Document Type : Research Note

**Authors**

College of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524088, China

**Abstract**

User satisfaction and loyalty are very important in the mobile communications market because mobile is frequently updated. It is very necessary work that builds up a scientific assessment method to assist product in understanding and knowing well the trend of customers. This paper is intend to build up a scientific assessment method for measuring user satisfaction and loyalty. First, combining the group decision making and TOPSIS (technique for order preference by similarity to ideal solution) technique, a theoretical framework of evaluation method is established. Second, the respondents are allowed to express their opinions by using some simple symbols or by leaving the lack of answers to some measurement questions, even whole questionnaire. Then the symbol information along with the nonresponses in questionnaires are fused into an intuitionistic fuzzy information. Third, the levels of user satisfaction are ranked based on TOPSIS technique and projection measure in an intuitionistic fuzzy environment. Finally, the theoretical and practical implications of current model are discussed, the important limitations are recognized and future research directions are suggested.

**Keywords**

References:

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7. Aktepe, A., Ersoz, S., and Toklu, B. "Customer satisfaction and loyalty analysis with classification algorithms and structural equation modeling", Computers & Industrial Engineering, 86, pp. 95-105 (2015).

8. Li, L., Liu, F., and Li, C. "Customer satisfaction evaluation method for customized product development using entropy weight and analytic hierarchy process", Computers & Industrial Engineering, 77, pp. 80-87 (2014).

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10. Yue, Z. "An intuitionistic fuzzy projection-based approach for partner selection", Applied Mathematical Modelling, 37(23), pp. 9538-9551 (2013).

11. Yue, Z. and Jia, Y. "A group decision making model with hybrid intuitionistic fuzzy information", Computers & Industrial Engineering, 87, pp. 202-212 (2015).

12. Zhao, L., Lu, Y., Zhang, L., and Chau, P.Y. "Assessing the effects of service quality and justice on customer satisfaction and the continuance intention of mobile value-added services: An empirical test of a multidimensional model", Decision Support Systems, 52(3), pp. 645-656 (2012).

13. Bayraktar, E., Tatoglu, E., Turkyilmaz, A., Delen, D., and Zaim, S. "Measuring the efficiency of customer satisfaction and loyalty for mobile phone brands with DEA", Expert Systems with Applications, 39(1), pp. 99-106 (2012).

14. Kim, Y.H., Kim, D.J., and Wachter, K. "A study of mobile user engagement (MoEN): Engagement motivations, perceived value, satisfaction, and continued engagement intention", Decision Support Systems, 56, pp. 361-370 (2013).

15. Haverila, M. "Mobile phone feature preferences, customer satisfaction and repurchase intent among male users", Australasian Marketing Journal, 19(4), pp. 238-246 (2011).

16. Qi, J.-Y., Zhou, Y.-P., Chen, W.-J., and Qu, Q.- X. "Are customer satisfaction and customer loyalty drivers of customer lifetime value in mobile data services: A comparative cross-country study", Information Technology and Management, 13(4), pp. 281- 296 (2012).

17. Bandarua, S., Gaura, A., Deba, K., Khareb, V., and Chougulec, R. "Development, analysis and applications of a quantitative methodology for assessing customer satisfaction using evolutionary optimization", Applied Soft Computing, 30, pp. 265-278 (2015).

18. Kang D. and Park, Y. "Review-based measurement of customer satisfaction in mobile service: Sentiment analysis and VIKOR approach", Expert Systems with Applications, 41(4), pp. 1041-1050 (2014).

19. Yue, Z. and Jia, Y. "A method to aggregate crisp values into interval-valued intuitionistic fuzzy information for group decision making", Applied Soft Computing, 13(5), pp. 2304-2317 (2013).

20. Yue, Z. and Jia, Y. "An application of soft computing technique in group decision making under intervalvalued intuitionistic fuzzy environment", Applied Soft Computing, 13(5), pp. 2490-2503 (2013).

21. Yue, Z. "Group decision making with multi-attribute interval data," Information Fusion, 14(4), pp. 551-561 (2013).

22. Yue, Z. "An avoiding information loss approach to group decision making", Applied Mathematical Modelling, 37(1-2), pp. 112-126 (2013).

