Skip to main content
Log in

Intuitionistic fuzzy divergence measure-based ELECTRE method for performance of cellular mobile telephone service providers

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In India, Telecom sector has been enduring a massive growth for over two and half decades in the bandwidth, preference of services and depth of penetration in urban, semi-urban and rural areas. Exploring the service providers or selecting the best cellular mobile telephone service providers (CMTSPs/TSPs) according to operational performance parameter can help to achieve the goal of telecom service provider selection (TSPS). Here, this assessment generally comprises various TSPs alternatives and different operational performance criteria; therefore, TSPS could be considered as a multi-criteria decision-making (MCDM) problem. The analytical data have been taken from the Telecom Regulatory Authority of India (TRAI), Jan–Mar 2017. Most of the data vary from 1 month to another. Thus, these small ranges of variation in the data are incorporated with the intuitionistic fuzzy numbers (IFNs). In this paper, we develop an outranking method, intuitionistic fuzzy ELECTRE (IF-ELECTRE), for MCDM problems. Proposed method is based on divergence measure, operators of IFNs, some modifications of classical ELECTRE method. In the MCDM, the criterion weight determination is a vital issue for the accuracy of evaluation results. In the process of calculation of criterion weight, concordance and discordance values, we propose new Jensen–Shannon divergence (JS-divergence) for IFSs to overcome the shortcoming of the existing ones and demonstrate different elegant properties of the proposed one. Since the uncertainty is an inevitable feature of MCDM problems, the proposed method can be a valuable tool for decision-making in an uncertain atmosphere to determine the partial-preference outranking order. To express the strength and reasonableness of the proposed method in the real-world MCDM problems, a TSPS problem is implemented. Using the proposed framework, a decision expert can make a strategy to improve the performance by benchmarking operational parameters. Finally, a comparison is discussed between the results of the proposed method and the existing ones for validating the proposed method. This analysis shows that the proposed method is efficient and well consistent with the other methods.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Ansari MD, Mishra AR, Ansari FT (2018) New divergence and entropy measures for intuitionistic fuzzy sets on edge detection. Int J Fuzzy Syst 20(2):474–487 https://doi.org/10.1007/s40815-017-0348-4

    Article  MathSciNet  Google Scholar 

  2. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    MATH  Google Scholar 

  3. Benayoun R, Roy B, Sussmann B (1966) Manuel de reference du programme ELECTRE, documentation Inria Mai (1966 August), pp 25–39

  4. Bhandari D, Pal NR (1993) Some new information measure for fuzzy sets. Inf Sci 67:209–228

    MathSciNet  MATH  Google Scholar 

  5. Boran FE, Genc S, Kurt M, Akay D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36:11363–11368

    Google Scholar 

  6. Bottero M, Ferretti V, Figueira JR, Greco S, Roy B (2015) Dealing with a multiple criteria environmental problem with interaction effects between criteria through an extension of the ELECTRE III method. Eur J Oper Res 245:837–850

    MathSciNet  MATH  Google Scholar 

  7. Cobuloglu HI, Büyüktahtakın İE (2015) A stochastic multi-criteria decision analysis for sustainable biomass crop selection. Expert Syst Appl 42(15–16):6065–6074

    Google Scholar 

  8. De Luca A, Termini S (1972) A definition of non-probabilistic entropy in the setting of fuzzy sets theory. Inf Control 20(4):301–312

    MATH  Google Scholar 

  9. Debnath RM, Shankar R (2008) Benchmarking telecommunication service in India. Benchmarking Int J 15:584–598

    Google Scholar 

  10. Ebrahimnejad S, Naeini MA, Gitinavard H, Mousavi SM (2017) Selection of IT outsourcing services’ activities considering services cost and risks by designing an interval-valued hesitant fuzzy-decision approach. J Intell Fuzzy Syst 32(6):4081–4093

