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Volumn 21, Issue 6, 2013, Pages 1150-1162

A new approach to interval-valued choquet integrals and the problem of ordering in interval-valued fuzzy set applications

Author keywords

Interval valued Choquet integral; Interval valued decision making; Interval valued fuzzy set; Interval valued linear order; Interval valued ordered weighted aggregation (OWA) operators; Shapley value

Indexed keywords

CHOQUET INTEGRAL; INTERVAL-VALUED; INTERVAL-VALUED FUZZY SETS; LINEAR ORDER; ORDERED WEIGHTED AGGREGATIONS; SHAPLEY VALUE;

EID: 84897584161     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2013.2265090     Document Type: Article
Times cited : (184)

References (52)
  • 2
    • 0029403788 scopus 로고
    • Interval-valued fuzzy backward reasoning
    • Nov
    • T. Arnould and S. Tano, "Interval-valued fuzzy backward reasoning," IEEE Trans. Fuzzy Syst., vol. 3, no. 4, pp. 425-437, Nov. 1995.
    • (1995) IEEE Trans. Fuzzy Syst. , vol.3 , Issue.4 , pp. 425-437
    • Arnould, T.1    Tano, S.2
  • 3
    • 0001334287 scopus 로고
    • Interval-valued intuitionistic fuzzy sets
    • K. Atanassov and G. Gargov, "Interval-valued intuitionistic fuzzy sets," Fuzzy Sets Syst., vol. 31, no. 3, pp. 343-349, 1989.
    • (1989) Fuzzy Sets Syst. , vol.31 , Issue.3 , pp. 343-349
    • Atanassov, K.1    Gargov, G.2
  • 4
    • 50549204934 scopus 로고    scopus 로고
    • Integrals of set-valued functions
    • R. J. Aumann, "Integrals of set-valued functions," J. Math. Anal. Appl., vol. 12, pp. 1-12, 1965.
    • J. Math. Anal. Appl. , vol.12 , Issue.1965 , pp. 1-12
    • Aumann, R.J.1
  • 5
    • 80053633453 scopus 로고    scopus 로고
    • Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images
    • Oct
    • E. Barrenechea, H. Bustince, B. De Baets, and C. Lopez-Molina, "Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images," IEEE Trans. Fuzzy Syst., vol. 19, no. 5, pp. 819-830, Oct. 2011.
    • (2011) IEEE Trans. Fuzzy Syst. , vol.19 , Issue.5 , pp. 819-830
    • Barrenechea, E.1    Bustince, H.2    De Baets, B.3    Callison-Burch, C.4
  • 6
    • 79251596994 scopus 로고    scopus 로고
    • On averaging operators foratanassov's intuitionistic fuzzy sets
    • G. Beliakov, H. Bustince, D. P. Goswami, U. K. Mukherjee, and N. R. Pal, "On averaging operators forAtanassov's intuitionistic fuzzy sets," Inf. Sci., vol. 181, pp. 1116-1124, 2010.
    • (2010) Inf. Sci. , vol.181 , pp. 1116-1124
    • Beliakov, G.1    Bustince, H.2    Goswami, D.P.3    Mukherjee, U.K.4    Pal, N.R.5
  • 7
    • 84867583764 scopus 로고    scopus 로고
    • Aggregation for atanassov's intuitionistic and interval valued fuzzy sets: The median operator
    • Jun.
    • G. Beliakov, H. Bustince S. James, T. Calvo, and J. Fernandez, "Aggregation for Atanassov's intuitionistic and interval valued fuzzy sets: The median operator," IEEE Trans. Fuzzy Syst., vol. 20, pp. 487-498, Jun. 2012.
    • (2012) IEEE Trans. Fuzzy Syst. , vol.20 , pp. 487-498
    • Beliakov, G.1    Joho, H.2    Calvo, T.3    Fernandez, J.4
  • 8
    • 78650711538 scopus 로고    scopus 로고
    • Interval-valued fuzzy sets in soft computing
    • H.Bustince, "Interval-valued fuzzy sets in soft computing," Int. J. Comput. Intell. Syst., vol. 3, no. 2, pp. 215-222, 2010.
