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A signed-distance-based approach to importance assessment and multi-criteria group decision analysis based on interval type-2 fuzzy set

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Abstract

Interval type-2 fuzzy sets are associated with greater imprecision and more ambiguities than ordinary fuzzy sets. This paper presents a signed-distance-based method for determining the objective importance of criteria and handling fuzzy, multiple criteria group decision-making problems in a flexible and intelligent way. These advantages arise from the method’s use of interval type-2 trapezoidal fuzzy numbers to represent alternative ratings and the importance of various criteria. An integrated approach to determine the overall importance of the criteria is also developed using the subjective information provided by decision-makers and the objective information delivered by the decision matrix. In addition, a linear programming model is developed to estimate criterion weights and to extend the proposed multiple criteria decision analysis method. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a group decision-making problem of patient-centered medicine in basilar artery occlusion.

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References

  1. Aisbett J, Rickard JT, Morgenthaler D (2011) Multivariate modeling and type-2 fuzzy sets. Fuzzy Sets Syst 163(1): 78–95

    Article  MathSciNet  MATH  Google Scholar 

  2. Akay D, Kulak O, Henson B (2011) Conceptual design evaluation using interval type-2 fuzzy information axiom. Comput Ind 62(2): 138–146

    Article  Google Scholar 

  3. Al-khazraji A, Essounbouli N, Hamzaoui A, Nollet F, Zaytoon J (2011) Type-2 fuzzy sliding mode control without reaching phase for nonlinear system. Eng Appl Artif Intell 24(1): 23–38

    Article  Google Scholar 

  4. Asciutto AJ, Haddad E, Green J, Sandberg DE (2011) Patient-centered care: caring for families affected by disorders of sex development. In: New MI, Simpson JL (eds) Hormonal and genetic basis of sexual differentiation disorders and hot topics in endocrinology, advances in experimental medicine and biology 707. Springer Science+Business Media, LLC, Berlin, pp 135–142

    Google Scholar 

  5. Benayoun R, de Montgolfier J, Tergny J, Laritchev O (1971) Linear programming with multiple objective functions: step method (STEM). Math Program 1(3): 366–375

    Article  MATH  Google Scholar 

  6. Bigand A, Colot O (2010) Fuzzy filter based on interval-valued fuzzy sets for image filtering. Fuzzy Sets Syst 161(1): 96–117

    Article  MathSciNet  Google Scholar 

  7. Biglarbegian M, Melek W, Mendel J (2011) On the robustness of type-1 and interval type-2 fuzzy logic systems in modeling. Inf Sci 181(7): 1325–1347

    Article  MathSciNet  MATH  Google Scholar 

  8. Bustince H, Barrenechea E, Pagola M, Fernandez J (2009) Interval-valued fuzzy sets constructed from matrices: application to edge detection. Fuzzy Sets Syst 160(13): 1819–1840

    Article  MathSciNet  MATH  Google Scholar 

  9. Cercone N, An X, Li J, Gu Z, An A (2011) Finding best evidence for evidence-based best practice recommendations in health care: the initial decision support system design. Knowl Inf Syst 29(1): 159–201

    Article  Google Scholar 

  10. Chen SM (1996) New methods for subjective mental workload assessment and fuzzy risk analysis. Cybern Syst 27(5): 449–472

    Article  MATH  Google Scholar 

  11. Chen S-J (2011) Measure of similarity between interval-valued fuzzy numbers for fuzzy recommendation process based on quadratic-mean operator. Expert Syst Appl 38(3): 2386–2394

    Article  Google Scholar 

  12. Chen T-Y (2011) Multi-criteria decision-making method with leniency reduction based on interval-valued fuzzy sets. J Chin Inst Ind Eng 28(1): 1–19

    MATH  Google Scholar 

  13. Chen T-Y (2011) Optimistic and pessimistic decision making with dissonance reduction using interval-valued fuzzy sets. Inf Sci 181(3): 479–502

    Article  MATH  Google Scholar 

  14. Chen T-Y (2011) Multiple criteria group decision-making with generalized interval-valued fuzzy numbers based on signed distances and incomplete weights. Appl Math Model 36(7): 3029–3052

    Article  Google Scholar 

  15. Chen T-Y (2011) Signed distanced-based TOPSIS method for multiple criteria decision analysis based on generalized interval-valued fuzzy numbers. Int J Inf Technol Decis Making 10(6): 1131–1159

    Article  MATH  Google Scholar 

  16. Chen S-J, Chen S-M (2008) Fuzzy risk analysis based on measures of similarity between interval-valued fuzzy numbers. Comput Math Appl 55(8): 1670–1685

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen S-M, Chen J-H (2009) Fuzzy risk analysis based on similarity measures between interval-valued fuzzy numbers and interval-valued fuzzy number arithmetic operators. Expert Syst Appl 36(3–2): 6309–6317

