Neutrosophic AHP-Delphi Group decision making model based on trapezoidal neutrosophic numbers

  • Mohamed Abdel-Basset
  • Mai Mohamed
  • Arun Kumar Sangaiah
Original Research
First Online:
Received:
Accepted:

Abstract

The main objective of this research is to study the integration of Analytic Hierarchy Process (AHP) into Delphi framework in neutrosophic environment and present a new technique for checking consistency and calculating consensus degree of expert’s opinions. In some pragmatism bearings, the experts might be not able to assign deterministic evaluation values to the comparison judgments due to his/her confined knowledge or the differences of individual judgments in group decision making. To overcome these challenges, we have used neutrosophic set theory to handle the integration of AHP into Delphi framework, where each pairwise comparison judgment is symbolized as a trapezoidal neutrosophic number. The power of AHP is enhanced by adding Delphi technique, since it can reduce noise which result from focusing on group and/or individual interests rather than concentriciting on problem disband and it also increase consensus degree about ideas. Obtaining a consistent trapezoidal neutrosophic preference relation is very difficult in decision making process because in creating a consistent trapezoidal preference relation; each expert should make \(\frac{{n \times \left( {n - 1} \right)}}{2}\) consistent judgments for \(n\) alternatives. When the number of alternatives is increasing, the workload of giving judgments for the experts is heavy and it makes them tired and leads to inconsistent judgments. In the proposed model,experts will focus only on \(\left( {n - 1} \right)\) restricted judgments and this also enhances the performance of AHP over the traditional version that is proposed by Saaty. A real life example is developed based on expert opinions about evaluation process of many international search engines. The problem is solved to show the validation of the suggested method in neutrosophic path.

Keywords

Analytic hierarchy process (AHP) Delphi technique Neutrosophic set theory Trapezoidal neutrosophic numbers Consistency Consensus degree 
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Notes

Acknowledgements

The authors would like to thank the anonymous referees, Editor-in-Chief, and Associate Editors for their constructive comments and suggestions that have helped a lot to come up with this improved form of the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

