTRE I) method in group decision-making environment, as Pythagorean fuzzy set model is more superior tool to capture vagueness and incompleteness in human evaluations. The developed method has ability to solve multi-criteria group decision-making problems in which the assessment information on available alternatives, provided by the experts, is presented as Pythagorean fuzzy decision matrices having each entry characterized by Pythagorean fuzzy number (PFN). The approach is formulated by introducing the concepts of strong, midrange and weak Pythagorean fuzzy concordance and discordance sets to elaborate the outranking relation among alternatives with respect to conflicting criteria. Framework of group decision supporting system based on PF-ELECTRE I is demonstrated by a flowchart. Finally, two illustrative examples in the field of health safety and environment management are given to verify and demonstrate the applicability of our proposed approach.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Aiello G, Enea M, Galante G (2006) A multi-objective approach to facility layout problem by genetic search algorithm and Electre method. Robot Comput Integr Manuf 22(5–6):447–455

    Article  Google Scholar 

  • Akram M, Ali G (2018) Hybrid models for decision-making based on rough Pythagorean fuzzy bipolar soft information. Granul Comput. https://doi.org/10.1007/s41066-018-0132-3

    Article  Google Scholar 

  • Akram M, Naz S (2018) Energy of Pythagorean fuzzy graphs with applications. Mathematics 6(8):136. https://doi.org/10.3390/math6080136

    Article  MATH  Google Scholar 

  • Akram M, Shumaiza Smarandache F (2018) Decision-making with bipolar neutrosophic TOPSIS and bipolar neutrosophic ELECTRE-I. Axioms 7(2):33. https://doi.org/10.3390/axioms7020033

    Article  Google Scholar 

  • Akram M, Habib A, Ilyas F, Dar JM (2018) Specific types of Pythagorean fuzzy graphs and application to decision-making. Math Comput Appl 23(3):42. https://doi.org/10.3390/mca23030042

    Article  MathSciNet  Google Scholar 

  • Akram M, Dar JM, Farooq A (2018) Planar graphs under Pythagorean fuzzy environment. Mathematics 6(12):278. https://doi.org/10.3390/math6120278

    Article  MATH  Google Scholar 

  • Akram M, Ilyas F, Saeid AB (2019a) Certain notions of Pythagorean fuzzy graphs. J Intell Fuzzy Syst. https://doi.org/10.3233/JIFS-181697

    Article  Google Scholar 

  • Akram M, Ilyas F, Dudek WA (2019b) Group decisionĄmaking based on pythagorean fuzzy TOPSIS method. Int J Intell Syst. https://doi.org/10.1002/int.22103

    Article  Google Scholar 

  • Akram M, Dar JM, Naz S (2019c) Certain graphs under Pythagorean fuzzy environment. Complex Intell Syst. https://doi.org/10.1007/s40747-018-0089-5

    Article  Google Scholar 

  • Akram M, Habib A, Davvaz B (2019d) Direct sum of n Pythagorean fuzzy graphs with application to group decision-making. J Multiple Valued Log Soft Comput (in press)

  • Alghamdi MA, Alshehri NO, Akram M (2018) Multi-criteria decision-making methods in bipolar fuzzy environment. Int J Fuzzy Syst 20(6):2057–2064

    Article  Google Scholar 

  • Arkan E, Kalender ZTS, Vayvay Ö (2017) Solid waste disposal methodology selection using multi-criteria decision making methods and an application in Turkey. J Clean Prod 142:403–412

    Article  Google Scholar 

  • Atanassov KT (1983) Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia, Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84, (in Bulgarian)

  • Aytac E, Kundaki N, Isik AT (2011) Fuzzy ELECTRE I method for evaluating catering firm alternatives. Ege Acad Rev 11:125–134

    Google Scholar 

  • Beccali M, Cellura M, Mistretta M (2003) Decision-making in energy planning. Application of the Electre method at regional level for the diffusion of renewable energy technology. Renew Energy 28(13):2063–2087

    Article  Google Scholar 

  • Benayoun R, Roy B, Sussman B (1966) ELECTRE: Une méthode pour guider le choix en présence de points de vue multiples. Note de travail 49, SEMA-METRA international, direction scientifique

  • Botti L, Peypoch N (2013) Multi-criteria ELECTRE method and destination competitiveness. Tour Manag Perspect 6:108–113

    Article  Google Scholar 

  • Brans JP, Vinvke P, Mareschal B (1986) How to select and how to rank projects: the PROMETHEE method. Eur J Oper Res 24:228–238

    Article  MathSciNet  Google Scholar 

  • Chen TY (2014) An ELECTRE-based outranking method for multiple criteria group decision making using interval type-2 fuzzy sets. Inf Sci 263:1–21