23. Yue, Z. "A group decision making approach based on aggregating interval data into interval-valued intuitionistic fuzzy information", Applied Mathematical Modelling, 38(2), pp. 683-698 (2014).

24. Perez, I.J., Cabrerizo, F.J., Alonso, S., and Herrera-Viedma, E. "A new consensus model for group decision making problems with non-homogeneous experts", IEEE Transactions on Systems, Man, and Cybernetics: Systems, 44(4), pp. 494-498 (2014).

25. Hashemi, H., Bazargan, J., and Mousavi, S.M. "A compromise ratio method with an application to water resources management: An intuitionistic fuzzy set", Water Resources Management, 27(7), pp. 2029-2051 (2013).

26. Liu, P. "Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making", IEEE Transactions on Fuzzy Systems, 22(1), pp. 83-97 (2014).

27. Vahdani, B., Mousavi, S.M., and Tavakkoli- Moghaddam, R. "Group decision making based on novel fuzzy modified TOPSIS method", Applied Mathematical Modelling, 35(9), pp. 4257-4269 (2011).

28. Morente-Molinera, J.A., Perez, I.J., Urena, M.R., and Herrera-Viedma, E. "On multi-granular fuzzy linguistic modeling in group decision making problems: A systematic review and future trends", Knowledge- Based Systems, 74, pp. 49-60 (2015).

29. Mousavi, S.M., Jolai, F., and Tavakkoli-Moghaddam, R. "A fuzzy stochastic multi-attribute group decisionmaking approach for selection problems", Group Decision and Negotiation, 22(2), pp. 207-233 (2013).

30. Ebrahimnejad, S., Mousavi, S., Tavakkoli- Moghaddam, R., Hashemi, H., and Vahdani, B. "A novel two-phase group decision making approach for construction project selection in a fuzzy environment", Applied Mathematical Modelling, 36(9), pp. 4197-4217 (2012).

31. Liao, H., Xu, Z., and Xia, M. "Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making", International Journal of Information Technology & Decision Making, 13(1), pp. 47-76 (2014).

32. Mousavi, S.M., Torabi, S.A., and Tavakkoli-Moghaddam, R. "A hierarchical group decisionmaking approach for new product selection in a fuzzy environment", Arabian Journal for Science and Engineering, 38(11), pp. 3233-3248 (2013).

33. Mousavi, S.M., Jolai, F., Tavakkoli-Moghaddam, R., and Vahdani, B. "A fuzzy grey model based on the compromise ranking for multi-criteria group decision making problems in manufacturing systems", Journal of Intelligent & Fuzzy Systems, 24(4), pp. 819-827 (2013).

34. Wan, S.-P. and Li, D.-F. "Atanassov's intuitionistic fuzzy programming method for heterogeneous multiattribute group decision making with Atanassov's intuitionistic fuzzy truth degrees", IEEE Transactions on Fuzzy Systems, 22(2), pp. 300-312 (2014).

35. Mousavi, S.M., Vahdani, B., Tavakkoli-Moghaddam, R., and Tajik, N. "Soft computing based on a fuzzy grey group compromise solution approach with an application to the selection problem of material handling equipment", International Journal of Computer Integrated Manufacturing, 27(6), pp. 547-569 (2014).

36. Mousavi, S.M., Mirdamadi, S., Siadat, A., Dantan, J., and Tavakkoli-Moghaddam, R. "An intuitionistic fuzzy grey model for selection problems with an application to the inspection planning in manufacturing firms", Engineering Applications of Artificial Intelligence, 39, pp. 157-167 (2015).

37. Meng, F. and Chen, X. "A new method for group decision making with incomplete fuzzy preference relations", Knowledge-Based Systems, 73, pp. 111-123 (2015).

38. Gitinavard, H., Mousavi, S.M., and Vahdani, B. "A new multi-criteria weighting and ranking model for group decision-making analysis based on intervalvalued hesitant fuzzy sets to selection problems", Neural Computing and Applications, 27, pp. 1593-1605 (2016).

