Alpha-level aggregation: A practical approach to type-1 OWA operation for aggregating uncertain information with applications to breast cancer treatments

IEEE Transactions on Knowledge and Data Engineering

Volumn 23, Issue 10, 2011, Pages 1455-1468

  Zhou, Shang Ming ^a   Chiclana, Francisco ^b   John, Robert I ^b   Garibaldi, Jonathan M ^c  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b DE MONTFORT UNIVERSITY   (United Kingdom)

^c UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

aggregation; Alpha level; Alpha cuts; breast cancer treatments; fuzzy sets; OWA operators; soft decision making; type 1 OWA operators; uncertain information

Indexed keywords

ALPHA LEVEL; ALPHA-CUTS; BREAST CANCER TREATMENT; OWA OPERATORS; SOFT DECISION; UNCERTAIN INFORMATIONS;

DECISION MAKING; DISEASES; FUZZY SETS; STATISTICAL METHODS;

DATA MINING;

EID: 79955562977     PISSN: 10414347     EISSN: None     Source Type: Journal    
DOI: 10.1109/TKDE.2010.191     Document Type: Review

References (55)

1. S. McClean, B. Scotney, and M. Shapcott, "Aggregation of Imprecise and Uncertain Information in Databases", IEEE Trans. Knowledge and Data Eng., vol. 13, no. 6, pp. 902-912, Nov./Dec. 2001. (Pubitemid 34035583)
2. B. Moon, I. F. V. Lopez, and V. Immanuel, "Efficient Algorithms for Large-Scale Temporal Aggregation", IEEE Trans. Knowledge and Data Eng., vol. 15, no. 3, pp. 744-759, May/June 2003.
3. A. L. P. Chen, J.-S. Chiu, and F. S. C. Tseng, "Eva1uating Aggregate Operations over Imprecise Data", IEEE Trans. Knowledge and Data Eng., vol. 8, no. 2, pp. 273-284, Apr. 1996. (Pubitemid 126776295)
4. V. Torra and J. Nin, "Record Linkage for Database Integration Using Fuzzy Integrals", Int'l J. Intelligent Systems, vol. 23, no. 6, pp. 715-734, 2008.
5. D. Dubois and H. Prade, "On the Use of Aggregation Operations in Information Fusion Processes", Fuzzy Sets and Systems, vol. 142, pp. 143-161, 2004.
6. F. Herrera and E. Herrera-Viedma, "Linguistic Decision Analysis: Steps for Solving Decision Problems under Linguistic Information", Fuzzy Sets and Systems, vol. 115, pp. 67-82, 2000.
7. V. Cutello and J. Montero, "Hierarchies of Aggregation Operators", Int'l J. Intelligent Systems, vol. 9, pp. 1025-1045, 1994.
8. E. Herrera-Viedma, L. Martínez, F. Mata, and F. Chiclana, "A Consensus Support System Model for Group Decision-Making Problems with Multigranular Linguistic Preference Relations", IEEE Trans. Fuzzy Systems, vol. 13, no. 5, pp. 644-658, Oct. 2005. (Pubitemid 41555591)
9. D. Dubois and H. Prade, "A Review of Fuzzy Set Aggregation Connectives", Information Science, vol. 36, pp. 85-121, 1985. (Pubitemid 15604334)
10. T. Calvo, G. Mayor, J. Torrens, J. Suner, M. Mas, and M. Carbonell, "Generation on Weighting Triangles Associated with Aggregation Functions", Int'l J. Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 8, no. 4, pp. 417-451, 2000.
11. G. Beliakov and T. Calvo, "Construction of Aggregation Operators with Noble Reinforcement", IEEE Trans. Fuzzy Systems, vol. 15, no. 6, pp. 1209-1218, Dec. 2007. (Pubitemid 350268650)
12. T. Calvo and R. Mesiar, "Criteria Importances in Median-Like Aggregation", IEEE Trans. Fuzzy Systems, vol. 9, no. 4, pp. 662-666, Aug. 2001. (Pubitemid 32933050)
13. H.-J. Zimmermann, Fuzzy Sets, Decision Making and Expert Systems. Kluwer Academic Publishers, 1987.
14. Z. S. Xu and Q. L. Da, "An Overview of Operators for Aggregating Information", Int'l J. Intelligent Systems, vol. 18, pp. 953-969, 2003.
15. F. Herrera, E. Herrera-Viedma, and F. Chiclana, "A Study of the Origin and Uses of the Ordered Weighted Geometric Operator in Multicriteria Decision Making", Int'l J. Intelligent Systems, vol. 18, no. 6, pp. 689-707, 2003.