    Article  Google Scholar 

  18. Chen Y-S, Cheng C-H (2010) Forecasting PGR of the financial industry using a rough sets classifier based on attribute-granularity. Knowl Inf Syst 25(1): 57–79

    Article  Google Scholar 

  19. Chen S-M, Lee L-W (2010) Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method. Expert Syst Appl 37(4): 2790–2798

    Article  Google Scholar 

  20. Chen T-Y, Tsao C-Y (2008) The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets Syst 159(11): 1410–1428

    Article  MathSciNet  MATH  Google Scholar 

  21. Chen T-Y, Wang J-C (2009) Interval-valued fuzzy permutation method and experimental analysis on cardinal and ordinal evaluations. J Comput Syst Sci 75(7): 371–387

    Article  MATH  Google Scholar 

  22. Chiang J (2001) Fuzzy linear programming based on statistical confidence interval and interval-valued fuzzy set. Eur J Oper Res 129(1): 65–86

    Article  MATH  Google Scholar 

  23. Colman AM, Norris CE, Preston CC (1997) Comparing rating scales of different lengths: equivalence of scores from 5-point and 7-point scales. Psychol Rep 80(2): 355–362

    Article  Google Scholar 

  24. Coulter A. (2002) The autonomous patient: ending paternalism in medical care. Nuffield Trust, London

    Google Scholar 

  25. Cox EP III (1980) The optimal number of response alternatives for a scale: a review. J Market Res 17(4): 407–422

    Article  Google Scholar 

  26. Deschrijver G (2007) Arithmetic operators in interval-valued fuzzy set theory. Inf Sci 177(14): 2906–2924

    Article  MathSciNet  MATH  Google Scholar 

  27. Epstein RM, Street RL Jr. (2011) The values and value of patient-centered care. Ann Family Med 9(2): 100–103

    Article  Google Scholar 

  28. Fernández A, Morales M, Rodríguez C, Salmerón A (2011) A system for relevance analysis of performance indicators in higher education using Bayesian networks. Knowl Inf Syst 27(3): 327–344

    Article  Google Scholar 

  29. Greenfield S, Chiclana F, Coupland S, John R (2009) The collapsing method of defuzzification for discretised interval type-2 fuzzy sets. Inf Sci 179(13): 2055–2069

    Article  MathSciNet  MATH  Google Scholar 

  30. Hudon B, Fortin M, Haggerty JL, Lambert M, Poitras M-E (2011) Measuring patients’ perceptions of patient-centered care: a systematic review of tools for family medicine. Ann Family Med 9(2): 155–164

    Article  Google Scholar 

  31. Kaya T, Kahraman C (2011) Multicriteria decision making in energy planning using a modified fuzzy TOPSIS methodology. Expert Syst Appl 38(6): 6577–6585

    Article  Google Scholar 

  32. Leal-Ramírez B, Castillo O, Melin P, Rodríguez-Díaz A (2011) Simulation of the bird age-structured population growth based on an interval type-2 fuzzy cellular structure. Inf Sci 181(3): 519–535

    Article  Google Scholar 

  33. Lin TC (2010) Based on interval type-2 fuzzy-neural network direct adaptive sliding mode control for SISO nonlinear systems. Commun Nonlinear Sci Numer Simul 15(12): 4084–4099

    Article  MathSciNet  MATH  Google Scholar 

  34. Lin T-C, Chen M-C, Roopaei M (2011) Synchronization of uncertain chaotic systems based on adaptive type-2 fuzzy sliding mode control. Eng Appl Artif Intell 24(1): 39–49

    Article  Google Scholar 

  35. Liu S, Duffy AHB, Whitfield RI, Boyle IM (2010) Integration of decision support systems to improve decision support performance. Knowl Inf Syst 22(3): 261–286

    Article  Google Scholar 

  36. Lu HW, Huang GH, He L (2010) Development of an interval-valued fuzzy linear-programming method based on infinite α-cuts for water resources management. Environ Model Softw 25(3): 354–361

    Article  Google Scholar 

  37. Lutz BJ, Bowers BJ (2000) Patient-centered care: understanding its interpretation and implementation in health care. Sch Inq Nurs Pract 14(2): 165–182

    Google Scholar 

  38. Malhotra NK (2009) Marketing research: an applied orientation. Prentice Hall, Upper Saddle River

    Google Scholar 

  39. Mendel JM (2007) Type-2 fuzzy sets and systems: an overview. IEEE Comput Intell Mag 2(1): 20–29

    Article  MathSciNet  Google Scholar 

  40. Meterko M, Wright S, Lin H, Lowy E, Cleary PD (2010) Mortality among patients with acute myocardial infarction: the influences of patient-centered care and evidence-based medicine. Health Serv Res 45(5): 1188–1204

    Article  Google Scholar 

  41. Milliman RE, Decker PJ (1990) The use of post-purchase communication to reduce dissonance and improve direct marketing effectiveness. J Bus Commun 27(2): 159–170

