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Volumn 16, Issue 1, 2008, Pages 73-84

An efficient procedure for solving a fuzzy relational equation with max-Archimedean t-norm composition

Author keywords

Archimedean triangular norm (t norm); Fuzzy relational equations; Minimal solutions

Indexed keywords

FUZZY LOGIC; FUZZY SETS; MATRIX ALGEBRA; NUMERICAL METHODS;

EID: 40549107164     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2007.902018     Document Type: Article
Times cited : (61)

References (41)
  • 1
    • 0003471143 scopus 로고
    • Fuzzy Sets and Fuzzy Logic: Theory and Applications
    • Prentice-Hall NJ, Englewood Cliffs
    • G. J. Klir B. Yuan Fuzzy Sets and Fuzzy Logic: Theory and Applications 1995 Prentice-Hall NJ, Englewood Cliffs
    • (1995)
    • Klir, G.J.1    Yuan, B.2
  • 2
    • 0013176975 scopus 로고
    • Fuzzy relation equations theory as a basis of fuzzy modelling: An overview
    • A. Di Nola S. Sessa W. Pedrycz E. Sanchez Fuzzy relation equations theory as a basis of fuzzy modelling: An overview Fuzzy Sets Syst. 40 415 429 1991
    • (1991) Fuzzy Sets Syst. , vol.40 , pp. 415-429
    • Di Nola, A.1    Sessa, S.2    Pedrycz, W.3    Sanchez, E.4
  • 3
    • 0004197396 scopus 로고    scopus 로고
    • Fundamentals of Fuzzy Sets
    • Analytical Solution Methods for Fuzzy Relational Equations Kluwer MA, Norwell
    • B. D. Baets Fundamentals of Fuzzy Sets 291 340 2000 Kluwer MA, Norwell Analytical Solution Methods for Fuzzy Relational Equations
    • (2000) , pp. 291-340
    • Baets, B.D.1
  • 5
    • 0021422683 scopus 로고
    • Resolution of finite fuzzy relation equations
    • M. Higashi G. J. Klir Resolution of finite fuzzy relation equations Fuzzy Sets Syst. 13 65 82 1984
    • (1984) Fuzzy Sets Syst. , vol.13 , pp. 65-82
    • Higashi, M.1    Klir, G.J.2
  • 6
    • 0006445031 scopus 로고
    • Algorithm for the solution of fuzzy relations
    • M. Prevot Algorithm for the solution of fuzzy relations Fuzzy Sets Syst. 5 319 322 1981
    • (1981) Fuzzy Sets Syst. , vol.5 , pp. 319-322
    • Prevot, M.1
  • 7
    • 0005460204 scopus 로고
    • Fuzzy linear systems
    • K. Peeva Fuzzy linear systems Fuzzy Sets Syst. 49 339 355 1992
    • (1992) Fuzzy Sets Syst. , vol.49 , pp. 339-355
    • Peeva, K.1
  • 8
    • 0039784032 scopus 로고
    • Latticized linear programming and fuzzy relation inequalities
    • P. Z. Wang D. Z. Zhang E. Sanchez E. S. Lee Latticized linear programming and fuzzy relation inequalities J. Math. Anal. Appl. 159 1 72 87 1991
    • (1991) J. Math. Anal. Appl. , vol.159 , Issue.1 , pp. 72-87
    • Wang, P.Z.1    Zhang, D.Z.2    Sanchez, E.3    Lee, E.S.4
  • 9
    • 0006480837 scopus 로고
    • Further contributions to the study of finite fuzzy relation equations
    • S. Z. Guo P. Z. Wang A. Di Nola S. Sessa Further contributions to the study of finite fuzzy relation equations Fuzzy Sets Syst. 26 93 104 1988
    • (1988) Fuzzy Sets Syst. , vol.26 , pp. 93-104
    • Guo, S.Z.1    Wang, P.Z.2    Di Nola, A.3    Sessa, S.4
  • 10
    • 0020772093 scopus 로고
    • Fuzzy relational equations with generalized connectives and their applications