    • (2010) Int. J. Comput. Intell. Syst. , vol.3 , Issue.2 , pp. 215-222
    • Bustince, H.1
  • 9
    • 84888286997 scopus 로고    scopus 로고
    • Consensus in multi-expert decision making problems using penalty functions defined over a cartesian product of lattices
    • [Online]. Available:
    • H. Bustince, E. Barrenechea, T. Calvo, S. James, and G. Beliakov. (2011). Consensus in multi-expert decision making problems using penalty functions defined over a Cartesian product of lattices, Inf. Fus. [Online]. Available:http://dx.doi.org/10.1016/j.inffus.2011.10.002
    • (2011) Inf. Fus.
    • Bustince, H.1    Barrenechea, E.2    Calvo, T.3    James, S.4    Beliakov, G.5
  • 10
    • 67349130884 scopus 로고    scopus 로고
    • Intervalvalued fuzzy sets constructed from matrices: Application to edge detection
    • H. Bustince, E. Barrenechea, M. Pagola, and J. Fernandez, "Intervalvalued fuzzy sets constructed from matrices: Application to edge detection," Fuzzy Sets Syst., vol. 160, pp. 1819-1840, 2009.
    • (2009) Fuzzy Sets Syst. , vol.160 , pp. 1819-1840
    • Bustince, H.1    Barrenechea, E.2    Pagola, M.3    Fernandez, J.4
  • 12
    • 84875739316 scopus 로고    scopus 로고
    • Generation of linear orders for intervals by means of aggregation functions
    • H. Bustince, J. Fernandez, A. Koleśarov́a, and R. Mesiar, "Generation of linear orders for intervals by means of aggregation functions," Fuzzy Sets Syst., vol. 220, pp. 69-77, 2013.
    • (2013) Fuzzy Sets Syst. , vol.220 , pp. 69-77
    • Bustince, H.1    Fernandez, J.2    Koleśarov́a, A.3    Mesiar, R.4
  • 13
    • 0002262966 scopus 로고    scopus 로고
    • Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations
    • PII S0165011496003399
    • F. Chiclana, F. Herrera, and E. Herrera-Viedma, "Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations," Fuzzy Sets Syst., vol. 97, pp. 33-48, 1998. (Pubitemid 128654877)
    • (1998) Fuzzy Sets and Systems , vol.97 , Issue.1 , pp. 33-48
    • Chiclana, F.1    Herrera, F.2    Herrera-Viedma, E.3
  • 14
    • 84875241738 scopus 로고    scopus 로고
    • Type-reduction of general type-2 fuzzy sets: The type-1 owa approach
    • F. Chiclana and S. M. Zhou, "Type-reduction of general type-2 fuzzy sets: The type-1 OWA approach," Int. J. Intell. Syst., vol. 28, pp. 505-522, 2013.
    • (2013) Int. J. Intell. Syst. , vol.28 , pp. 505-522
    • Chiclana, F.1    Zhou, S.M.2
  • 16
    • 34147105314 scopus 로고    scopus 로고
    • Additive and multiplicative generators in interval-valued fuzzy set theory
    • DOI 10.1109/TFUZZ.2006.879999
    • G. Deschrijver, "Additive and multiplicative generators in interval-valued fuzzy set theory," IEEE Trans. Fuzzy Syst., vol. 15, no. 2, pp. 222-237, Apr. 2007. (Pubitemid 46563423)
    • (2007) IEEE Transactions on Fuzzy Systems , vol.15 , Issue.2 , pp. 222-237
    • Deschrijver, G.1
  • 17
    • 0013417955 scopus 로고
    • Fuzzy preference modelling multicriteria decision support
    • New York, NY, USA: Kluwer
    • J. Fodor and M. Roubens, "Fuzzy preference modelling multicriteria decision support," in Theory and Decision Library, New York, NY, USA: Kluwer, 1994
    • (1994) Theory and Decision Library
    • Fodor, J.1    Roubens, M.2
  • 18
    • 79959578748 scopus 로고    scopus 로고
    • Interval-valued fuzzy sets applied to stereo matching of color images
    • Jul
    • M. Galar, J. Fernandez, G. Beliakov, and H. Bustince, "Interval-valued fuzzy sets applied to stereo matching of color images," IEEE Trans. Image Process., vol. 20, no. 7, pp. 1949-1961, Jul. 2011.