39. Gitinavard, H., Mousavi, S., Vahdani, B., and Siadat, A. "A distance-based decision model in interval-valued hesitant fuzzy setting for industrial selection problems",Scientia Iranica, 23(4), pp. 1928-1940 (2016).

40. Zhang, F., Ignatius, J., Lim, C.P., and Zhao, Y. "A new method for ranking fuzzy numbers and its application to group decision making", Applied Mathematical Modelling, 38(4), pp. 1563-1582 (2014).

41. Xu, J. and Shen, F. "A new outranking choice method for group decision making under Atanassov's intervalvalued intuitionistic fuzzy environment", Knowledge-Based Systems, 70, pp. 177-188 (2014).

42. Yue, C. "A geometric approach for ranking intervalvalued intuitionistic fuzzy numbers with an application to group decision-making", Computers & Industrial Engineering, 102, pp. 233-245 (2016).

43. Kucukvar, M., Gumus, S., Egilmez, G., and Tatari, O. "Ranking the sustainability performance of pavements: An intuitionistic fuzzy decision making method", Automation in Construction, 40, pp. 33-43 (2014).

44. Chen, T.-Y. "An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis", Applied Soft Computing, 42, pp. 390- 409 (2016).

45. Vahdani, B., Mousavi, S.M., Tavakkoli-Moghaddam, R., and Hashemi, H. "A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment", Applied Mathematical Modelling, 37(4), pp. 1781-1799 (2013).

46. Hashemi, H., Bazargan, J., Mousavi, S.M., and Vahdani, B. "An extended compromise ratio model with an application to reservoir flood control operation under an interval-valued intuitionistic fuzzy environment", Applied Mathematical Modelling, 38(14), pp. 3495- 3511 (2014).

47. Dymova, L. and Sevastjanov, P. "The operations on interval-valued intuitionistic fuzzy values in the framework of Dempster-Shafer theory", Information Sciences, 360, pp. 256-272 (2016).

48. Verma, H., Agrawal, R.K., and Sharan, A. "An improved intuitionistic fuzzy c-means clustering algorithm incorporating local information for brain image segmentation", Applied Soft Computing, 46, pp. 543- 557 (2016).

49. Nguyen, H. "A new interval-valued knowledge measure for interval-valued intuitionistic fuzzy sets and application in decision making", Expert Systems with Applications, 56, pp. 143-155 (2016).

50. Ouyang, Y. and Pedrycz, W. "A new model for intuitionistic fuzzy multi-attributes decision making", European Journal of Operational Research, 249(2), pp. 677-682 (2016).

51. Mousavi, S.M., Vahdani, B., and Behzadi, S.S. "Designing a model of intuitionistic fuzzy VIKOR in multiattribute group decision-making problems," Iranian Journal of Fuzzy Systems, 13(1), pp. 45-65 (2016).

52. Yue, C. "A model for evaluating software quality based on symbol information", Journal of Guangdong Ocean University, 36(1), pp. 85-92 (2016).

53. Yue, Z. "An extended TOPSIS for determining weights of decision makers with interval numbers," Knowledge- Based Systems, 24(1), pp. 146-153 (2011).

54. Mokhtarian, M., Sadi-nezhad, S., and Makui, A. "A new flexible and reliable IVF-TOPSIS method based on uncertainty risk reduction in decision making process", Applied Soft Computing, 23, pp. 509-520 (2014).

55. Beikkhakhian, Y., Javanmardi, M., Karbasian, M., and Khayambashi, B. "The application of ISM model in evaluating agile suppliers selection criteria and ranking suppliers using fuzzy TOPSIS-AHP methods", Expert Systems with Applications, 42(15), pp. 6224- 6236 (2015).

56. Roszkowska, E. and Wachowicz, T. "Application of fuzzy TOPSIS to scoring the negotiation offers in illstructured negotiation problems", European Journal of Operational Research, 242(3), pp. 920-932 (2015).

57. Chai, J., Liu, J.N., and Ngai, E.W. "Application of decision-making techniques in supplier selection: A systematic review of literature", Expert Systems with Applications, 40(10), pp. 3872-3885 (2013).