    • W. Pedrycz Fuzzy relational equations with generalized connectives and their applications Fuzzy Sets Syst. 10 185 201 1983
    • (1983) Fuzzy Sets Syst. , vol.10 , pp. 185-201
    • Pedrycz, W.1
  • 11
    • 3543082094 scopus 로고    scopus 로고
    • On the optimal three-tier multimedia streaming services
    • H.-C. Lee S.-M. Guu On the optimal three-tier multimedia streaming services Fuzzy Optim. Decision Making 2 3 31 39 2002
    • (2002) Fuzzy Optim. Decision Making , vol.2 , Issue.3 , pp. 31-39
    • Lee, H.-C.1    Guu, S.-M.2
  • 12
    • 11144331448 scopus 로고    scopus 로고
    • Minimizing a linear function under a fuzzy max-min relational equation constraint
    • Y.-K. Wu S.-M. Guu Minimizing a linear function under a fuzzy max-min relational equation constraint Fuzzy Sets Syst. 150 147 162 2005
    • (2005) Fuzzy Sets Syst. , vol.150 , pp. 147-162
    • Wu, Y.-K.1    Guu, S.-M.2
  • 13
    • 0016900196 scopus 로고
    • Resolution of composite fuzzy relation equations
    • E. Sanchez Resolution of composite fuzzy relation equations Inf. Control 30 38 48 1976
    • (1976) Inf. Control , vol.30 , pp. 38-48
    • Sanchez, E.1
  • 14
    • 0022054643 scopus 로고
    • On generalized fuzzy relational equations and their applications
    • W. Pedrycz On generalized fuzzy relational equations and their applications J. Math. Anal. Appl. 107 520 536 1985
    • (1985) J. Math. Anal. Appl. , vol.107 , pp. 520-536
    • Pedrycz, W.1
  • 15
    • 0003397941 scopus 로고
    • Fuzzy Relation Equations and Their Applications in Knowledge Engineering
    • Kluwer The Netherlands, Dordrecht
    • A. Di Nola S. Sessa W. Pedrycz E. Sanchez Fuzzy Relation Equations and Their Applications in Knowledge Engineering 1989 Kluwer The Netherlands, Dordrecht
    • (1989)
    • Di Nola, A.1    Sessa, S.2    Pedrycz, W.3    Sanchez, E.4
  • 16
    • 0000652239 scopus 로고
    • Theory of t-norms and fuzzy inference
    • M. M. Gupta J. Qi Theory of t-norms and fuzzy inference Fuzzy Sets Syst. 40 431 450 1991
    • (1991) Fuzzy Sets Syst. , vol.40 , pp. 431-450
    • Gupta, M.M.1    Qi, J.2
  • 17
    • 0026137347 scopus 로고
    • Design of fuzzy logic controllers based on generalized T-operators
    • M. M. Gupta J. Qi Design of fuzzy logic controllers based on generalized T-operators Fuzzy Sets Syst. 40 473 489 1991
    • (1991) Fuzzy Sets Syst. , vol.40 , pp. 473-489
    • Gupta, M.M.1    Qi, J.2
  • 18
    • 0348192487 scopus 로고
    • $s-t$ Fuzzy relational equations
    • W. Pedrycz $s-t$ Fuzzy relational equations Fuzzy Sets Syst. 59 189 195 1993
    • (1993) Fuzzy Sets Syst. , vol.59 , pp. 189-195
    • Pedrycz, W.1
  • 19
    • 3543137085 scopus 로고    scopus 로고
    • Solution sets of interval-valued fuzzy relational equations
    • S. Wang S.-C. Fang H. L. W. Nuttle Solution sets of interval-valued fuzzy relational equations Fuzzy Optim. Decision Making 2 1 41 60 2003
    • (2003) Fuzzy Optim. Decision Making , vol.2 , Issue.1 , pp. 41-60
    • Wang, S.1    Fang, S.-C.2    Nuttle, H.L.W.3
  • 20
    • 18444362435 scopus 로고    scopus 로고
    • On the relation between equations with max-product composition and the covering problem