    MATH  Google Scholar 

  11. Espino DJ, Rodriguez-Hernandez J, Andrés-Valeri VC, Ballester-Muñoz F (2014) A fuzzy stochastic multi-criteria model for the selection of urban pervious pavements. Expert Syst Appl 41(15):6807–6817

    Google Scholar 

  12. Fan J, Xie W (1999) Distance measure and induced fuzzy entropy. Fuzzy Sets Syst 104(2):305–314

    MathSciNet  MATH  Google Scholar 

  13. Galo NR, Rosso LDD, Carpinetti LCR (2018) A group decision approach for supplier categorization based on hesitant fuzzy and ELECTRE TRI. Int J Prod Econ 202:182–196

    Google Scholar 

  14. Garg H, Agarwal N, Tripathi A (2017) A new generalized directed divergence measure for intuitionistic fuzzy sets and applications in expert systems. Ann Fuzzy Math Inform 13(6):699–723

    Google Scholar 

  15. Garg H (2016) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999

    Google Scholar 

  16. Garg H (2017) Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng Appl Artif Intell 60:164–174

    Google Scholar 

  17. Garg H (2017) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multi-criteria decision-making process. Int J Intell Syst 32(6):597–630

    Google Scholar 

  18. Garg H (2017) Some picture fuzzy aggregation operators and their applications to multi-criteria decision-making. Arab J Sci Eng 42(12):5275–5290

    MathSciNet  MATH  Google Scholar 

  19. Garg H (2018) Some robust improved geometric aggregation operators under interval-valued intuitionistic fuzzy environment for multi-criteria decision-making process. J Ind Manag Optim 14(1):283–308. https://doi.org/10.3934/jimo.2017047

    Article  MathSciNet  MATH  Google Scholar 

  20. Garg H, Kumar K (2018) Distance measures for connection number sets based on set pair analysis and its applications to decision-making process. Appl Intell. https://doi.org/10.1007/s10489-018-1152-z

    Article  Google Scholar 

  21. Garg H, Arora R (2018) Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision making. Eng Appl Artif Intell 71:100–112

    Google Scholar 

  22. Garg H, Singh S (2018) A novel triangular interval type-2 intuitionistic fuzzy sets and their aggregation operators. Iran J Fuzzy Syst. https://doi.org/10.22111/IJFS.2018.3559

    Article  MathSciNet  MATH  Google Scholar 

  23. Ghaderi H, Gitinavard H, Mousavi SM, Vahdani B (2017) A hesitant fuzzy cognitive mapping approach with risk preferences for student accommodation problems. Int J Appl Manag Sci 9(4):253–293

    Google Scholar 

  24. Giokas DI, Pentzaropoulos GC (2000) Evaluating productive efficiency in telecommunications: evidence from Greece. Telecommun Policy 24:781–794

    Google Scholar 

  25. Gitinavard H, Mousavi SM, Vahdani B (2017) Soft computing-based new interval-valued hesitant fuzzy multi-criteria group assessment method with last aggregation to industrial decision problems. Soft Comput 21(12):3247–3265

    MATH  Google Scholar 

  26. Gitinavard H, Mousavi SM, Vahdani B (2017) Soft computing based on hierarchical evaluation approach and criteria interdependencies for energy decision-making problems: a case study. Energy 118:556–577

    Google Scholar 

  27. Hashemi H, Mousavi SM, Zavadskas EK, Chalekaee A, Turskis Z (2018) A new group decision model based on grey-intuitionistic fuzzy-ELECTRE and VIKOR for contractor assessment problem. Sustainability 10(5):16–35

    Google Scholar 

  28. Hung WL, Yang MS (2008) On the J-divergence of intuitionistic fuzzy sets with its applications to pattern recognition. Inf Sci 178(6):1641–1650