58. Yue, Z. and Jia, Y. "A projection-based approach to intuitionistic fuzzy group decision making", Scientia Iranica, 24(3), pp. 1505-1518 (2017).

59. Zadeh, L. "Fuzzy sets", Information and Control, 8(3), pp. 338-353 (1965).

60. Atanassov, K. "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20(1), pp. 87-96 (1986).

61. Xu, Z. and Cai, X. "Recent advances in intuitionistic fuzzy information aggregation", Fuzzy Optimization and Decision Making, 9(4), pp. 359-381 (2010).

62. Atanassov, G. and Gargov, G. "Interval valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 31(3), pp. 343-349 (1989).

63. Xu, Z. and Chen, J. "An approach to group decision making based on interval-valued intuitionistic judgment matrices", Systems Engineering: Theory and Practice, 27(4), pp. 126-132 (2007).

64. Xu, Z. and Hu, H. "Projection models for intuitionistic fuzzy multiple attribute decision making", International Journal of Information Technology & Decision Making, 9(2), pp. 267-280 (2010).

65. Yue, Z. "TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting", Information Sciences, 277, pp. 141-153 (2014).

66. Hu, S.-K., Lu, M.-T., and Tzeng, G.-H. "Exploring smart phone improvements based on a hybrid MCDM model", Expert Systems with Applications, 41(9), pp. 4401-4413 (2014).

67. Yue, Z. "A method for group decision-making based on determining weights of decision makers using TOPSIS", Applied Mathematical Modelling, 35(4), pp. 1926-1936 (2011).

68. Yue, Z. and Jia, Y. "A direct projection-based group decision-making methodology with crisp values and interval data", Soft Computing, 21(9), pp. 2395-2405 (2017).

2. Rahul, T. and Majhi, R. "An adaptive nonlinear approach for estimation of consumer satisfaction and loyalty in mobile phone sector of India", Journal of Retailing and Consumer Services, 21(4), pp. 570-580 (2014).

3. Cronin Jr, J.J., Brady, M.K., and Hult, G.T.M. "Assessing the effects of quality, value, and customer satisfaction on consumer behavioral intentions in service environments", Journal of Retailing, 76(2), pp. 193- 218 (2000).

4. Seiders, K., Voss, G.B., Grewal, D., and Godfrey, A.L. "Do satisfied customers buy more? Examining moderating influences in a retailing context", Journal of Marketing, 69(4), pp. 26-43 (2005).

5. Li, G., Bie, Z., Xie, H., and Lin, Y. "Customer satisfaction based reliability evaluation of active distribution networks", Applied Energy, 162, pp. 1571-1578 (2016).

6. Leong, L.-Y., Hew, T.-S., Lee, V.-H., and Ooi, K.-B. "An SEM-artificial-neural-network analysis of the relationships between SERVPERF, customer satisfaction and loyalty among low-cost and full-service airline", Expert Systems with Applications, 42(19), pp. 6620- 6634 (2015).

7. Aktepe, A., Ersoz, S., and Toklu, B. "Customer satisfaction and loyalty analysis with classification algorithms and structural equation modeling", Computers & Industrial Engineering, 86, pp. 95-105 (2015).

8. Li, L., Liu, F., and Li, C. "Customer satisfaction evaluation method for customized product development using entropy weight and analytic hierarchy process", Computers & Industrial Engineering, 77, pp. 80-87 (2014).

9. Hwang, C. and Yoon, K., Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag, Berlin (1981).

10. Yue, Z. "An intuitionistic fuzzy projection-based approach for partner selection", Applied Mathematical Modelling, 37(23), pp. 9538-9551 (2013).

11. Yue, Z. and Jia, Y. "A group decision making model with hybrid intuitionistic fuzzy information", Computers & Industrial Engineering, 87, pp. 202-212 (2015).

12. Zhao, L., Lu, Y., Zhang, L., and Chau, P.Y. "Assessing the effects of service quality and justice on customer satisfaction and the continuance intention of mobile value-added services: An empirical test of a multidimensional model", Decision Support Systems, 52(3), pp. 645-656 (2012).

