Advertisement

A ranking method based on interval type-2 fuzzy sets for multiple attribute group decision making

  • Avijit De
  • Pradip Kundu
  • Sujit Das
  • Samarjit KarEmail author
Focus
First Online:
  • 39 Downloads

Abstract

Ranking of fuzzy numbers has become an important research direction for decision-making problems due to its role to find the best objects under uncertainty. In this paper, we propose a new approach to perform multiple attribute group decision-making (MAGDM) problems using the ranking of interval type-2 fuzzy sets. Initially, a new ranking method for interval type-2 fuzzy numbers based on centroid and rank index has been proposed. Next, we present a comparative study to analyze the ranking values of the proposed method with the existing approaches, where we explore the necessity of the proposed ranking method. After that, a new MAGDM approach has been developed using the proposed ranking procedure to solve uncertain MAGDM problems. Finally, the applicability of the proposed approach has been illustrated using two numerical examples and a case study related to car-sharing problems. The proposed study exhibits a useful way to solve fuzzy MAGDM problems with much efficient manner since it applies interval type-2 fuzzy sets compared to type-1 fuzzy sets to signify the evaluating values and weights of the attributes.

Keywords

Multi-attribute group decision making Interval type-2 fuzzy set Ranking method Centroid point 
This is a preview of subscription content, log in to check access.

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this article.

Human and animal rights

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

Informed consent

Informed consent is obtained from all individual participants included in the study.