    • (2011) IEEE Trans. Image Process. , vol.20 , Issue.7 , pp. 1949-1961
    • Galar, M.1    Fernandez, J.2    Beliakov, G.3    Bustince, H.4
  • 20
    • 13544267454 scopus 로고    scopus 로고
    • Managing non-homogeneous information in group decision making
    • DOI 10.1016/j.ejor.2003.11.031, PII S0377221704001237
    • F. Herrera, L. Mart́inez, and P. J. Śanchez, "Managing non-homogeneous information in group decision making," Eur. J. Oper. Res., vol. 166, no. 1, pp. 115-132, 2005. (Pubitemid 40219818)
    • (2005) European Journal of Operational Research , vol.166 , Issue.1 SPEC. ISS. , pp. 115-132
    • Herrera, F.1    Martinez, L.2    Sanchez, P.J.3
  • 21
    • 0002781537 scopus 로고    scopus 로고
    • Linguistic decision analysis: Steps for solving decision problems under linguistic information
    • 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.
    • (2000) Fuzzy Sets Syst. , vol.115 , pp. 67-82
    • Herrera, F.1    O'Brien-Strain, E.2
  • 22
    • 80055026644 scopus 로고    scopus 로고
    • Interval-valued choquet integrals and their applications
    • L. C. Jang, "Interval-valued Choquet integrals and their applications," J. Appl. Math. Comput., vol. 16, pp. 429-443, 2004.
    • (2004) J. Appl. Math. Comput. , vol.16 , pp. 429-443
    • Jang, L.C.1
  • 23
    • 76849090447 scopus 로고    scopus 로고
    • A universal integral as common frame for choquet and sugeno integral
    • Feb
    • E. P. Klement, R. Mesiar, and E. Pap, "A universal integral as common frame for Choquet and Sugeno integral," IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 178-187, Feb. 2010.
    • (2010) IEEE Trans. Fuzzy Syst. , vol.18 , Issue.1 , pp. 178-187
    • Klement, E.P.1    Mesiar, R.2    Pap, E.3
  • 24
    • 79956276670 scopus 로고    scopus 로고
    • Aggregation functions on bounded partially ordered sets and their classification
    • M. Komorńikov́a and R. Mesiar, "Aggregation functions on bounded partially ordered sets and their classification," Fuzzy Sets Syst., vol. 175, pp. 48-56, 2011.
    • (2011) Fuzzy Sets Syst. , vol.175 , pp. 48-56
    • Komorńikov́a, M.1    Mesiar, R.2
  • 25
    • 84877686558 scopus 로고    scopus 로고
    • Owa operators defined on complete lattices
    • [Online]. Available:
    • I. Lizasoain and C. Moreno. (2013). OWA operators defined on complete lattices, Fuzzy Sets Syst. [Online]. Available:http://dx.doi.org/10.1016/j. fss.2012.10.012
    • (2013) Fuzzy Sets Syst
    • Lizasoain, I.1    Callison-Burch, C.2
  • 27
    • 0031119769 scopus 로고    scopus 로고
    • A general model for deriving preference structures from data
    • J. Montero, J. Tejada, and C. Cutello, "A general model for deriving preference structures from data," Eur. J. Oper. Res., vol. 98, no. 1, pp. 98-110, 1997. (Pubitemid 127412673)
    • (1997) European Journal of Operational Research , vol.98 , Issue.1 , pp. 98-110
    • Montero, J.1    Tejada, J.2    Cutello, C.3
  • 28
    • 0004293209 scopus 로고
    • Englewood Cliffs NJ USA: Prentice-Hall
    • R. E. Moore, Interval Analysis. Englewood Cliffs, NJ, USA: Prentice-Hall, 1966.
    • (1966) Interval Analysis
    • Moore, R.E.1
  • 29
    • 79955558037 scopus 로고    scopus 로고
    • A genetic tuning to improve the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets: Degree of ignorance and lateral position
    • J. Sanz, A. Fernandez, H. Bustince, and F. Herrera, "A genetic tuning to improve the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets: Degree of ignorance and lateral position," Int. J. Approx. Reason., vol. 52, pp. 751-766, 2011.
    • (2011) Int. J. Approx. Reason. , vol.52 , pp. 751-766
    • Sanz, J.1    Fernandez, A.2    Bustince, H.3    Herrera, F.4
  • 30
    • 84968501330 scopus 로고    scopus 로고
    • Integral representation without additivity
    • D. Schmeidler, "Integral representation without additivity," Proc. Amer. Math. Soc., vol. 97, pp. 255-261, 1986.