16. F. Chiclana, E. Herrera-Viedma, F. Herrera, and S. Alonso, "Induced Ordered Weighted Geometric Operators and Their Use in the Aggregation of Multiplicative Preference Relations", Int'l J. Intelligent Systems, vol. 19, no. 3, pp. 233-255, 2004.
17. F. Chiclana, E. Herrera-Viedma, F. Herrera, and S. Alonso, "Some Induced Ordered Weighted Averaging Operators and Their Use for Solving Group Decision-Making Problems Based on Fuzzy Preference Relations", European J. Operational Research, vol. 182, no. 1, pp. 383-399, 2007. (Pubitemid 46561160)
18. R. R. Yager, "On Ordered Weighted Averaging Aggregation Operators in Multi-Criteria Decision Making", IEEE Trans. Systems, Man and Cybernetics, vol. 18, no. 1, pp. 183-190, Jan./Feb. 1988.
19. R. R. Yager, "Families of OWA Operators", Fuzzy Sets and Systems, vol. 59, pp. 125-148, 1993.
20. L. A. Zadeh, "From Computing with Numbers to Computing with Words-From Manipulation of Measurements to Manipulation of Perceptions", IEEE Trans. Circuits and Systems, vol. 45, no. 1, pp. 105-119, Jan. 1999.
21. G. Bordogna, M. Fedrizzi, and G. Pasi, "A Linguistic Modelling of Consensus in Group Decision Making Based on OWA Operators", IEEE Trans. Systems, Man and Cybernetics-Part A, vol. 27, no. 1, pp. 126-133, Jan. 1997.
22. R. R. Yager, "A General Approach to Criteria Aggregation Using Fuzzy Measures", Int'l J. Man-Machine Study, vol. 38, pp. 187-213, 1993.
23. R. R. Yager and D. P. Filev, "Generalizing the Modeling of Fuzzy Logic Controllers by Parameterized Aggregation Operators", Fuzzy Sets and Systems, vol. 70, pp. 303-313, 1995.
24. R. R. Yager, D. P. Filev, and T. Sadeghi, "Analysis of Flexible Structured Fuzzy Logic Controllers", IEEE Trans. Systems, Man and Cybernetics, vol. 24, no. 7, pp. 1035-1043, July 1994.
25. R. R. Yager, L. S. Goldstein, and E. Mendels, "FUZMAR: An Approach to Aggregating Market Research Data Based on Fuzzy Reasoning", Fuzzy Sets and Systems, vol. 68, no. 1, pp. 1-11, 1994.
26. H. B. Mitchell and D. D. Estrakh, "A Modified OWA Operator and Its Use in Lossless DPCM Image Compression", Int'l J. Uncertain Fuzziness, Knowledge Based Systems, vol. 5, pp. 429-436, 1997. (Pubitemid 127531671)
27. 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 and Systems, vol. 159, no. 24, pp. 3281-3296, 2008.
28. S.-M. Zhou, F. Chiclana, R. I. John, and J. M. Garibaldi, "Fuzzification of the OWA Operators in Aggregating Uncertain Information", Recent Developments in the Ordered Weighted Averaging Operators-Theory and Practice, R. R. Yager, J. Kacprzyk, and G. Beliakov, eds., Springer, 2010.
29. Z. S. Xu, "EOWA And EOWG Operators for Aggregating Linguistic Labels Based on Linguistic Preference Relations", Int'l J. Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 12, no. 6, pp. 791-810, 2004. (Pubitemid 40493397)
30. M. T. Lamata, "Ranking of Alternatives with Ordered Weighted Averaging Operators", Int'l J. Intelligent Systems, vol. 19, no. 5, pp. 473-482, 2004.
31. Z. Xu, "Intuitionistic Fuzzy Aggregation Operators", IEEE Trans. Fuzzy Systems, vol. 15, no. 6, pp. 1179-1187, Dec. 2007. (Pubitemid 350268647)
32. B. S. Ahn, "The OWA Aggregation with Uncertain Descriptions on Weights and Input Arguments", IEEE Trans Fuzzy Systems, vol. 15, no. 6, pp. 1130-1134, Dec. 2007. (Pubitemid 350268643)
33. H. B. Mitchell and P. A. Schaefer, "On Ordering Fuzzy Numbers", Int'l J. Intelligent Systems, vol. 15, pp. 981-993, 2000. (Pubitemid 32032384)
34. R. Yang, Z. Wang, P.-A. Heng, and K.-S. Leung, "Fuzzy Numbers and Fuzzification of the Choquet Integral", Fuzzy Sets and Systems, vol. 153, pp. 95-113, 2005. (Pubitemid 40612573)