References

  1. Abdullah L, Adawiyah CWR, Kamal CW (2018) A decision making method based on interval type-2 fuzzy sets: an approach for ambulance location preference. Appl Comput Inform 14:65–72CrossRefGoogle Scholar
  2. Banihabib ME, Shabestari MH (2017) Fuzzy hybrid MCDM model for ranking the agricultural water demand management strategies in arid areas. Water Resour Manag 31:495–513CrossRefGoogle Scholar
  3. Castillo O, Amador-Angulo L (2018) A generalized type-2 fuzzy logic approach for dynamic parameter adaptation in bee colony optimization applied to fuzzy controller design. Inf Sci 460:476–496CrossRefGoogle Scholar
  4. Castillo O, Cervantes L, Soria J, Sanchez M, Castro JR (2016) A generalized type-2 fuzzy granular approach with applications to aerospace. Inf Sci 354:165–177CrossRefGoogle Scholar
  5. Chen CT (2000) Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 114(1):1–9zbMATHCrossRefGoogle Scholar
  6. Chen SM (2001) Fuzzy group decision making for evaluating the rate of aggregative risk in software development. Fuzzy Sets Syst 118(1):75–88MathSciNetCrossRefGoogle Scholar
  7. Chen TY (2014) A Promethee-based outranking method for multiple criteria decision analysis with interval type-2 fuzzy sets. Soft Comput 18(5):923–940zbMATHCrossRefGoogle Scholar
  8. Chen SM, Chen SJ (2007) Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Appl Intell 26(1):1–11CrossRefGoogle Scholar
  9. Chen SM, Chen JH (2009) Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Syst Appl 36(3):6833–6842CrossRefGoogle Scholar
  10. Chen SM, Lee LW (2010a) Fuzzy multiple attributes group decision-making based on ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert Syst Appl 37(1):824–833CrossRefGoogle Scholar
  11. Chen SM, Lee LW (2010b) Fuzzy multiple attributes group decision-making based on interval type-2 TOPSIS method. Expert Syst Appl 37(4):2790–2798CrossRefGoogle Scholar
  12. Chen SM, Yang MY, Lee LW (2011) A new method for multiple attributes group decision making based on ranking interval type-2 fuzzy sets. In: Proceedings of the 2011 international conference on machine learning and cybernetics, Guilin, Guangxi, China, pp 142–147Google Scholar
  13. Chen SM, Yang MY, Lee LW, Yang SW (2012) Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets. Expert Syst Appl 39:5295–5308CrossRefGoogle Scholar
  14. Cheng CH (1998) A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst 95:307–317MathSciNetzbMATHCrossRefGoogle Scholar
  15. Chi HTX, Yu VF (2018) Ranking generalized fuzzy numbers based on centroid and rank index. Appl Soft Comput 68:283–292CrossRefGoogle Scholar
  16. Chu TC, Tsao CT (2002) Ranking fuzzy numbers with an area between the centroid point and original point. Comput Math Appl 43:111–117MathSciNetzbMATHCrossRefGoogle Scholar
  17. Cong B (2014) Picture fuzzy sets. J Comput Sci Cybern 30:409–420Google Scholar
  18. Das S, Kumar S, Kar S, Pal T (2017) Group decision making using neutrosophic soft matrix: an algorithmic approach. J King Saud Univ Comput Inf Sci.  https://doi.org/10.1016/j.jksuci.2017.05.001 CrossRefGoogle Scholar
  19. Das S, Malakar D, Kar S, Pal T (2018a) A brief review and future outline on decision making using fuzzy soft set. Int J Fuzzy Syst Appl 7(2):1–43CrossRefGoogle Scholar
  20. Das S, Kar MB, Kar S, Pal T (2018b) An approach for decision making using intuitionistic trapezoidal fuzzy soft set. Ann Fuzzy Math Inform 16(1):85–102MathSciNetGoogle Scholar
  21. Deveci M, Canıtez F, Gokasar I (2018) WASPAS and TOPSIS based interval type-2 fuzzy MCDM method for a selection of a car sharing station. Sustain Cities Soc 41:777–791CrossRefGoogle Scholar
  22. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, LondonzbMATHGoogle Scholar
  23. Dutta A, Jana DK (2017) Expectations of the reductions for type-2 trapezoidal fuzzy variables and its application to a multi-objective solid transportation problem via goal programming technique. J Uncertain Anal Appl 5(1):3CrossRefGoogle Scholar
  24. Fan ZP, Liu Y (2010) A method for group decision-making based on multi-granularity uncertain linguistic information. Expert Syst Appl 37(5):4000–4008CrossRefGoogle Scholar
  25. Fu G (2008) A fuzzy optimization method for multi criteria decision making: an application to reservoir flood control operation. Expert Syst Appl 34(1):145–149CrossRefGoogle Scholar
  26. Ghorabaee MK, Zavadskas EK, Amiri M, Esmaeili A (2016) Multi-criteria evaluation of green suppliers using an extended WASPAS method with interval type-2 fuzzy sets. J Clean Prod 137:213–229CrossRefGoogle Scholar
  27. Gonzalez CI, Melin P, Castro JR, Castillo O, Mendoza O (2016) Optimization of interval type-2 fuzzy systems for image edge detection. Appl Soft Comput 47:631–643CrossRefGoogle Scholar
  28. Grzegorzewski P, Mrowka E (2005) Trapezoidal approximations of fuzzy numbers. Fuzzy Sets Syst 153(1):115–135MathSciNetzbMATHCrossRefGoogle Scholar
  29. Hisdal E (1981) The If THEN ELSE statement and interval-valued fuzzy sets of higher type. Int J Man Mach Stud 15:385–455MathSciNetzbMATHCrossRefGoogle Scholar
  30. John RI (1998) Type 2 fuzzy sets: an appraisal of theory and applications. Int J Uncertain Fuzziness Knowl Based Syst 6:563–576MathSciNetzbMATHCrossRefGoogle Scholar
  31. John RI, Czarnecki C (1998) A type-2 adaptive fuzzy inferencing system. In: Proceedings of international conference on systems, man and cybernet, pp 2068–2073Google Scholar
  32. Kundu P, Kar S, Maiti M (2014) A fuzzy MCDM method and an application to solid transportation problem with mode preference. Soft Comput 18:1853–1864zbMATHCrossRefGoogle Scholar