    Article  MathSciNet  Google Scholar 

  • de Almeida AT (2007) Multicriteria decision model for outsourcing contracts selection based on utility function and ELECTRE method. Comput Oper Res 34(12):3569–3574

    Article  Google Scholar 

  • Figueira JR, Mousseau V, Roy B (2005) ELECTRE methods. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: the state of the art surveys. Springer, New York, pp 133–162

    Chapter  Google Scholar 

  • Garg H (2016) A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst Wiley 31(12):1234–1253

    Article  Google Scholar 

  • Garg H (2018) Linguistic Pythagorean fuzzy sets and its applications in multi attribute decision making process. Int J Intell Syst Wiley 33(6):1234–1263

    Article  Google Scholar 

  • Garg H (2018) Hesitant Pythagorean fuzzy sets and their aggregation operators in multiple-attribute decision-making. Int J Uncertain Quantif 8(3):267–289

    Article  MathSciNet  Google Scholar 

  • Hajeeh M, AI-Othman A (2005) Application of the analytical hierarchy process in the selection of desalination plants. Desalination 174:97–108

    Article  Google Scholar 

  • Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, Berlin

    Book  Google Scholar 

  • Krylovas A (2014) New KEMIRA method for determining criteria priority and weights in solving MCDM problem. Int J Inf Technol Decis Mak 13:1119–1133

    Article  Google Scholar 

  • Naz S, Ashraf S, Akram M (2018) A novel approach to decision making with Pythagorean fuzzy information. Mathematics 6(6):95. https://doi.org/10.3390/math6060095

    Article  MATH  Google Scholar 

  • Opricovic S, Tzeng GH (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156(2):445–455

    Article  Google Scholar 

  • Peng X, Selvachandran G (2017) Pythagorean fuzzy set: state of the art and future directions. Artif Intell Rev. https://doi.org/10.1007/s10462-017-9596-9

    Article  Google Scholar 

  • Peng XD, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30(11):1133–1160

    Article  MathSciNet  Google Scholar 

  • Peng X, Yang Y (2016) Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 31:444–487

    Article  Google Scholar 

  • Peng JJ, Wang JQ, Zhang HY, Chen XH (2014) An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl Soft Comput 25:336–346

    Article  Google Scholar 

  • Pramanik T, Samanta S, Sarkar B, Pal M (2016) Fuzzy \(\phi \)-tolerance competition graphs. Soft Comput. https://doi.org/10.1007/s00500-015-2026-5

    Article  MATH  Google Scholar 

  • Ren PJ, Xu ZS, Gou XJ (2016) Pythagorean fuzzy TODIM approach to multicriteria decision making. Appl Soft Comput 42:246–259

    Article  Google Scholar 

  • Rogers M, Bruen M (1998) Choosing realistic values of indifference, preference and veto thresholds for use with environmental criteria within ELECTRE. Eur J Oper Res 107(3):542–551

    Article  Google Scholar 

  • Roy B (1968) Classement et choix en présence de points de vue multiples (la méthode ELECTRE). RIRO 8:57–75

    Google Scholar 

  • Singh PK, Kumar AC, Li J (2016) Knowledge representation using interval-valued fuzzy formal concept lattice. Soft Comput 20(4):1485–1502

    Article  Google Scholar 

  • Vahdani B, Hadipour H (2011) Extension of the ELECTRE method based on interval-valued fuzzy sets. Soft Comput 15(3):569–579

    Article  Google Scholar 

  • Vahdani B, Mousavi SM, Moghaddam RT, Hashemi H (2013) A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment. Appl Math Model 37:1781–1799

    Article  MathSciNet  Google Scholar 

  • Wu MC, Chen TY (2011) The ELECTRE multicriteria analysis approach based on Atanssov’s intuitionistic fuzzy sets. Expert Syst Appl 38:12318–12327

    Article  Google Scholar 

  • Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of the Joint IFSA world congress and NAFIPS annual meeting, Edmonton, Canada, pp 57-61

  • Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28(5):436–452

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

  • Zhan J, Masood H, Akram M (2018a) Novel decision-making algorithms based on intuitionistic fuzzy rough environment. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-018-0827-4

    Article  Google Scholar 

  • Zhan J, Akram M, Sitara M (2018b) Novel decision-making method based on bipolar neutrosophic information. Soft Comput. https://doi.org/10.1007/s00500-018-3552-8

    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(6):593–611

    Article  Google Scholar 

  • Zhang X, Xu Z (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, 4590, Pakistan

    Muhammad Akram & Farwa Ilyas

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

    Harish Garg

Authors
  1. Muhammad Akram
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Farwa Ilyas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Harish Garg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Akram.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by V. Loia.

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

Akram, M., Ilyas, F. & Garg, H. Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Comput 24, 3425–3453 (2020). https://doi.org/10.1007/s00500-019-04105-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-019-04105-0

Keywords

Search

Navigation