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Volumn 178, Issue 5, 2008, Pages 1293-1308

An algorithm for solving fuzzy relation equations with max-T composition operator

Author keywords

Fuzzy relation equations; Infinitely distributive strong pseudo t norm; Maximum solution; Minimal solution; Strong pseudo t norm

Indexed keywords

ALGORITHMS; FINITE DIFFERENCE METHOD; SYSTEMS ANALYSIS;

EID: 37249037693     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2007.10.010     Document Type: Article
Times cited : (55)

References (76)
  • 2
    • 18444370334 scopus 로고    scopus 로고
    • Fuzzy relations and fuzzy relation equations
    • (in Chinese)
    • Dai F.M., and Wang Z.D. Fuzzy relations and fuzzy relation equations. Journal of Yangzhou University 5 2 (2002) 8-10 (in Chinese)
    • (2002) Journal of Yangzhou University , vol.5 , Issue.2 , pp. 8-10
    • Dai, F.M.1    Wang, Z.D.2
  • 3
    • 0011835506 scopus 로고
    • An order-theoretic approach to solving sup-Tequations
    • Ruan D. (Ed), Kluwer Academic Publishers, Dordrecht
    • De Baets B. An order-theoretic approach to solving sup-Tequations. In: Ruan D. (Ed). Fuzzy Set Theory and Advanced Mathematical Applications (1995), Kluwer Academic Publishers, Dordrecht 67-87
    • (1995) Fuzzy Set Theory and Advanced Mathematical Applications , pp. 67-87
    • De Baets, B.1
  • 4
    • 0001634914 scopus 로고    scopus 로고
    • Analytical solution methods for fuzzy relational equations
    • Fundamentals of Fuzzy Sets. Dubois D., and Prade H. (Eds), Kluwer Academic Publishers, Dordrecht
    • De Baets B. Analytical solution methods for fuzzy relational equations. In: Dubois D., and Prade H. (Eds). Fundamentals of Fuzzy Sets. The Handbooks of Fuzzy Sets Series vol. 1 (2000), Kluwer Academic Publishers, Dordrecht 291-340
    • (2000) The Handbooks of Fuzzy Sets Series , vol.1 , pp. 291-340
    • De Baets, B.1
  • 5
    • 0013338162 scopus 로고
    • Fuzzy relation equations under a class of triangular norms: a survey and new results
    • Di Nola A., Pedrycz W., Sessa S., and Wang P.Z. Fuzzy relation equations under a class of triangular norms: a survey and new results. Stochastica 2 (1984) 99-145
    • (1984) Stochastica , vol.2 , pp. 99-145
    • Di Nola, A.1    Pedrycz, W.2    Sessa, S.3    Wang, P.Z.4
  • 6
    • 0022207981 scopus 로고
    • Fuzzy relation equations and algorithms of inference mechanism in expert systems
    • Gupta M.M., Kandel A., Bandler W., and Kiszka J.B. (Eds), Elsevier Science Publishers (North-Holland), Amsterdam
    • Di Nola A., Pedrycz W., and Sessa S. Fuzzy relation equations and algorithms of inference mechanism in expert systems. In: Gupta M.M., Kandel A., Bandler W., and Kiszka J.B. (Eds). Approximate Reasoning in Expert System (1985), Elsevier Science Publishers (North-Holland), Amsterdam 355-367
    • (1985) Approximate Reasoning in Expert System , pp. 355-367
    • Di Nola, A.1    Pedrycz, W.2    Sessa, S.3
  • 7
    • 37249023975 scopus 로고
    • Fuzzy relation equations under LSC and USC t-norms and their Boolean solutions
    • Di Nola A., Pedrycz W., and Sessa S. Fuzzy relation equations under LSC and USC t-norms and their Boolean solutions. Stochastica 11 2-3 (1987) 151-183
    • (1987) Stochastica , vol.11 , Issue.2-3 , pp. 151-183
    • Di Nola, A.1    Pedrycz, W.2    Sessa, S.3