  33. Kundu P, Kar S, Maiti M (2017) A fuzzy multi-criteria group decision making based on ranking interval type-2 fuzzy variables and an application to transportation mode selection problem. Soft Comput 22(11):3051–3062zbMATHCrossRefGoogle Scholar
  34. Lin CJ, Wu WW (2008) A causal analytical method for group decision-making under fuzzy environment. Expert Syst Appl 34(1):205–213MathSciNetCrossRefGoogle Scholar
  35. Liu WL, Liao H (2017) A bibliometric analysis of fuzzy decision research during 1970–2015. Int J Fuzzy Syst 19:1–14CrossRefGoogle Scholar
  36. Mandal J, Dutta P, Mukhopadhyay S (eds) (2017) Communications in computer and information science, vol 776. Springer, Berlin, pp 540–551Google Scholar
  37. Mendel JM (2003) Fuzzy sets for words: a new beginning. In: Proceedings of IEEE international conference on fuzzy systems, St. Louis, pp 37–42Google Scholar
  38. Mendel JM (2007) Computing with words: Zadeh, Turing, Popper and Occam. IEEE Comput Intell Mag 2(4):10–17CrossRefGoogle Scholar
  39. Mendel JM, John RIB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127CrossRefGoogle Scholar
  40. Mendel JM, John RI, Liu F (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14(6):808–821CrossRefGoogle Scholar
  41. Merigó JM, Gil-Lafuente AM, Yager RR (2015) An overview of fuzzy research with bibliometric indicators. Appl Soft Comput 27:420–433CrossRefGoogle Scholar
  42. Mitchell HB (2006) Ranking type-2 fuzzy numbers. IEEE Trans Fuzzy Syst 14:287–294CrossRefGoogle Scholar
  43. Mizumoto M, Tanaka K (1976a) Some properties of fuzzy sets of type-2. Inf Control 31:312–340MathSciNetzbMATHCrossRefGoogle Scholar
  44. Mizumoto M, Tanaka K (1976b) Fuzzy sets of type-2 under algebraic product and algebraic sum. Fuzzy Sets Syst 5:277–290MathSciNetzbMATHCrossRefGoogle Scholar
  45. Murakami S, Maeda S, Imamura S (1983) Fuzzy decision analysis on thee development of centralized regional energy control system. In: Proceedings of the IFAC symposium on fuzzy information, knowledge representation and decision analysis, pp 363–368Google Scholar
  46. Ngan Shing-Chung (2019) A concrete and rational approach for building type-2 fuzzy subsethood and similarity measures via a generalized foundational model. Expert Syst Appl 130:236–264CrossRefGoogle Scholar
  47. Olivas F, Valdez F, Melin P, Sombra A, Castillo O (2019) Interval type-2 fuzzy logic for dynamic parameter adaptation in a modified gravitational search algorithm. Inf Sci 476:159–175CrossRefGoogle Scholar
  48. Pramanik S, Jana DK, Mondal SK, Maiti M (2015) A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments. Inf Sci 325:190–214MathSciNetzbMATHCrossRefGoogle Scholar
  49. Roy J, Das S, Kar S, Pamučar D (2019) An extension of the CODAS approach using interval-valued intuitionistic fuzzy set for sustainable material selection in construction projects with incomplete weight information. Symmetry 11:393.  https://doi.org/10.3390/sym11030393 CrossRefGoogle Scholar
  50. Si A, Das S (2017) Intuitionistic multi-fuzzy convolution operator and its application in decision making. In: Proceedings of the international conference on computational intelligence, communications, and business analytics (CICBA), KolkataGoogle Scholar
  51. Smarandache F (1999) A unifying field in logics: Neutrosophy. Neutrosophic probability, set and logic. American Research Press, RehobothzbMATHGoogle Scholar
  52. Tsai MJ, Wang CS (2008) A computing coordination based fuzzy group decision-making (CC-FGDM) for web service oriented architecture. Expert Syst Appl 34(4):2921–2936CrossRefGoogle Scholar
  53. Turksen IB (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20:191–210MathSciNetzbMATHCrossRefGoogle Scholar
  54. Turksen IB (2002) Type-2 representation and reasoning for CWW. Fuzzy Sets Syst 127:17–36MathSciNetzbMATHCrossRefGoogle Scholar
  55. Wu Z, Chen Y (2007) The maximizing deviation method for group multiple attribute decision making under linguistic environment. Fuzzy Sets Syst 158(14):1608–1617MathSciNetzbMATHCrossRefGoogle Scholar
  56. Wu D, Mendel JM (2009) A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets. Inf Sci 179:1169–1192MathSciNetCrossRefGoogle Scholar
  57. Xu Z, Qin J, Liu J, Martínez L (2019) Sustainable supplier selection based on AHPSort II in interval type-2 fuzzy environment. Inf Sci 483:273–293CrossRefGoogle Scholar
  58. Yager RR (1978) Ranking fuzzy subsets over the unit interval. In Proceedings of the 17th IEEE international conference on decision and control, pp 1435–1437Google Scholar
  59. Yager RR (1980) Fuzzy subsets of type II in decisions. J Cybern 10:137–159MathSciNetCrossRefGoogle Scholar
  60. Yu VF, Van LH, Dat LQ, Chi HTX, Chou S-Y, Duong TTT (2017) Analyzing the ranking method for fuzzy numbers in fuzzy decision making based on the magnitude concepts. Int J Fuzzy Syst 19:1279–1289CrossRefGoogle Scholar
  61. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353zbMATHCrossRefGoogle Scholar
  62. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning: I. Inf Sci 8(3):199–249MathSciNetzbMATHCrossRefGoogle Scholar
  63. Zhang F, Ignatius J, Lim CP, Zhao Y (2014) A new method for ranking fuzzy numbers and its application to group decision making. Appl Math Model 38:1563–1582MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Avijit De
    • 1
  • Pradip Kundu
    • 2
  • Sujit Das
    • 3
  • Samarjit Kar
    • 4
    Email author
  1. 1.Department of MathematicsDr. B. C. Roy Engineering CollegeDurgapurIndia
  2. 2.Decision Science and Operations ManagementBirla Global UniversityBhubaneswarIndia
  3. 3.Department of Computer Science and EngineeringNational Institute of Technology WarangalHanamkondaIndia
  4. 4.Department of MathematicsNational Institute of Technology DurgapurDurgapurIndia

Personalised recommendations

Cite article

Buy options