13. Bayraktar, E., Tatoglu, E., Turkyilmaz, A., Delen, D., and Zaim, S. "Measuring the efficiency of customer satisfaction and loyalty for mobile phone brands with DEA", Expert Systems with Applications, 39(1), pp. 99-106 (2012).

14. Kim, Y.H., Kim, D.J., and Wachter, K. "A study of mobile user engagement (MoEN): Engagement motivations, perceived value, satisfaction, and continued engagement intention", Decision Support Systems, 56, pp. 361-370 (2013).

15. Haverila, M. "Mobile phone feature preferences, customer satisfaction and repurchase intent among male users", Australasian Marketing Journal, 19(4), pp. 238-246 (2011).

16. Qi, J.-Y., Zhou, Y.-P., Chen, W.-J., and Qu, Q.- X. "Are customer satisfaction and customer loyalty drivers of customer lifetime value in mobile data services: A comparative cross-country study", Information Technology and Management, 13(4), pp. 281- 296 (2012).

17. Bandarua, S., Gaura, A., Deba, K., Khareb, V., and Chougulec, R. "Development, analysis and applications of a quantitative methodology for assessing customer satisfaction using evolutionary optimization", Applied Soft Computing, 30, pp. 265-278 (2015).

18. Kang D. and Park, Y. "Review-based measurement of customer satisfaction in mobile service: Sentiment analysis and VIKOR approach", Expert Systems with Applications, 41(4), pp. 1041-1050 (2014).

19. Yue, Z. and Jia, Y. "A method to aggregate crisp values into interval-valued intuitionistic fuzzy information for group decision making", Applied Soft Computing, 13(5), pp. 2304-2317 (2013).

20. Yue, Z. and Jia, Y. "An application of soft computing technique in group decision making under intervalvalued intuitionistic fuzzy environment", Applied Soft Computing, 13(5), pp. 2490-2503 (2013).

21. Yue, Z. "Group decision making with multi-attribute interval data," Information Fusion, 14(4), pp. 551-561 (2013).

22. Yue, Z. "An avoiding information loss approach to group decision making", Applied Mathematical Modelling, 37(1-2), pp. 112-126 (2013).

23. Yue, Z. "A group decision making approach based on aggregating interval data into interval-valued intuitionistic fuzzy information", Applied Mathematical Modelling, 38(2), pp. 683-698 (2014).

24. Perez, I.J., Cabrerizo, F.J., Alonso, S., and Herrera-Viedma, E. "A new consensus model for group decision making problems with non-homogeneous experts", IEEE Transactions on Systems, Man, and Cybernetics: Systems, 44(4), pp. 494-498 (2014).

25. Hashemi, H., Bazargan, J., and Mousavi, S.M. "A compromise ratio method with an application to water resources management: An intuitionistic fuzzy set", Water Resources Management, 27(7), pp. 2029-2051 (2013).

26. Liu, P. "Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making", IEEE Transactions on Fuzzy Systems, 22(1), pp. 83-97 (2014).

27. Vahdani, B., Mousavi, S.M., and Tavakkoli- Moghaddam, R. "Group decision making based on novel fuzzy modified TOPSIS method", Applied Mathematical Modelling, 35(9), pp. 4257-4269 (2011).

28. Morente-Molinera, J.A., Perez, I.J., Urena, M.R., and Herrera-Viedma, E. "On multi-granular fuzzy linguistic modeling in group decision making problems: A systematic review and future trends", Knowledge- Based Systems, 74, pp. 49-60 (2015).

29. Mousavi, S.M., Jolai, F., and Tavakkoli-Moghaddam, R. "A fuzzy stochastic multi-attribute group decisionmaking approach for selection problems", Group Decision and Negotiation, 22(2), pp. 207-233 (2013).

30. Ebrahimnejad, S., Mousavi, S., Tavakkoli- Moghaddam, R., Hashemi, H., and Vahdani, B. "A novel two-phase group decision making approach for construction project selection in a fuzzy environment", Applied Mathematical Modelling, 36(9), pp. 4197-4217 (2012).