  • 8
    • 37249034430 scopus 로고
    • Fuzzy relation equations with equality and difference composition operators
    • Di Nola A., Pedrycz W., and Sessa S. Fuzzy relation equations with equality and difference composition operators. Fuzzy Sets and Systems 25 (1988) 205-215
    • (1988) Fuzzy Sets and Systems , vol.25 , pp. 205-215
    • Di Nola, A.1    Pedrycz, W.2    Sessa, S.3
  • 10
    • 33845932089 scopus 로고    scopus 로고
    • Lukasiewicz transform and its application to compression and reconstruction of digital images
    • Di Nola A., and Russo C. Lukasiewicz transform and its application to compression and reconstruction of digital images. Information Sciences 177 (2007) 1481-1498
    • (2007) Information Sciences , vol.177 , pp. 1481-1498
    • Di Nola, A.1    Russo, C.2
  • 11
    • 0021594252 scopus 로고
    • Some theoretical aspects of fuzzy-relation equations describing fuzzy systems
    • Di Nola A., Pedrycz W., and Sessa S. Some theoretical aspects of fuzzy-relation equations describing fuzzy systems. Information Sciences 34 (1984) 241-264
    • (1984) Information Sciences , vol.34 , pp. 241-264
    • Di Nola, A.1    Pedrycz, W.2    Sessa, S.3
  • 12
    • 0001046583 scopus 로고    scopus 로고
    • Solving fuzzy relation equations with a linear objective function
    • Fang S.-C., and Li G. Solving fuzzy relation equations with a linear objective function. Fuzzy Sets and Systems 103 (1999) 107-113
    • (1999) Fuzzy Sets and Systems , vol.103 , pp. 107-113
    • Fang, S.-C.1    Li, G.2
  • 13
    • 3042750198 scopus 로고    scopus 로고
    • Some specific types of fuzzy relation equations
    • Fernandez M.J., and Gil P. Some specific types of fuzzy relation equations. Information Sciences 164 (2004) 189-195
    • (2004) Information Sciences , vol.164 , pp. 189-195
    • Fernandez, M.J.1    Gil, P.2
  • 15
    • 0000584801 scopus 로고
    • Strict preference relations based on weak t-norms
    • Fodor J.C. Strict preference relations based on weak t-norms. Fuzzy Sets and Systems 43 (1991) 327-336
    • (1991) Fuzzy Sets and Systems , vol.43 , pp. 327-336
    • Fodor, J.C.1
  • 16
    • 0006106252 scopus 로고
    • Nonstandard conjunctions and implications in fuzzy logic
    • Fodor J.C., and Keresztfalvi T. Nonstandard conjunctions and implications in fuzzy logic. Internat. J. Approx. Reason. 12 (1995) 69-84
    • (1995) Internat. J. Approx. Reason. , vol.12 , pp. 69-84
    • Fodor, J.C.1    Keresztfalvi, T.2
  • 17
    • 0035900853 scopus 로고    scopus 로고
    • Solvability and unique solvability of max-min fuzzy equations
    • Gavalec M. Solvability and unique solvability of max-min fuzzy equations. Fuzzy Sets and Systems 124 (2001) 385-393
    • (2001) Fuzzy Sets and Systems , vol.124 , pp. 385-393
    • Gavalec, M.1
  • 18
    • 0021405478 scopus 로고
    • On the existence of solutions of systems of fuzzy equation
    • Gottwald S. On the existence of solutions of systems of fuzzy equation. Fuzzy Sets and Systems 12 (1984) 301-302
    • (1984) Fuzzy Sets and Systems , vol.12 , pp. 301-302
    • Gottwald, S.1
  • 19
    • 37249050104 scopus 로고
    • Generalized solvability criteria for fuzzy equations
    • Gottwald S. Generalized solvability criteria for fuzzy equations. Fuzzy Sets and Systems 17 (1985) 258-296
    • (1985) Fuzzy Sets and Systems , vol.17 , pp. 258-296
