Linguistic computational model based on 2-tuples and intervals

IEEE Transactions on Fuzzy Systems

Volumn 21, Issue 6, 2013, Pages 1006-1018

  Dong, Yucheng ^a   Zhang, Guiqing ^b   Hong, Wei Chiang ^c   Yu, Shui ^d  

^a Department of Management Science and System Science   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

^c ORIENTAL INSTITUTE OF TECHNOLOGY   (Taiwan)

^d DEAKIN UNIVERSITY   (Australia)

Author keywords

Computing with words (CW); Interval; The 2 tuple fuzzy linguistic representation model; Type 2 fuzzy sets.

Indexed keywords

2-TUPLE FUZZY LINGUISTIC REPRESENTATIONS; COMPUTATIONAL MODEL; COMPUTING WITH WORDS; EXTENSIVE SIMULATIONS; GENERALIZED INVERSE; INTERVAL; INTERVAL TYPE2 FUZZY SETS (IT2 FSS); TYPE-2 FUZZY SET;

COMPUTATIONAL METHODS; COMPUTER SIMULATION; FUZZY SETS; SEMANTICS;

LINGUISTICS;

EID: 84897583965     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2013.2239650     Document Type: Article

References (67)

1. B. S. Ahn, "The uncertain OWA aggregation with weighting functions having a constant level of orness," Int. J. Intell. Syst., vol. 21, no. 5, pp. 469-483, 2006. (Pubitemid 43671873)
2. R. Alcaĺa, J. Alcaĺa-Fdez, F. Herrera, and J. Otero, "Genetic learning of accurate and compact fuzzy rule based systems based on the 2-tuples linguistic representation," Int. J. Approx. Reason., vol. 44, pp. 45-64, 2007.
3. S. Alonso, F. Chiclana, F. Herrera, E. Herrera-Viedma, and J. Alcaĺa-Fdez, C. Porcel, "A consistency-based procedure to estimate missing pairwise preference values," Int. J. Intell. Syst., vol. 23, no. 2, pp. 155-175, 2008. (Pubitemid 351225011)
4. S. Alonso, F. J. Cabrerizo, F. Chiclana, F. Herrera, and E. Herrera-Viedma, "Group decision-making with incomplete fuzzy linguistic preference relations," Int. J. Intell. Syst., vol. 24, no. 2, pp. 201-222, 2009.
5. A.Arbel, "Approximate articulation of preference and priority derivation," Eur. J. Oper. Res., vol. 43, pp. 317-326, 1989. (Pubitemid 20634228)
6. F. J. Cabrerizo, S. Alonso, and E. Herrera-Viedma, "A consensus model for group decision making problems with unbalanced fuzzy linguistic information," Int. J. Inf. Tech. Decis. Making., vol. 8, no. 1, pp. 109-131, 2009.
7. F. J. Cabrerizo, R. Heradio, I. J. Ṕerez, and E. Herrera-Viedma, "A selection process based on additive consistency to deal with incomplete fuzzy linguistic information," J. Univ. Comput. Sci., vol. 16, pp. 62-81, 2010.
8. F. J. Cabrerizo, I. J. Ṕerez, and E. Herrera-Viedma, "Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information," Knowl.-Based Syst., vol. 23, pp. 169-181, 2010.
9. R. Degani and G. Bortolan, "The problem of linguistic approximation in clinical decision making," Int. J. Approx. Reason., vol. 2, pp. 143-162, 1988.
10. M. Delgado, M. A. Vila, and W. Voxman, "On a canonical representation of fuzzy numbers," Fuzzy Sets Syst., vol. 93, pp. 125-135, 1998. (Pubitemid 128654361)
11. Y. C. Dong,W. C. Hong, Y. F. Xu, and S. Yu, "Selecting the individual numerical scale and prioritization method in the analytic hierarchy process: A 2-tuple fuzzy linguistic approach," IEEE Trans. Fuzzy Syst., vol. 19, no. 1, pp. 13-25, Feb. 2011.
12. Y. C. Dong, Y. F. Xu, and S. Yu, "Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model," IEEE Trans. Fuzzy Syst., vol. 17, no. 6, pp. 1366-1378, Dec. 2009.