31. Liao, H., Xu, Z., and Xia, M. "Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making", International Journal of Information Technology & Decision Making, 13(1), pp. 47-76 (2014).

32. Mousavi, S.M., Torabi, S.A., and Tavakkoli-Moghaddam, R. "A hierarchical group decisionmaking approach for new product selection in a fuzzy environment", Arabian Journal for Science and Engineering, 38(11), pp. 3233-3248 (2013).

33. Mousavi, S.M., Jolai, F., Tavakkoli-Moghaddam, R., and Vahdani, B. "A fuzzy grey model based on the compromise ranking for multi-criteria group decision making problems in manufacturing systems", Journal of Intelligent & Fuzzy Systems, 24(4), pp. 819-827 (2013).

34. Wan, S.-P. and Li, D.-F. "Atanassov's intuitionistic fuzzy programming method for heterogeneous multiattribute group decision making with Atanassov's intuitionistic fuzzy truth degrees", IEEE Transactions on Fuzzy Systems, 22(2), pp. 300-312 (2014).

35. Mousavi, S.M., Vahdani, B., Tavakkoli-Moghaddam, R., and Tajik, N. "Soft computing based on a fuzzy grey group compromise solution approach with an application to the selection problem of material handling equipment", International Journal of Computer Integrated Manufacturing, 27(6), pp. 547-569 (2014).

36. Mousavi, S.M., Mirdamadi, S., Siadat, A., Dantan, J., and Tavakkoli-Moghaddam, R. "An intuitionistic fuzzy grey model for selection problems with an application to the inspection planning in manufacturing firms", Engineering Applications of Artificial Intelligence, 39, pp. 157-167 (2015).

37. Meng, F. and Chen, X. "A new method for group decision making with incomplete fuzzy preference relations", Knowledge-Based Systems, 73, pp. 111-123 (2015).

38. Gitinavard, H., Mousavi, S.M., and Vahdani, B. "A new multi-criteria weighting and ranking model for group decision-making analysis based on intervalvalued hesitant fuzzy sets to selection problems", Neural Computing and Applications, 27, pp. 1593-1605 (2016).

39. Gitinavard, H., Mousavi, S., Vahdani, B., and Siadat, A. "A distance-based decision model in interval-valued hesitant fuzzy setting for industrial selection problems",Scientia Iranica, 23(4), pp. 1928-1940 (2016).

40. Zhang, F., Ignatius, J., Lim, C.P., and Zhao, Y. "A new method for ranking fuzzy numbers and its application to group decision making", Applied Mathematical Modelling, 38(4), pp. 1563-1582 (2014).

41. Xu, J. and Shen, F. "A new outranking choice method for group decision making under Atanassov's intervalvalued intuitionistic fuzzy environment", Knowledge-Based Systems, 70, pp. 177-188 (2014).

42. Yue, C. "A geometric approach for ranking intervalvalued intuitionistic fuzzy numbers with an application to group decision-making", Computers & Industrial Engineering, 102, pp. 233-245 (2016).

43. Kucukvar, M., Gumus, S., Egilmez, G., and Tatari, O. "Ranking the sustainability performance of pavements: An intuitionistic fuzzy decision making method", Automation in Construction, 40, pp. 33-43 (2014).

44. Chen, T.-Y. "An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis", Applied Soft Computing, 42, pp. 390- 409 (2016).

45. Vahdani, B., Mousavi, S.M., Tavakkoli-Moghaddam, R., and Hashemi, H. "A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment", Applied Mathematical Modelling, 37(4), pp. 1781-1799 (2013).

46. Hashemi, H., Bazargan, J., Mousavi, S.M., and Vahdani, B. "An extended compromise ratio model with an application to reservoir flood control operation under an interval-valued intuitionistic fuzzy environment", Applied Mathematical Modelling, 38(14), pp. 3495- 3511 (2014).

47. Dymova, L. and Sevastjanov, P. "The operations on interval-valued intuitionistic fuzzy values in the framework of Dempster-Shafer theory", Information Sciences, 360, pp. 256-272 (2016).

