Skip to main content
SpringerLink
Log in

Dual probabilistic linguistic consensus reaching method for group decision-making

  • ORIGINAL PAPER
  • Published:
Granular Computing Aims and scope Submit manuscript

Abstract

The interactive group decision-making method with dual probabilistic linguistic term sets (DPLTSs) is talked about in this paper. The benefit of choosing DPLTSs is that they take into account both random and stochastic uncertainties at the same time. The DPLTSs are superior to hesitant fuzzy sets (HFSs), probabilistic HFSs, and probabilistic dual HFSs with uncertainty. Here, we combine the merits of DPLTSs, the Archimedean copula aggregator, and the generalized Maclaurin symmetric mean (GMSM) operator and develop a consensus-based group decision-making methodology. In this methodology, the concepts of consistency and similarity between the experts are used to calculate their weights of subjective and objective types, respectively. We propose an optimization model based on cross-entropy measure and dispersion measure to generate the criteria weights. For aggregating preferences, we propose DPL weighted GMSM aggregation operator utilizing the Archimedean Copula operations between DPL elements. A case study exhibits the proposed method's applicability in group decision-making. The sensitivity analysis of criteria weights establishes the stability of the developed approach. To validate the robustness of the suggested method, a comparison study has been performed, which ensures the effectiveness of the proposed methodology.

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

Data availability

No data were used to support this study.

References

  • Akram M, Zahid S (2023) Group decision-making method with Pythagorean fuzzy rough number for the evaluation of best design concept. Granular Computing 8(6):1121–1148

    Article  Google Scholar 

  • Akram M, Habib A, Allahviranloo T (2022) A new maximal flow algorithm for solving optimization problems with linguistic capacities and flows. Inf Sci 612:201–230

    Article  Google Scholar 

  • Akram M, Niaz Z, Feng F (2023) Extended CODAS method for multi-attribute group decision-making based on 2-tuple linguistic Fermatean fuzzy Hamacher aggregation operators. Granul Comput 8(3):441–466

    Article  Google Scholar 

  • Bacigal T, Mesiar R, Najjari V (2015) Generators of Copulas and aggregation. Inf Sci 306:81–87

    Article  Google Scholar 

  • Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. In: Kacprzyk (ed) Studies in fuzziness and soft computing. Springer, Berlin

    Google Scholar 

  • Bonferroni C (1950) Sulle medie multiple di potenze. Bulletin Math Italiana 5(3):267–270

    MathSciNet  Google Scholar 

  • Cheng X, Gu J, Xu ZS (2018) Venture capital group decision-making with interaction under probabilistic linguistic environment. Knowl Based Syst 140:82–91

    Article  Google Scholar 

  • Dai S, Zheng J (2023) On probabilistic linguistic term set operations. J Intell Fuzzy Syst 44(6):9993–10003

    Article  Google Scholar 

  • Feng F, Zhang C, Akram M, Zhang J (2023) Multiple attribute decision making based on probabilistic generalized orthopair fuzzy sets. Granul Comput 8(4):863–891

    Article  Google Scholar 

  • Gou XJ, Xu ZS, Liao H (2017) Multi-criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information. Soft Comput 21:6515–6529

    Article  Google Scholar 

  • Grabisch M, Maricha JL, Mesiar R, Pap E (2011) Aggregation functions: Construction methods, conjunctive, disjunctive and mixed classes. Inf Sci 181:23–43

    Article  MathSciNet  Google Scholar 

  • Han XL, Li SR (1994) The priority method in view of consistency harmonious weight index. Syst Eng-Theory Methodol 3(1):41–45

    Google Scholar 

  • Han B, Tao Z, Chen H, Zhou L, Liu J (2020) A new computational model based on Archimedean copula for probabilistic unbalanced linguistic term set and its application to multi-attribute group decision-making. Comput Ind Eng 140:106264

    Article  Google Scholar 

  • Han X, Zhang C, Zhan J (2022) A three-way decision method under probabilistic linguistic term sets and its application to air quality index. Inf Sci 617:254–276