    • Proc. Amer. Math. Soc. , vol.97 , Issue.1986 , pp. 255-261
    • Schmeidler, D.1
  • 33
    • 70349466357 scopus 로고    scopus 로고
    • Intuitionistic fuzzy choquet integral operator for multi-criteria decision making
    • C. Tan and X. Chen, "Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making," Expert Syst. Appl., vol. 37, pp. 149-157, 2010.
    • (2010) Expert Syst. Appl. , vol.37 , pp. 149-157
    • Tan, C.1    Chen, X.2
  • 34
    • 0000316805 scopus 로고    scopus 로고
    • Interval-valued strict preference with zadeh triples
    • I. B. Turksen and T. Bilgic, "Interval-valued strict preference with Zadeh triples," Fuzzy Sets Syst., vol. 78, pp. 162-183, 1996.
    • Fuzzy Sets Syst. , vol.78 , Issue.1996 , pp. 162-183
    • Turksen, I.B.1    Bilgic, T.2
  • 35
    • 33947365579 scopus 로고    scopus 로고
    • Discrete interval type 2 fuzzy system models using uncertainty in learning parameters
    • DOI 10.1109/TFUZZ.2006.889765, Extensions of Type-1 Fuzzy Sets
    • O. Uncu and I. B. Turksen, "Discrete interval type 2 fuzzy system models using uncertainty in learning parameters," IEEE Trans. Fuzzy Syst., vol. 15, no. 1, pp. 90-106, Feb. 2007. (Pubitemid 46444306)
    • (2007) IEEE Transactions on Fuzzy Systems , vol.15 , Issue.1 , pp. 90-106
    • Uncu, O.1    Turksen, I.B.2
  • 37
    • 84864198766 scopus 로고    scopus 로고
    • Enhanced interval approach for encoding words into interval type-2 fuzzy sets and its convergence analysis
    • Jun
    • 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.
    • (2012) IEEE Trans. Fuzzy Syst. , vol.20 , Issue.3 , pp. 499-513
    • Wu, D.1    Mendel, J.M.2    Coupland, S.3
  • 38
    • 4043084216 scopus 로고    scopus 로고
    • On compatibility of interval fuzzy preference relations
    • Z. S. Xu, "On compatibility of interval fuzzy preference relations," Fuzzy Optim. Decis. Making, vol. 3, pp. 217-225, 2004.
    • (2004) Fuzzy Optim. Decis. Making , vol.3 , pp. 217-225
    • Xu, Z.S.1
  • 39
    • 37249067095 scopus 로고    scopus 로고
    • Intuitionistic fuzzy aggregation operators
    • Dec
    • Z. S. Xu, "Intuitionistic fuzzy aggregation operators," IEEE Trans. Fuzzy Syst., vol. 15, no. 6, pp. 1179-1187, Dec. 2007.
    • (2007) IEEE Trans. Fuzzy Syst. , vol.15 , Issue.6 , pp. 1179-1187
    • Xu, Z.S.1
  • 40
    • 71849091509 scopus 로고    scopus 로고
    • Choquet integrals of weighted intuitionistic fuzzy information
    • Z. S. Xu, "Choquet integrals of weighted intuitionistic fuzzy information," Inf. Sci., vol. 180, pp. 726-736, 2010.
    • (2010) Inf. Sci. , vol.180 , pp. 726-736
    • Xu, Z.S.1
  • 42
    • 33750916532 scopus 로고    scopus 로고
    • Some geometric aggregation operators based on intuitionistic fuzzy sets
    • DOI 10.1080/03081070600574353, PII W37X361G57UR56K2
    • Z. S. Xu and R. Yager, "Some geometric aggregation operators based on intuitionistic fuzzy sets," Int. J. General Syst., vol. 35, pp. 417-433, 2006. (Pubitemid 44726498)
    • (2006) International Journal of General Systems , vol.35 , Issue.4 , pp. 417-433
    • Xu, Z.1    Yager, R.R.2
  • 43
    • 84881335555 scopus 로고    scopus 로고
    • Priority weights derived from intuitionistic multiplicative preference relations in decision making
    • to be published, doi.10.1109/TFUZZ.2012.2226893
    • Z. S. Xu, "Priority weights derived from intuitionistic multiplicative preference relations in decision making," IEEE Trans. Fuzzy Syst., 2012, to be published, doi.10.1109/TFUZZ.2012.2226893
    • (2012) IEEE Trans. Fuzzy Syst.