48. Verma, H., Agrawal, R.K., and Sharan, A. "An improved intuitionistic fuzzy c-means clustering algorithm incorporating local information for brain image segmentation", Applied Soft Computing, 46, pp. 543- 557 (2016).

49. Nguyen, H. "A new interval-valued knowledge measure for interval-valued intuitionistic fuzzy sets and application in decision making", Expert Systems with Applications, 56, pp. 143-155 (2016).

50. Ouyang, Y. and Pedrycz, W. "A new model for intuitionistic fuzzy multi-attributes decision making", European Journal of Operational Research, 249(2), pp. 677-682 (2016).

51. Mousavi, S.M., Vahdani, B., and Behzadi, S.S. "Designing a model of intuitionistic fuzzy VIKOR in multiattribute group decision-making problems," Iranian Journal of Fuzzy Systems, 13(1), pp. 45-65 (2016).

52. Yue, C. "A model for evaluating software quality based on symbol information", Journal of Guangdong Ocean University, 36(1), pp. 85-92 (2016).

53. Yue, Z. "An extended TOPSIS for determining weights of decision makers with interval numbers," Knowledge- Based Systems, 24(1), pp. 146-153 (2011).

54. Mokhtarian, M., Sadi-nezhad, S., and Makui, A. "A new flexible and reliable IVF-TOPSIS method based on uncertainty risk reduction in decision making process", Applied Soft Computing, 23, pp. 509-520 (2014).

55. Beikkhakhian, Y., Javanmardi, M., Karbasian, M., and Khayambashi, B. "The application of ISM model in evaluating agile suppliers selection criteria and ranking suppliers using fuzzy TOPSIS-AHP methods", Expert Systems with Applications, 42(15), pp. 6224- 6236 (2015).

56. Roszkowska, E. and Wachowicz, T. "Application of fuzzy TOPSIS to scoring the negotiation offers in illstructured negotiation problems", European Journal of Operational Research, 242(3), pp. 920-932 (2015).

57. Chai, J., Liu, J.N., and Ngai, E.W. "Application of decision-making techniques in supplier selection: A systematic review of literature", Expert Systems with Applications, 40(10), pp. 3872-3885 (2013).

58. Yue, Z. and Jia, Y. "A projection-based approach to intuitionistic fuzzy group decision making", Scientia Iranica, 24(3), pp. 1505-1518 (2017).

59. Zadeh, L. "Fuzzy sets", Information and Control, 8(3), pp. 338-353 (1965).

60. Atanassov, K. "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20(1), pp. 87-96 (1986).

61. Xu, Z. and Cai, X. "Recent advances in intuitionistic fuzzy information aggregation", Fuzzy Optimization and Decision Making, 9(4), pp. 359-381 (2010).

62. Atanassov, G. and Gargov, G. "Interval valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 31(3), pp. 343-349 (1989).

63. Xu, Z. and Chen, J. "An approach to group decision making based on interval-valued intuitionistic judgment matrices", Systems Engineering: Theory and Practice, 27(4), pp. 126-132 (2007).

64. Xu, Z. and Hu, H. "Projection models for intuitionistic fuzzy multiple attribute decision making", International Journal of Information Technology & Decision Making, 9(2), pp. 267-280 (2010).

65. Yue, Z. "TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting", Information Sciences, 277, pp. 141-153 (2014).

66. Hu, S.-K., Lu, M.-T., and Tzeng, G.-H. "Exploring smart phone improvements based on a hybrid MCDM model", Expert Systems with Applications, 41(9), pp. 4401-4413 (2014).

67. Yue, Z. "A method for group decision-making based on determining weights of decision makers using TOPSIS", Applied Mathematical Modelling, 35(4), pp. 1926-1936 (2011).

68. Yue, Z. and Jia, Y. "A direct projection-based group decision-making methodology with crisp values and interval data", Soft Computing, 21(9), pp. 2395-2405 (2017).

Transactions on Industrial Engineering (E)

January and February 2019Pages 589-604