    • A. V. Markovskii On the relation between equations with max-product composition and the covering problem Fuzzy Sets Syst. 153 261 273 2005
    • (2005) Fuzzy Sets Syst. , vol.153 , pp. 261-273
    • Markovskii, A.V.1
  • 21
    • 11144286917 scopus 로고    scopus 로고
    • Fuzzy relation equations (I): The general and specialized solving algorithms
    • L. Chen P. P. Wang Fuzzy relation equations (I): The general and specialized solving algorithms Soft Comput. 6 428 435 2002
    • (2002) Soft Comput. , vol.6 , pp. 428-435
    • Chen, L.1    Wang, P.P.2
  • 22
    • 0037331406 scopus 로고    scopus 로고
    • Matrix-pattern-based computer algorithm for solving fuzzy relation equations
    • L. Luoh W.-J. Wang Y.-K. Liaw Matrix-pattern-based computer algorithm for solving fuzzy relation equations IEEE Trans. Fuzzy Syst. 11 1 100 108 Feb. 2003
    • (2003) IEEE Trans. Fuzzy Syst. , vol.11 , Issue.1 , pp. 100-108
    • Luoh, L.1    Wang, W.-J.2    Liaw, Y.-K.3
  • 23
    • 0010051169 scopus 로고    scopus 로고
    • Solution algorithms for fuzzy relational equations with max-product composition
    • M. M. Bourke D. G. Fisher Solution algorithms for fuzzy relational equations with max-product composition Fuzzy Sets Syst. 94 61 69 1998
    • (1998) Fuzzy Sets Syst. , vol.94 , pp. 61-69
    • Bourke, M.M.1    Fisher, D.G.2
  • 24
    • 0032595167 scopus 로고    scopus 로고
    • An efficient solution procedure for fuzzy relational equations with max-product composition
    • J. Loetamonphong S.-C. Fang An efficient solution procedure for fuzzy relational equations with max-product composition IEEE Trans. Fuzzy Syst. 7 4 441 445 Aug. 1999
    • (1999) IEEE Trans. Fuzzy Syst. , vol.7 , Issue.4 , pp. 441-445
    • Loetamonphong, J.1    Fang, S.-C.2
  • 25
    • 3543122400 scopus 로고    scopus 로고
    • Minimizing a linear objective function with fuzzy relation equation constraints
    • S.-M. Guu Y.-K. Wu Minimizing a linear objective function with fuzzy relation equation constraints Fuzzy Optim. Decision Making 1 4 347 360 2002
    • (2002) Fuzzy Optim. Decision Making , vol.1 , Issue.4 , pp. 347-360
    • Guu, S.-M.1    Wu, Y.-K.2
  • 26
    • 4043096989 scopus 로고    scopus 로고
    • A note on fuzzy relation programming problems with max-strict-t-norm composition
    • Y.-K. Wu S.-M. Guu A note on fuzzy relation programming problems with max-strict-t-norm composition Fuzzy Optim. Decision Making 3 271 278 2004
    • (2004) Fuzzy Optim. Decision Making , vol.3 , pp. 271-278
    • Wu, Y.-K.1    Guu, S.-M.2
  • 27
    • 0035898958 scopus 로고    scopus 로고
    • Continuous Archimedean t-norms and their bounds
    • V. Marko R. Mesiar Continuous Archimedean t-norms and their bounds Fuzzy Sets Syst. 121 183 190 2001
    • (2001) Fuzzy Sets Syst. , vol.121 , pp. 183-190
    • Marko, V.1    Mesiar, R.2
  • 28
    • 0035371744 scopus 로고    scopus 로고
    • Resolution of composite fuzzy relation equations based on Archimedean triangular norms
    • G. B. Stamou S. G. Tzafestas Resolution of composite fuzzy relation equations based on Archimedean triangular norms Fuzzy Sets Syst. 120 395 407 2001
    • (2001) Fuzzy Sets Syst. , vol.120 , pp. 395-407
    • Stamou, G.B.1    Tzafestas, S.G.2
  • 29
    • 0034515137 scopus 로고    scopus 로고