    • Xu, Z.S.1
  • 44
    • 0023855863 scopus 로고
    • Ordered weighted averaging aggregation operators in multicriteria decisionmaking
    • DOI 10.1109/21.87068
    • R. Yager, "On ordered weighted averaging aggregation operators in multicriteria decision making," IEEE Trans. Syst., Man Cybern., vol. 18, no. 1, pp. 183-190, Jan./Feb. 1988. (Pubitemid 18612263)
    • (1988) IEEE Transactions on Systems, Man and Cybernetics , vol.18 , Issue.1 , pp. 183-190
    • Yager Ronald, R.1
  • 45
    • 74949095084 scopus 로고    scopus 로고
    • Owa aggregation of intuitionistic fuzzy sets
    • R. Yager, "OWA aggregation of intuitionistic fuzzy sets," Int. J. General Syst., vol. 38, pp. 617-641, 2009.
    • (2009) Int. J. General Syst. , vol.38 , pp. 617-641
    • Yager, R.1
  • 46
    • 84866358268 scopus 로고    scopus 로고
    • On prioritized multiple-criteria aggregation
    • Oct
    • R.Yager, "On prioritized multiple-criteria aggregation," IEEE Trans. Syst. Man Cybern. B, Cybern., vol. 42, no. 5, pp. 1297-1305, Oct. 2012.
    • (2012) IEEE Trans. Syst. Man Cybern. B, Cybern. , vol.42 , Issue.5 , pp. 1297-1305
    • Yager, R.1
  • 47
    • 75849153235 scopus 로고    scopus 로고
    • Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment
    • J. Ye, "Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment," Eur. J. Oper. Res., vol. 205, pp. 202-204, 2010.
    • (2010) Eur. J. Oper. Res. , vol.205 , pp. 202-204
    • Ye, J.1
  • 48
    • 49949126152 scopus 로고    scopus 로고
    • Probability measures of fuzzy events
    • L. A. Zadeh, "Probability measures of fuzzy events," J. Math. Anal. Appl., vol. 23, pp. 421-427, 1968.
    • J. Math. Anal. Appl. , vol.23 , Issue.1968 , pp. 421-427
    • Zadeh, L.A.1
  • 49
    • 0016458950 scopus 로고
    • The concept of a linguistic variable and its applications to approximate reasoning
    • Part II, pp. 301-357 Inf Sci vol 9 Part III 43-80
    • L. A. Zadeh, "The concept of a linguistic variable and its applications to approximate reasoning," Inf. Sci., vol. 8, Part I, pp. 199-251, 1975, Part II, pp. 301-357, Inf. Sci., vol. 9, Part III, pp. 43-80.
    • (1975) Inf. Sci. , vol.8 , Issue.PART I , pp. 199-251
    • Zadeh, L.A.1
  • 50
    • 38248999424 scopus 로고    scopus 로고
    • On set-valued fuzzy integrals
    • D. Zhang and Z. Wang, "On set-valued fuzzy integrals," Fuzzy Sets Syst., vol. 56, pp. 237-247, 1993.
    • Fuzzy Sets Syst. , vol.56 , Issue.1993 , pp. 237-247
    • Zhang, D.1    Wang, Z.2
  • 51
    • 53249101336 scopus 로고    scopus 로고
    • Type-1 owa operators for aggregating uncertain information with uncertain weights induced by type-2 linguistic quantifiers
    • 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, pp. 3281-3296, 2008.
    • (2008) Fuzzy Sets Syst. , vol.159 , pp. 3281-3296
    • Zhou, S.M.1    Chiclana, F.2    John, R.I.3    Garibaldi, J.M.4
  • 52
    • 79955562977 scopus 로고    scopus 로고
    • Alpha-level aggregation: A practical approach to type-1 owa operation for aggregating uncertain information with applications to breast cancer treatments
    • Oct
    • 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. 2008.
    • (2008) IEEE Trans. Knowl. Data Eng. , vol.23 , Issue.10 , pp. 1455-1468
    • Zhou, S.M.1    Chiclana, F.2    John, R.I.3    Garibaldi, J.M.4


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