    MathSciNet  MATH  Google Scholar 

  29. Hwang C, Yoon K (1981) Multiple attribute decision making. Springer, Berlin

    MATH  Google Scholar 

  30. Hwang CH, Yang MS (2008) On entropy of fuzzy sets. Int J Uncertain Fuzziness Knowl Based Syst 16(4):519–527

    MathSciNet  MATH  Google Scholar 

  31. Kumar K, Garg H (2018) TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math 37(2):1319–1329

    MathSciNet  MATH  Google Scholar 

  32. Kumar A, Shankar R, Debnath RM (2015) Analyzing customer preference and measuring relative efficiency in telecom sector: a hybrid fuzzy AHP/DEA study. Telemat Inform 32:447–462

    Google Scholar 

  33. Kumar P, Singh RK, Kharab K (2017) A comparative analysis of operational performance of cellular mobile telephone service providers in the Delhi working area using an approach of fuzzy ELECTRE. Appl Soft Comput 59:438–447. https://doi.org/10.1016/j.asoc.2017.06.019

    Article  Google Scholar 

  34. Kumar S, Kumar YS (2013) Evaluation of comparative performance of telecom service providers in India using TOPSIS and AHP. Int J Bus Excell 6:192–213

    Google Scholar 

  35. Lin J (1991) Divergence measure based on Shannon entropy. IEEE Trans Inf Theory 37(1):145–151

    MathSciNet  MATH  Google Scholar 

  36. Mao J, Dengbao Y, Cuicui W (2013) A novel cross-entropy and entropy measures of IFSs and their applications. Knowl Based Syst 48:37–45

    Google Scholar 

  37. Mishra AR (2016) Intuitionistic fuzzy information measures with application in rating of township development. Iran J Fuzzy Syst 13(3):49–70

    MathSciNet  MATH  Google Scholar 

  38. Mishra AR, Jain D, Hooda DS (2016) On fuzzy distance and induced fuzzy information measures. J Inf Optim Sci 37:193–211

    MathSciNet  Google Scholar 

  39. Mishra AR, Jain D, Hooda DS (2016) On logarithmic fuzzy measures of information and discrimination. J Inf Optim Sci 37:213–231

    MathSciNet  Google Scholar 

  40. Mishra AR, Jain D, Hooda DS (2016) Intuitionistic fuzzy similarity and information measures with physical education teaching quality assessment. Adv Intell Syst Comput 379:387–399

    Google Scholar 

  41. Mishra AR, Rani P (2017) Shapley divergence measures with VIKOR method for multi-attribute decision making problems. Neural Comput Appl. https://doi.org/10.1007/s00521-017-3101-x

    Article  Google Scholar 

  42. Mishra AR, Jain D, Hooda DS (2017) Exponential intuitionistic fuzzy information measure with assessment of service quality. Int J Fuzzy Syst 19(3):788–798. https://doi.org/10.1007/s40815-016-0278-6

    Article  MathSciNet  Google Scholar 

  43. Mishra AR, Rani P, Jain D (2017) Information measures based TOPSIS method for multi-criteria decision making problem in intuitionistic fuzzy environment. Iran J Fuzzy Syst 14(6):41–63. https://doi.org/10.22111/ijfs.2017.2796

    Article  MathSciNet  MATH  Google Scholar 

  44. Mishra AR, Kumari R, Sharma DK (2017) Intuitionistic fuzzy divergence measure-based multi-criteria decision-making method. Neural Comput Appl. https://doi.org/10.1007/s00521-017-3187-1

    Article  Google Scholar 

  45. Mishra AR, Rani P (2018) Biparametric information measures based TODIM technique for interval-valued intuitionistic fuzzy environment. Arab J Sci Eng 43(6):3291–3309. https://doi.org/10.1007/s13369-018-3069-6

    Article  MATH  Google Scholar 

  46. Mishra AR, Rani P, Pardasani KR (2018) Multiple-criteria decision making for service quality selection based on Shapley COPRAS method under hesitant fuzzy sets. Granul Comput. https://doi.org/10.1007/s41066-018-0103-8