    • Compatibility of systems of fuzzy relation equations
    • I. Perfilieva A. Tonis Compatibility of systems of fuzzy relation equations Int. J. General Syst. 29 4 511 528 2000
    • (2000) Int. J. General Syst. , vol.29 , Issue.4 , pp. 511-528
    • Perfilieva, I.1    Tonis, A.2
  • 30
    • 0000980589 scopus 로고
    • Statistical metrics
    • K. Menger Statistical metrics Proc. Nat. Acad. Sci. 28 535 537 Proc. Nat. Acad. Sci. 1942
    • (1942) , vol.28 , pp. 535-537
    • Menger, K.1
  • 31
    • 0001594582 scopus 로고
    • Probabilistic uniformization of fuzzy topologies
    • U. Hhle Probabilistic uniformization of fuzzy topologies Fuzzy Sets Syst. 1 311 332 1978
    • (1978) Fuzzy Sets Syst. , vol.1 , pp. 311-332
    • Hhle, U.1
  • 33
    • 0001544891 scopus 로고    scopus 로고
    • On Archimedean triangular norms
    • S. Jenei On Archimedean triangular norms Fuzzy Sets Syst. 99 179 186 1998
    • (1998) Fuzzy Sets Syst. , vol.99 , pp. 179-186
    • Jenei, S.1
  • 34
    • 0001819136 scopus 로고    scopus 로고
    • On continuous triangular norms
    • S. Jenei J. C. Fodor On continuous triangular norms Fuzzy Sets Syst. 100 273 282 1998
    • (1998) Fuzzy Sets Syst. , vol.100 , pp. 273-282
    • Jenei, S.1    Fodor, J.C.2
  • 35
    • 2942666059 scopus 로고    scopus 로고
    • Triangular norms. Position paper III: Continuous t-norms
    • E. P. Klement R. Mesiar E. Pap Triangular norms. Position paper III: Continuous t-norms Fuzzy Sets Syst. 145 439 454 2004
    • (2004) Fuzzy Sets Syst. , vol.145 , pp. 439-454
    • Klement, E.P.1    Mesiar, R.2    Pap, E.3
  • 36
    • 0004128728 scopus 로고    scopus 로고
    • Triangular Norms
    • Kluwer The Netherlands, Dordrecht
    • E. P. Klement R. Mesiar E. Pap Triangular Norms 2000 Kluwer The Netherlands, Dordrecht
    • (2000)
    • Klement, E.P.1    Mesiar, R.2    Pap, E.3
  • 37
    • 0003611241 scopus 로고
    • Fuzzy Sets and Fuzzy Logic
    • Springer-Verlag France, Toulouse
    • S. Gottwald Fuzzy Sets and Fuzzy Logic 1993 Springer-Verlag France, Toulouse
    • (1993)
    • Gottwald, S.1
  • 38
    • 0000316125 scopus 로고
    • On the structure of semigroups on a compact manifold with boundary
    • P. S. Mostert A. L. Shields On the structure of semigroups on a compact manifold with boundary Ann. Math. 65 117 143 1957
    • (1957) Ann. Math. , vol.65 , pp. 117-143
    • Mostert, P.S.1    Shields, A.L.2
  • 39
    • 0037521097 scopus 로고
    • Triangular norms and TNF-sigma-algebras
    • Y. D. Yu Triangular norms and TNF-sigma-algebras Fuzzy Sets Syst. 16 3 251 264 1985
    • (1985) Fuzzy Sets Syst. , vol.16 , Issue.3 , pp. 251-264
    • Yu, Y.D.1
  • 40
    • 33646173689 scopus 로고
    • Measures of fuzzy sets and measures of fuzziness
    • S. Weber Measures of fuzzy sets and measures of fuzziness Fuzzy Sets Syst. 13 3 247 271 1983
    • (1983) Fuzzy Sets Syst. , vol.13 , Issue.3 , pp. 247-271
    • Weber, S.1
  • 41
    • 0004264593 scopus 로고
    • Probabilistic Metric Spaces
    • North-Holland New York
    • B. Schweizer A. Sklar Probabilistic Metric Spaces 1983 North-Holland New York
    • (1983)
    • Schweizer, B.1    Sklar, A.2


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