13. M. Espinilla, J. Liu, and L.Mart'inez, "An extended hierarchical linguistic model for decision-making problems," Comput. Intell., vol. 27, pp. 489- 512, 2011.
14. Z. P. Fan, B. Feng, and W. L. Suo, "A fuzzy linguistic method for evaluating collaboration satisfaction of NPD team using mutual-evaluation information," Int. J. Prod. Econ., vol. 122, no. 2, pp. 547-557, 2009.
15. F. Herrera, S. Alonso, F. Chiclana, and E. Herrera-Viedma, "Computing with words in decision making: Foundations, trends and prospects," Fuzzy Opt. Decis. Making., vol. 8, no. 4, pp. 337-364, 2009.
16. F. Herrera and E. Herrera-Viedma, "Linguistic decision analysis: Steps for solving decision problems under linguistic information," Fuzzy Sets Syst., vol. 115, pp. 67-82, 2000.
17. F. Herrera, E. Herrera-Viedma, and L. Mart́inez, "A fuzzy linguistic methodology to deal with unbalanced linguistic term sets," IEEE Trans. Fuzzy Syst., vol. 16, no. 2, pp. 354-370, Apr. 2008. (Pubitemid 351586037)
18. F. Herrera, E. Herrera-Viedma, and J. L. Verdegay, "Direct approach processes in group decision making using linguistic OWA operators," Fuzzy Sets Syst., vol. 79, pp. 175-190, 1996. (Pubitemid 126667399)
19. F. Herrera and L. Mart́inez, "A 2-tuple fuzzy linguistic representation model for computing with words," IEEE Trans. Fuzzy Syst., vol. 8, no. 6, pp. 746-752, Dec. 2000.
20. F. Herrera and L. Mart́inez, "A model based on linguistic 2-tuples for dealing with multigranularity hierarchical linguistic contexts in multiexpert decision-making," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 31, no. 2, pp. 227-234, Apr. 2001. (Pubitemid 32415888)
21. E. Herrera-Viedma and A. G. Ĺopez-Herrera, "A model of information retrieval system with unbalanced fuzzy linguistic information," Int. J. Intell. Syst., vol. 22, no. 11, pp. 1197-1214, 2007. (Pubitemid 350076105)
22. E. Herrera-Viedma, L. Mart́inez, F. Mata, and F. Chiclana, "A consensus support system model for group decision-making problems with multigranular linguistic preference relations," IEEE Trans. Fuzzy Syst., vol. 13, no. 5, pp. 644-658, Oct. 2005. (Pubitemid 41555591)
23. H. Ishibuchi and H. Tanaka, "Multiobjective programming in optimization of the interval objective function," Eur. J. Oper. Res., vol. 48, pp. 219-225, 1990.
24. N. N. Karnik and J. M.Mendel, "Centroid of a type-2 fuzzy set," Inf. Sci., vol. 132, pp. 195-220, 2001. (Pubitemid 32273094)
25. J. Lawry, "An alternative approach to computing with words," Int. J. Uncertain. Fuzzy Knowl.-Based Syst., vol. 9, pp. 3-16, 2001. (Pubitemid 33682995)
26. D. F. Li, "Multiattribute group decision making method using extended linguistic variables," Int. J. Uncertain. Fuzzy Knowl.-Based Syst., vol. 17, no. 6, pp. 793-806, 2009.
27. F. Liu and J. M. Mendel, "Encoding words into interval type-2 fuzzy sets using an interval approach," IEEE Trans. Fuzzy Syst., vol. 16, no. 6, pp. 1503-1521, Dec. 2008.
28. X. Liu and J. M. Mendel, "Connect Karnik-Mendel algorithms to rootfinding for computing the centroid of an interval type-2 fuzzy set," IEEE Trans. Fuzzy Syst., vol. 19, no. 4, pp. 652-665, Aug. 2011.
29. L. Mart́inez, "Sensory evaluation based on linguistic decision analysis," Int. J. Approx. Reason., vol. 44, pp. 148-164, 2007.