    Article  Google Scholar 

  47. Mishra AR, Singh RK, Motwani D (2018) Multi-criteria assessment of cellular mobile telephone service providers using intuitionistic fuzzy WASPAS method with similarity measures. Granul Comput. https://doi.org/10.1007/s41066-018-0114-5

    Article  Google Scholar 

  48. Mohagheghi V, Mousavi SM, Aghamohagheghi M, Vahdani B (2017) A new approach of multi-criteria analysis for the evaluation and selection of sustainable transport investment projects under uncertainty: a case study. Int J Comput Intell Syst 10(1):605–626

    Google Scholar 

  49. Mohagheghi V, Mousavi SM, Vahdani B, Shahriari MR (2017) R&D project evaluation and project portfolio selection by a new interval type-2 fuzzy optimization approach. Neural Comput Appl 28(12):3869–3888

    Google Scholar 

  50. Montes I, Pal NR, Janis V, Montes S (2015) Divergence measures for intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 23:444–456

    Google Scholar 

  51. Montes S, Couso I, Gil P, Bertoluzza C (2002) Divergence measure between fuzzy sets. Int J Approx Reason 30(2):91–105

    MathSciNet  MATH  Google Scholar 

  52. Mousavi M, Gitinavard H, Mousavi SM (2017) A soft computing based modified ELECTRE model for renewable energy policy selection with unknown information. Renew Sustain Energy Rev 68:774–787

    Google Scholar 

  53. Nigam V, Thakur T, Sethi VK, Singh RP (2012) Benchmarking of Indian mobile telecom operators using DEA with sensitivity analysis. Benchmarking Int J 19:219–238

    Google Scholar 

  54. Pal NR, Pal SK (1989) Object-background segmentation using new definitions of entropy. IEEE Proc 136(4):284–295

    Google Scholar 

  55. Peng JJ, Wang JQ, Wang J, Yang LJ, Chen XH (2015) An extension of ELECTRE to multi-criteria decision-making problems with multi-hesitant fuzzy sets. Inf Sci 307:113–126

    MathSciNet  MATH  Google Scholar 

  56. Rani P, Jain D (2017) Intuitionistic fuzzy PROMETHEE technique for multi-criteria decision making problems based on entropy measure. In: Proceedings of communications in computer and information science (CCIS), vol 721, pp 290–301

  57. Rani P, Jain D, Hooda DS (2018) Shapley function based interval-valued intuitionistic fuzzy VIKOR technique for correlative multi-criteria decision making problems. Iran J Fuzzy Syst 15(1):25–54

    MathSciNet  MATH  Google Scholar 

  58. Rani P, Jain D, Hooda DS (2018) Extension of intuitionistic fuzzy TODIM technique for multi-criteria decision making method based on Shapley weighted divergence measure. Granul Comput. https://doi.org/10.1007/s41066-018-0101-x

    Article  MATH  Google Scholar 

  59. Rashid T, Faizi S, Xu ZS, Zafar S (2018) Electre-based outranking method for multi-criteria decision making using hesitant intuitionistic fuzzy linguistic term sets. Int J Fuzzy Syst 20(1):78–92

    MathSciNet  Google Scholar 

  60. Resende M (2008) Efficiency measurement and regulation in US telecommunications: a robustness analysis. Int J Prod Econ 114:205–218

    Google Scholar 

  61. Rouyendegh BD (2018) The intuitionistic fuzzy ELECTRE model. Int J Manag Sci Eng Manag 13(2):139–145

    Google Scholar 

  62. Saxena V, Thakur T, Singh RP (2009) Evaluating the performance of mobile telecom operators in India. Int J Simul Syst Sci Technol 10:58–63

    Google Scholar 

  63. Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118:467–477

    MathSciNet  MATH  Google Scholar 

  64. Tolga AC (2012) A real options approach for software development projects using fuzzy ELECTRE. J Mult Valued Logic Soft Comput 18:541–560

    Google Scholar 

  65. TRAI (2017) The Indian Telecom services performance indicators, New Delhi, India. http://trai.gov.in/sites/default/files/Performance_Indicator_Reports_28092017.pdf. Accessed Jan–Mar 2017