    Article  Google Scholar 

  • Herrera F, Martinez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8:746–752

    Article  Google Scholar 

  • Krishankumar R, Saranya R, Nethra RP, Ravichandran KS, Kar S (2019) A decision-making framework under probabilistic linguistic term set for multi-criteria group decision-making problem J. Intell Syst 36(6):5783–5795

    Google Scholar 

  • Li B, Xu ZS, Zhang YX (2020) A probabilistic linguistic evaluation based multi-stage medical system selection process related to referral system. Expert Syst Appl 170:114523

    Article  Google Scholar 

  • Liao H, Wu X (2020) DNMA: A double normalization-based multiple aggregation method for multi-expert multi-criteria decision making. Omega 94:102058. https://doi.org/10.1016/j.omega.2019.04.001

    Article  Google Scholar 

  • Liao H, Jiang L, Xu Z, Xu J (2017) A linear programming method for multiple criteria decision making with probabilistic linguistic information. Inf Sci 416:341–355

    Article  Google Scholar 

  • Liao H, Mi X, Xu X (2020) A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions. Fuzzy Optim Decis Making 19:81–134

    Article  MathSciNet  Google Scholar 

  • Liu P, Teng F (2019) Probabilistic linguistic TODIM method for selecting products through online product reviews. Inf Sci 485:441–455

    Article  ADS  Google Scholar 

  • Liu P, Wang Y (2020) Multiple-attribute decision-making based on q-rung orthopair fuzzy generalized Maclaurin symmetric mean operators. Inf Sci 518:181–210

    Article  Google Scholar 

  • Maclaurin C (1729) A second letter to Martin Folkes, Esq concerning the roots of equations, with demonstration of other rules of algebra. Philos Trans R Soc Lond 36:59–96

    Google Scholar 

  • Mishra AR, Rani P, Hezam IM, Devechi M (2023) Dual probabilistic linguistic full consistency additive ratio assessment model for medical equipment supplier selection. Int J Fuzzy Syst 25(8):3216–3232

    Article  Google Scholar 

  • Nather W (2010) Copulas and t-norms: Mathematical tools for combining probabilistic and fuzzy information with application to error propagation and interaction. Struct Saf 32:366–371

    Article  Google Scholar 

  • Nelsen RB (2013) An introduction to Copula. Springer Science and Business Media, Lecture Notes in Statistics. Springer New York, https://doi.org/10.1007/978-1-4757-3076-0

  • Pang Q, Wang H, Xu ZS (2016) probabilistic linguistic term sets in multi-attribute group decision making. Inf Sci 369:128–143

    Article  Google Scholar 

  • Ramadass S, Krishankumar R, Ravichandran KS, Liao H, Kar S (2020) Evaluation of cloud vendors from probabilistic linguistic information with unknown/partial weight values. Appl Soft Comput 97:106801

    Article  Google Scholar 

  • Rodríguez RM, Martínez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20:109–119

    Article  Google Scholar 

  • Saha A, Senapati T, Yager RR (2021) Hybridizations of Generalized Dombi operators and Bonferroni Mean operators under dual probabilistic linguistic environment for group decision-making. Int J Intell Syst 36(11):6645–6679

    Article  Google Scholar 

  • Saha A, Simic V, Senapati T, Dabic-Miletic S, Ala A (2023a) A dual hesitant fuzzy sets based methodology for advantage prioritization of zero-mile delivery solutions for sustainable city logistics. IEEE Trans Fuzzy Syst 31(2):407–420

    Article  Google Scholar 

  • Saha A, Mishra AR, Rani P, Senapati T, Yager RR (2023b) A dual probabilistic linguistic MARCOS approach based on the generalized Dombi operator for decision-making. Iran J Fuzzy Syst 20(2):83–102

    Google Scholar 

  • Sklar M (1959) Fonctions de repartition a n dimensions et leurs marges. Universite Paris 8:229–231

    Google Scholar 

  • Tao Z, Han B, Chen H (2018) On Intuitionistic fuzzy Copula aggregation operators in multiple-attribute decision-making. Cogn Comput 10:610–624