30. L. Mart́inez, M. Espinilla, J. Liu, L. G. Ṕerez, and P. J. Śanchez, "An evaluation model with unbalanced linguistic information applied to olive oil sensory evaluation," J. Multi.-Valued Logic Soft Comput., vol. 15, pp. 229-251, 2009.
31. L. Mart́inez, M. Espinilla, and L. G. Ṕerez, "A linguistic multigranular sensory evaluation model for olive oil," Int. J. Comput. Intell. Syst., vol. 1, no. 2, pp. 148-158, 2008.
32. L. Mart́inez and F. Herrera, "An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges," Inf. Sci., vol. 207, pp. 1-18, 2012.
33. L. Mart́inez, J. Liu, D. Ruan, and J. B. Yang, "Dealing with heterogeneous information in engineering evaluation processes," Inf. Sci., vol. 177, no. 7, pp. 1533-1542, 2007. (Pubitemid 46107424)
34. L. Mart́inez, D. Ruan, and F. Herrera, "Computing with words in decision support systems: An overviewonmodels and applications," Int. J. Comput. Intell. Syst., vol. 3, no. 4, pp. 382-395, 2010.
35. S. McClean, B. Scotney, and M. Shapcott, "Aggregation of imprecise and uncertain information in databases," IEEE Trans. Knowl. Data Eng., vol. 13, no. 6, pp. 902-912, Nov./Dec. 2001. (Pubitemid 34035583)
36. J. M. Mendel, "An architecture for making judgments using computing with words," Int. J. Appl. Math. Comput. Sci., vol. 12, no. 3, pp. 325-335, 2002.
37. J. M. Mendel, "Computing with words and its relationships with fuzzistics," Inf. Sci., vol. 177, no. 4, pp. 988-1006, 2007. (Pubitemid 44791318)
38. J. M. Mendel and H.Wu, "Type-2 fuzzistics for symmetric interval type-2 fuzzy sets - Part 1: Forward problems," IEEE Trans. Fuzzy Syst., vol. 14, no. 6, pp. 781-792, Dec. 2006. (Pubitemid 46432458)
39. J. M. Mendel and H.Wu, "Type-2 fuzzistics for symmetric interval type-2 fuzzy sets - Part 2: Inverse problems," IEEE Trans. Fuzzy Syst., vol. 15, no. 2, pp. 301-308, Apr. 2007. (Pubitemid 46563429)
40. J. M. Mendel and D.Wu, Perceptual Computing: Aiding People inMaking Subjective Judgments. Hoboken, NJ, USA: Wiley, 2010.
41. R. E. Moore, Method and Application of Interval Analysis. Philadelphia, PA, USA: SIAM, 1979.
42. C. Porcel, A. G. Ĺopez-Herrera, and E. Herrera-Viedma, "Arecommender system for research resources based on fuzzy linguistic modeling," Expert Syst. Appl., vol. 36, pp. 5173-5183, 2009.
43. R. M. Rodŕiguez, L. Mart́inez, and F. Herrera, "Hesitant fuzzy linguistic term sets for decision making," IEEE Trans. Fuzzy Syst., vol. 20, no. 1, pp. 109-119, Feb. 2012.
44. T. L. Saaty and L. G. Vargas, "Uncertainty and rank order in the analytic hierarchy process," Eur. J. Oper. Res., vol. 32, pp. 107-117, 1987.
45. A. Sengupta and T. K. Pal, "On comparing interval numbers," Eur. J. Oper. Res., vol. 127, pp. 28-43, 2000.
46. S. Tong, "Interval number and fuzzy number linear programming," Fuzzy Sets Syst., vol. 66, pp. 301-306, 1994.
47. S.-Y. Wang, "Applying 2-tuple multigranularity linguistic variables to determine the supply performance in dynamic environment based on product-oriented strategy," IEEE Trans. Fuzzy Syst., vol. 16, no. 1, pp. 29- 39, Feb. 2008. (Pubitemid 351359126)
48. J. H. Wang and J. Y. Hao, "A new version of 2-tuple fuzzy linguistic representationmodel for computingwithwords," IEEE Trans. Fuzzy Syst., vol. 14, no. 3, pp. 435-445, Jun. 2006.