    Article  Google Scholar 

  42. Natarajan S, Tadepalli P, Fern A (2011) A relational hierarchical model for decision-theoretic assistance. Knowl Inf Syst. doi:10.1007/s10115-011-0435-z

  43. Olatunji SO, Selamat A, Abdulraheem A (2011) Modeling the permeability of carbonate reservoir using type-2 fuzzy logic systems. Comput Ind 62(2): 147–163

    Article  Google Scholar 

  44. Pelzang R (2010) Time to learn: understanding patient-centred care. Br J Nurs 19(14): 912–917

    Google Scholar 

  45. Rajpathak B, Chougule R, Bandyopadhyay P (2011) A domain-specific decision support system for knowledge discovery using association and text mining. Knowl Inf Syst. doi:10.1007/s10115-011-0409-1

  46. Razavi M, Aliee FS, Badie K (2011) An AHP-based approach toward enterprise architecture analysis based on enterprise architecture quality attributes. Knowl Inf Syst 28(2): 449–472

    Article  Google Scholar 

  47. Redman RW (2004) Patient-centered care: an unattainable ideal?. Res Theory Nurs Pract 18(1): 11–14

    Article  Google Scholar 

  48. Sambuc R (1975) Fonctions \({\Phi}\) -floues. Application a l’aide au diagnostic en pathologie thyroidienne, Ph.D. thesis, University of Marseille, France

  49. Steiger NJ, Balog A (2010) Realizing patient-centered care: putting patients in the center, not the middle. Front Health Serv Manag 26(4): 15–25

    Google Scholar 

  50. Sudha KR, Vijaya Santhi R (2011) Robust decentralized load frequency control of interconnected power system with generation rate constraint using type-2 fuzzy approach. Electr Power Energy Syst 33(3): 699–707

    Article  Google Scholar 

  51. Tripathy M, Mishra S (2011) Interval type-2-based thyristor controlled series capacitor to improve power system stability. IET Gener Transm Distrib 5(2): 209–222

    Article  MathSciNet  Google Scholar 

  52. Vahdani B, Hadipour H (2010) Extension of the ELECTRE method based on interval-valued fuzzy sets. Soft Comput 15(3): 569–579

    Article  Google Scholar 

  53. Vahdani B, Jabbari AHK, Roshanaei V, Zandieh M (2010) Extension of the ELECTRE method for decision-making problems with interval weights and data. Int J Adv Manuf Technol 50(5–8): 793–800

    Article  Google Scholar 

  54. Viswanathan M, Bergen M, Dutta S, Childers T (1996) Does a single response category in a scale completely capture a response?. Psychol Market 13(5): 457–479

    Article  Google Scholar 

  55. Wang G, Li X (1998) The applications of interval-valued fuzzy numbers and interval-distribution numbers. Fuzzy Sets Syst 98(3): 331–335

    Article  MATH  Google Scholar 

  56. Wei G-W (2010) Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information. Knowl Inf Syst 25(3): 623–634

    Article  Google Scholar 

  57. Wei S-H, Chen S-M (2009) Fuzzy risk analysis based on interval-valued fuzzy numbers. Expert Syst Appl 36(2–1): 2285–2299

    Article  MathSciNet  Google Scholar 

  58. Wei G-W, Wang H-J, Lin R (2011) Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information. Knowl Inf Syst 26(2): 337–349

    Article  Google Scholar 

  59. Wu A, Mendel JM (2007) Uncertainty measures for interval type-2 fuzzy sets. Inf Sci 177(23): 5378–5393

    Article  MathSciNet  MATH  Google Scholar 

  60. Xu ZS (2005) An approach to group decision making based on incomplete linguistic preference relations. Int J Inf Technol Decis Making 4(1): 153–160

    Article  Google Scholar 

  61. Xu ZS (2005) An approach to pure linguistic multiple attribute decision making under uncertainty. Int J Inf Technol Decis Making 4(2): 197–206

    Article  Google Scholar 

  62. Xu ZS (2007) Multiple attribute group decision making with different formats of preference information on attributes. IEEE Trans Syst Man Cybern B Cybern 37(6): 1500–1511

    Article  Google Scholar 

  63. Yang X, Lin TY, Yang J, Li Y, Yu D (2009) Combination of interval-valued fuzzy set and soft set. Comput Math Appl 58(3): 521–527

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  65. Zeng W, Guo P (2008) Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship. Inf Sci 178(5): 1334–1342

    Article  MathSciNet  MATH  Google Scholar 

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  1. Department of Industrial and Business Management, Graduate Institute of Business and Management, College of Management, Chang Gung University, 259, Wen-Hwa 1st Road, Kwei-Shan, Taoyuan, 333, Taiwan

    Ting-Yu Chen

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Chen, TY. A signed-distance-based approach to importance assessment and multi-criteria group decision analysis based on interval type-2 fuzzy set. Knowl Inf Syst 35, 193–231 (2013). https://doi.org/10.1007/s10115-012-0497-6

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  • DOI: https://doi.org/10.1007/s10115-012-0497-6

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