35. P. Meyer and M. Roubens, "On the Use of the Choquet Integral with Fuzzy Numbers in Multiple Criteria Decision Support", Fuzzy Sets and Systems, vol. 157, no. 7, pp. 927-938, 2006.
36. W. M. Dong and F. S. Wong, "Fuzzy Weighted Averages and Implementation of the Extension Principle", Fuzzy Sets and Systems, vol. 21, pp. 183-199, 1987.
37. Y.-Y. Guh, C.-C. Hon, and E. S. Lee, "Fuzzy Weighted Average: The Linear Programming Approach via Charnes and Cooper's Rule", Fuzzy Sets and Systems, vol. 117, pp. 157-160, 2001.
38. C.-B. Chen and C. M. Klein, "A Simple Approach to Ranking a Group of Aggregated Fuzzy Utilities", IEEE Trans. Systems, Man, and Cybernetics-Part B, vol. 27, no. 1, pp. 26-35, Feb. 1997. (Pubitemid 127770632)
39. T. M. Apostol, Math. Analysis, second ed., Addison-Wesley, 1974.
40. L. A. Zadeh, "Fuzzy Sets", Information and Control, vol. 8, no. 3, pp. 338-353, 1965.
41. L. A. Zadeh, "The Concept of a Linguistic Variable and Its Application to Approximate Reasoning-II", Information Science, vol. 8, pp. 301-357, 1975.
42. M. Mizumoto and K. Tanaka, "Some Properties of Fuzzy Sets of Type 2", Information and Control, vol. 31, pp. 312-340, 1976.
43. J. M. Garibaldi and T. Ozen, "Uncertain Fuzzy Reasoning: A Case Study in Modelling Expert Decision Making", IEEE Trans. Fuzzy Systems, vol. 15, no. 1, pp. 16-30, Feb. 2007. (Pubitemid 46444301)
44. J. M. Garibaldi, M. Jaroszewski, and S. Musikasuwan, "Non-Stationary Fuzzy Sets", IEEE Trans. Fuzzy Systems, vol. 16, no. 4, pp. 1072-1086, Aug. 2008.
45. J. M. Garibaldi, S. Musikasuwan, and T. Ozen, "The Association between Non-Stationary and Interval Type-2 Fuzzy Sets: A Case Study", Proc. IEEE Int'l Conf. Fuzzy Systems (FUZZ'05), pp. 224-229, May 2005. (Pubitemid 41189511)
46. J. M. Garibaldi, S.-M. Zhou, X.-Y. Wang, and R. I. John, "Incorporation of Expert Variability into Breast Cancer Treatment Recommendation in Designing Clinical Protocol Guided Fuzzy Inference Systems", submitted to J. Biomedical Informatics, 2011.
47. P. Majlender, "OWA Operators with Maximal Renyi Entropy", Fuzzy Sets and Systems, vol. 155, pp. 340-360, 2005. (Pubitemid 41218277)
48. M. O'Hagan, "Aggregating Template or Rule Antecedents in Real-Time Expert Systems with Fuzzy Set Logic", Proc. 22nd Ann. IEEE Asilomar Conf. Signals, Systems and Computers, pp. 681-689, 1988. (Pubitemid 20629298)
49. D. Filev and R. R. Yager, "On the Issue of Obtaining OWA Operator Weights", Fuzzy Sets and Systems, vol. 94, pp. 157-169, 1998. (Pubitemid 128654784)
50. B. Llamazares, "Choosing OWA Operator Weights in the Field of Social Choice", Information Sciences, vol. 177, pp. 4745-4756, 2007. (Pubitemid 47238794)
51. Z. S. Xu, "An Overview of Methods for Determining OWA Weights", Int'l J. Intelligent Systems, vol. 20, pp. 843-865, 2005.
52. S.-M. Zhou and J. Q. Gan, "Constructing Parsimonious Fuzzy Classifiers Based on L2-SVM in High-Dimensional Space with Automatic Model Selection and Fuzzy Rule Ranking", IEEE Trans. Fuzzy Systems, vol. 15, no. 3, pp. 398-409, June 2007. (Pubitemid 46971552)
53. S.-M. Zhou and J. Q. Gan, "Extracting Takagi-Sugeno Fuzzy Rules with Interpretable Submodels via Regularization of Linguistic Modifiers", IEEE Trans. Knowledge and Data Eng., vol. 21, no. 8, pp. 1191-1204, Aug. 2009.
54. S.-M. Zhou and J. Q. Gan, "Low-Level Interpretability and High-Level Interpretability: A Unified View of Interpretable Fuzzy System Modelling from Data", Fuzzy Sets and Systems, vol. 159, no. 23, pp. 3091-3131, 2008.
55. R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, http://www.R-project.org, 2006.