References

  1. Abdel-Baset M, Hezam IM, Smarandache F (2016) Neutrosophic goal programming. Neutrosophic Sets Syst 11:112–118Google Scholar
  2. Daneshvar Rouyendegh B (2011) The DEA and intuitionistic fuzzy TOPSIS approach to departments’ performances: a pilot study. J Appl MathGoogle Scholar
  3. El-Hefenawy N, Metwally MA, Ahmed ZM, El-Henawy IM (2016) A review on the applications of neutrosophic sets. J Comput Theor Nanosci 13(1):936–944CrossRefGoogle Scholar
  4. Helmer O, Rescher N (1959) On the epistemology of the inexact sciences. Manag Sci 6(1):25–52CrossRefGoogle Scholar
  5. Hezam I M, Abdel-Baset M, Smarandache F (2015) Taylor series approximation to solve neutrosophic multiobjective programming problem. Neutrosophic Sets Syst 10:39–46Google Scholar
  6. Jain V, Sangaiah AK, Sakhuja S, Thoduka N, Aggarwal R (2016) Supplier selection using fuzzy AHP and TOPSIS: a case study in the Indian automotive industry. Neural Comput Appl. doi: 10.1007/s00521-016-2533-0 Google Scholar
  7. Kazemi S, Homayouni SM, Jahangiri J (2015) A fuzzy Delphi-analytical hierarchy process approach for ranking of effective material selection criteria. Adv Mater Sci Eng 2015:1–12Google Scholar
  8. Kerlinger FN, Lee HB (1999) Foundations of behavioral research. ISBN-13: 978-0155078970Google Scholar
  9. Kim M, Jang Y-C, Lee S (2013) Application of Delphi-AHP methods to select the priorities of WEEE for recycling in a waste management decision-making tool. J Environ Manag 128:941–948CrossRefGoogle Scholar
  10. Lewandowski D, Wu K, Sun X, Meng F (2011) Using a Delphi method and the analytic hierarchy process to evaluate Chinese search engines: a case study on Chinese search engines. Online Inf Rev 35(6):942–956CrossRefGoogle Scholar
  11. Liu W-K (2013) Application of the fuzzy Delphi Method and the fuzzy analytic hierarchy process for the managerial competence of multinational corporation executives. Int J e-Educ e-Bus e-Manag e-Learn 3(4):313Google Scholar
  12. Liu F, Pedrycz W, Zhang W G (2016) Limited rationality and its quantification through the interval number judgments with permutations. IEEE Trans Cybern 99:1–13Google Scholar
  13. Lv Y (2001) Research on scale system evaluation. AHP. In: System Engineering Society of China (ed) Theory and methods for decision science. Ocean Press, Beijing, pp 50–58Google Scholar
  14. Lv YJ, Zhang W, Ceng XL (2003) Comparative study on exponential scale and 1–9 scale. Chin J Eng Math 20(8):77–78Google Scholar
  15. Mahdi IM, Riley MJ, Fereig SM, Alex AP (2002) A multi-criteria approach to contractor selection. Eng Constr Archit Manag 9(1):29–37Google Scholar
  16. Miller LE (2006) Determining what could/should be: the Delphi technique and its application. In: Meeting of the 2006 annual meeting of the Mid-Western Educational Research Association, ColumbusGoogle Scholar
  17. Saaty TL (2008) Decision making with the analytic hierarchy process. Int J Serv Sci 1(1):83–98MathSciNetGoogle Scholar
  18. Saaty TL, Vargas LG (2006) Decision making with the analytic network process. Springer, BostonMATHGoogle Scholar
  19. Samuel OW, Asogbon GM, Sangaiah AK, Fang P, Li G (2017) An integrated decision support system based on ANN and Fuzzy_AHP for heart failure risk prediction. Expert Syst Appl 68:163–172CrossRefGoogle Scholar
  20. Sangaiah A, Thangavelu A (2013) An exploration of FMCDM approach for evaluating the outcome/success of GSD projects. Open Eng 3(3):419–435CrossRefGoogle Scholar
  21. Sangaiah AK, Jain V (2016) Fusion of fuzzy multi-criteria decision making approaches for discriminating risk with relate to software project performance. In: Handbook of research on fuzzy and rough set theory in organizational decision making 3:38Google Scholar
  22. Sangaiah AK, Subramaniam PR, Zheng X (2015) A combined fuzzy DEMATEL and fuzzy TOPSIS approach for evaluating GSD project outcome factors. Neural Comput Appl 26(5):1025–1040CrossRefGoogle Scholar
  23. Sangaiah AK, Gopal J, Basu A, Subramaniam PR (2017) An integrated fuzzy DEMATEL, TOPSIS, and ELECTRE approach for evaluating knowledge transfer effectiveness with reference to GSD project outcome. Neural Comput Appl 28(1):111–123CrossRefGoogle Scholar
  24. Tavana M, Kennedy DT, Rappaport J, Ugras YJ (1993) An AHP-Delphi group decision support system applied to conflict resolution in hiring decisions. J Manag Syst 5(1):49–74Google Scholar
  25. Wen J, Li D, Zhu F (2015) Stable recovery of sparse signals via lp-minimization. Appl Comput Harmon Anal 38(1):161–176MathSciNetCrossRefMATHGoogle Scholar
  26. Wen J, Zhou Z, Wang J, Tang X, Mo Q (2016) A sharp condition for exact support recovery of sparse signals with orthogonal matching pursuit. In: Information Theory (ISIT), IEEE International Symposium, pp 2364–2368Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Operations Research, Faculty of Computers and InformaticsZagazig UniversitySharqiyahEgypt
  2. 2.School of Computing Science and EngineeringVIT UniversityVelloreIndia

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