  66. TRAI (2017) Audit wireless report for MP (including CG) circle, Regional office Bhopal. http://www.trai.gov.in/sites/default/files/Audit_Report_MP_25072017.pdf. Accessed Jan–Mar 2017

  67. Vahdani B, Mousavi SM, Tavakkoli-Moghaddam R, 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(4):1781–1799

    MathSciNet  MATH  Google Scholar 

  68. Vahdani B, Mousavi SM, Tavakkolli-Maghaddam R, 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(4):1781–1799

    MathSciNet  MATH  Google Scholar 

  69. Vahdani B, Salimi M, Mousavi SM (2017) A new compromise solution model based on Dantzig–Wolfe decomposition for solving belief multi-objective nonlinear programming problems with block angular structure. Int J Inf Technol Decis Mak 16(02):333–387

    Google Scholar 

  70. Verma R, Maheshwari S (2017) A new measure of divergence with its application to multi-criteria decision making under fuzzy environment. Neural Comput Appl 28(8):2335–2350. https://doi.org/10.1007/s00521-016-2311-y

    Article  Google Scholar 

  71. Vlachos I, Sergiadis GD (2007) Intuitionistic fuzzy information: applications to pattern recognition. Pattern Recogn Lett 28(2):197–206

    Google Scholar 

  72. Walters SJ (2009) Quality of life outcomes in clinical trials and health-care evaluation: a practical guide to analysis and interpretation. Wiley, New York

    Google Scholar 

  73. Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 181:4273–4286

    MathSciNet  MATH  Google Scholar 

  74. Xia MM, Xu ZS (2012) Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Inf Fusion 13(1):31–47

    Google Scholar 

  75. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187

    Google Scholar 

  76. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433

    MathSciNet  MATH  Google Scholar 

  77. Yadav N (2014) Total interpretive structural modelling (TISM) of strategic performance management for Indian telecom service providers. Int J Product Perform Manag 63:421–445

    Google Scholar 

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

    MATH  Google Scholar 

  79. Yue Z, Jia Y (2017) A projection-based approach to intuitionistic fuzzy group decision making. Sci Iran Trans E Ind Eng 24(3):1505–1518

    Google Scholar 

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

    MATH  Google Scholar 

  81. Zarghami M, Szidarovszky F, Ardakanian R (2008) A fuzzy-stochastic OWA model for robust multi-criteria decision making. Fuzzy Optim Decis Mak 7(1):1–15

    MATH  Google Scholar 

  82. Zavadskas EK, Turskis Z, Antucheviciene J, Zakarevicius A (2012) Optimization of weighted aggregated sum product assessment. Elektron Elektrotech 122(6):3–6

    Google Scholar 

  83. Zhang QS, Jiang SY (2008) A note on information entropy measures for vague sets and its applications. Inf Sci 178(21):4184–4191

    MathSciNet  MATH  Google Scholar 

  84. Zhao H, Xu ZS, Ni M, Liu S (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25(1):1–30

    MATH  Google Scholar 

  85. Zhong L, Yao L (2017) An ELECTRE I-based multi-criteria group decision making method with interval type-2 fuzzy numbers and its application to supplier selection. Appl Soft Comput 57:556–576

    Google Scholar 

  86. Zhu J (2003) Quantitative models for performance evaluation and benchmarking: data envelopment analysis with spreadsheets. Kluwer Academic Publishers, Boston

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arunodaya Raj Mishra.

Ethics declarations

Conflict of interest

Author(s) declares that there is no conflict of interest.

Ethical approval

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mishra, A.R., Singh, R.K. & Motwani, D. Intuitionistic fuzzy divergence measure-based ELECTRE method for performance of cellular mobile telephone service providers. Neural Comput & Applic 32, 3901–3921 (2020). https://doi.org/10.1007/s00521-018-3716-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-018-3716-6

Keywords

Navigation