    Article  Google Scholar 

  • Wang JQ, Yang Y, Li L (2020) Multi criteria decision-making method based on single valued neutrosophic linguistic Maclaurin symmetric mean operators. Neural Comput Appl 30(5):1529–1547

    Article  Google Scholar 

  • Wang Z, Cai Q, Lu J, Wei G (2023) MABAC method based on cumulative prospect theory for MCGDM with dual probabilistic linguistic term set and application to sustainable supplier selection. J Intell Fuzzy Syst 45(3):3587–3608

    Article  Google Scholar 

  • Wei G, Wei C, Wu J, Guo Y (2021) Probabilistic linguistic multiple attribute group decision making for location planning of electric vehicle charging stations based on the generalized Dice similarity measures. Artif Intell Rev 54:4137–4167

    Article  Google Scholar 

  • Xie W, Xu ZS, Ren Z (2017) Dual probabilistic linguistic term set and its application on the multi-criteria group decision-making problems. In: 2017 IEEE International Conference on industrial engg. and engg. management. IEEE, pp 1469–1474

  • Xie W, Xu ZS, Ren Z, Viedma EH (2020) A new multi-criteria decision-making model based on incomplete dual probabilistic linguistic preference relations. Appl Soft Comput 91:106237

    Article  Google Scholar 

  • Xue WT, Xu ZS, Mi X, Ren ZL (2021) Dynamic reference point method with probabilistic linguistic information based on the regret theory for public health emergency decision-making. Econ Res Ekonomska Istrazivanja 34(1):3355–3381

    Article  Google Scholar 

  • Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision-making. IEEE Trans Syst Man Cybern 18(1):183–190

    Article  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8(3):199–249

    Article  MathSciNet  Google Scholar 

  • Zahid K, Akram M (2023) Multi-criteria group decision-making for energy production from municipal solid waste in Iran based on spherical fuzzy sets. Granul Comput 8(6):1299–1323

    Article  Google Scholar 

  • Zahid K, Akram M, Kahraman C (2022) A new ELECTRE-based method for group decision-making with complex spherical fuzzy information. Knowl-Based Syst 243:108525

    Article  Google Scholar 

Download references

Funding

There is no specific funding for this project.

Author information

Authors and Affiliations

  1. Department of Computing Technologies, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, 603203, India

    Abhijit Saha

  2. School of Mathematics and Statistics, Southwest University, Beibei, Chongqing, 400715, China

    Tapan Senapati

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

    Muhammad Akram

  4. Industrial Engineering Department, Istanbul Technical University, Macka, Istanbul, Turkey

    Cengiz Kahraman

  5. Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  6. Department of Computer Science and Engineering, College of Engineering, Koneru Lakshmiah Education Foundation, Vaddeswaram, AP, 522302, India

    Leena Arya

Authors
  1. Abhijit Saha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tapan Senapati
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Akram
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cengiz Kahraman
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Radko Mesiar
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Leena Arya
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Abhijit Saha: Conceptualization, Methodology, Software, Validation, Visualization, Investigation, Writing - Original Draft, Review & Editing. Tapan Senapati: Conceptualization, Writing - Original Draft, Review & Editing. Muhammad Akram: Writing - Original Draft, Review & Editing. Cengiz Kahraman: Conceptualization, Visualization, Writing - Original Draft, Review & Editing. Radko Mesiar: Writing - Original Draft, Review & Editing. Leena Arya: Writing - Original Draft, Review & Editing. All authors reviewed the manuscript.

Corresponding authors

Correspondence to Abhijit Saha or Tapan Senapati.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Ethical approval

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

Additional information

Publisher's Note

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

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 70 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saha, A., Senapati, T., Akram, M. et al. Dual probabilistic linguistic consensus reaching method for group decision-making. Granul. Comput. 9, 35 (2024). https://doi.org/10.1007/s41066-024-00458-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41066-024-00458-6

Keywords

Search

Navigation