49. J. H. Wang and J. Y. Hao, "Fuzzy linguistic PERT," IEEE Trans. Fuzzy Syst., vol. 15, no. 2, pp. 133-144, Apr. 2007.
50. J. H. Wang and J. Y. Hao, "An approach to computing with words based on canonical characteristic values of linguistic labels," IEEE Trans. Fuzzy Syst., vol. 15, no. 4, pp. 593-604, Aug. 2007.
51. Y. M.Wang and T. M. S. Elhag, "A goal programming method for obtaining interval weights from an interval comparison matrix," Eur. J. Oper. Res., vol. 177, pp. 458-471, 2007. (Pubitemid 44647615)
52. Y. MWang, J. B. Yang, D. L. Xu, and K. S. Chin, "The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees," Eur. J. Oper. Res., vol. 175, pp. 35-66, 2006.
53. Y. M Wang, J. B. Yang, D. L. Xu, and K. S. Chin, "On the combination and normalization of interval-valued belief structures," Inf. Sci., vol. 177, pp. 1230-1247, 2007.
54. D. Wu and J. M. Mendel, "Aggregation using the linguistic weighted average and interval type-2 fuzzy sets," IEEE Trans. Fuzzy Syst., vol. 15, no. 6, pp. 1145-1161, Dec. 2007. (Pubitemid 350268645)
55. D. Wu and J. M. Mendel, "A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets," Inf. Sci., vol. 179, pp. 1169-1192, 2009.
56. D. Wu and J. M. Mendel, "Enhanced Karnik-Mendel algorithms," IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 923-934, Aug. 2009.
57. D. Wu, J. M. Mendel, and S. Coupland, "Enhanced interval approach for encoding words into interval type-2 fuzzy sets and its convergence analysis," IEEE Trans. Fuzzy Syst., vol. 20, no. 3, pp. 499-513, Jun. 2012.
58. Z. S. Xu, "A method based on linguistic aggregation operators for group decision making with linguistic preference relations," Inf. Sci., vol. 166, pp. 19-30, 2004.
59. Z. S. Xu, "Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment," Inf. Sci., vol. 168, pp. 171-184, 2004.
60. Z. S. Xu, "Deviation measures of linguistic preference relations in group decision making," Omega, vol. 33, no. 3, pp. 249-254, 2005.
61. R. Yager, "On ordered weighted averaging aggregation operators in multicriteria decision making," IEEE Trans. Syst., Man, Cybern., vol. 18, pp. 183-190, 1988. (Pubitemid 18612263)
62. L. A. Zadeh, "The concept of a linguistic variable and its applications to approximate reasoning, Part I," Inf. Sci., vol. 8, pp. 199-249, 1975.
63. L. A. Zadeh, "Fuzzy logic = computing with words," IEEE Trans. Fuzzy Syst., vol. 4, no. 2, pp. 103-111, May 1996. (Pubitemid 126780540)
64. L. G. Zhou, H. Chen, J. M. Merigo, and A. M. Gil-Lafuente, "Uncertain generalized aggregation operators," Expert Syst. Appl., vol. 39, pp. 1105- 1117, 2012.
65. S.-M. Zhou, F. Chiclana, R. I. John, and J. M. Garibaldi, "Alpha-level aggregation: A practical approach to type-1 OWA operation for aggregating uncertain information with applications to breast cancer treatments," IEEE Trans. Knowl. Data Eng., vol. 23, no. 10, pp. 1455-1468, Oct. 2011.
66. S.-M. Zhou, F. Chiclana, R. I. John, and J. M. Garibaldi, "Type-1 OWA operators for aggregating uncertain information with uncertain weights induced by type-2 linguistic quantifiers," Fuzzy Sets Syst., vol. 159, no. 24, pp. 3281-3296, 2008.
67. S.-M. Zhou, R. I. John, F. Chiclana, and J. M. Garibaldi, "On aggregating uncertain information by type-2OWAoperators for soft decisionmaking," Int. J. Intell. Syst., vol. 25, no. 6, pp. 540-558, 2010.