    • Gottwald, S.1
  • 20
    • 0346356371 scopus 로고
    • Characterization of the solvability of fuzzy equations
    • Gottwald S. Characterization of the solvability of fuzzy equations. Elektron. Informationsverarb. Kybernet. 22 2/3 (1986) 67-91
    • (1986) Elektron. Informationsverarb. Kybernet. , vol.22 , Issue.2-3 , pp. 67-91
    • Gottwald, S.1
  • 21
    • 0039636330 scopus 로고
    • Solvability of fuzzy relational equations and manipulation of fuzzy data
    • Gottwald S., and Pedrycz W. Solvability of fuzzy relational equations and manipulation of fuzzy data. Fuzzy Sets and Systems 18 (1986) 45-65
    • (1986) Fuzzy Sets and Systems , vol.18 , pp. 45-65
    • Gottwald, S.1    Pedrycz, W.2
  • 22
    • 0038429699 scopus 로고
    • On the methodology of solving fuzzy relational equations and its impact on fuzzy modelling
    • Fuzzy Logic in Knowledge-Based Systems. Gupta M.M., and Yamakawa T. (Eds), North-Holland, Amsterdam
    • Gottwald S., and Pedrycz W. On the methodology of solving fuzzy relational equations and its impact on fuzzy modelling. In: Gupta M.M., and Yamakawa T. (Eds). Fuzzy Logic in Knowledge-Based Systems. Decision and Control (1988), North-Holland, Amsterdam 197-210
    • (1988) Decision and Control , pp. 197-210
    • Gottwald, S.1    Pedrycz, W.2
  • 23
    • 0026137347 scopus 로고
    • Design of fuzzy logic controllers based on generalized t-operators
    • Gupta M.M., and Qi J. Design of fuzzy logic controllers based on generalized t-operators. Fuzzy Sets and Systems 40 (1991) 473-486
    • (1991) Fuzzy Sets and Systems , vol.40 , pp. 473-486
    • Gupta, M.M.1    Qi, J.2
  • 24
    • 18444418843 scopus 로고    scopus 로고
    • Notes on "Pseudo-t-norms and implication operators on a complete Brouwerian lattice" and "Pseudo-t-norms and implication operators: direct products and direct product decompositions"
    • Han S.C., and Li H.X. Notes on "Pseudo-t-norms and implication operators on a complete Brouwerian lattice" and "Pseudo-t-norms and implication operators: direct products and direct product decompositions". Fuzzy Sets and Systems 153 (2005) 289-294
    • (2005) Fuzzy Sets and Systems , vol.153 , pp. 289-294
    • Han, S.C.1    Li, H.X.2
  • 25
    • 33646025810 scopus 로고    scopus 로고
    • Resolution of finite fuzzy relation equations based on strong pseudo-t-norms
    • Han S.-C., Li H.-X., and Wang J.-Y. Resolution of finite fuzzy relation equations based on strong pseudo-t-norms. Applied Mathematics Letters 19 (2006) 752-757
    • (2006) Applied Mathematics Letters , vol.19 , pp. 752-757
    • Han, S.-C.1    Li, H.-X.2    Wang, J.-Y.3
  • 26
    • 0021422683 scopus 로고
    • Resolution of finite fuzzy relation equations
    • Higashi M., and Klir G.J. Resolution of finite fuzzy relation equations. Fuzzy Sets and Systems 13 (1984) 65-82
    • (1984) Fuzzy Sets and Systems , vol.13 , pp. 65-82
    • Higashi, M.1    Klir, G.J.2
  • 27
    • 0040958822 scopus 로고    scopus 로고
    • Specificity shift in solving fuzzy relational equations
    • Hirota K., and Pedrycz W. Specificity shift in solving fuzzy relational equations. Fuzzy Sets and Systems 106 (1999) 211-220
    • (1999) Fuzzy Sets and Systems , vol.106 , pp. 211-220
    • Hirota, K.1    Pedrycz, W.2
  • 28
    • 0035480419 scopus 로고    scopus 로고
    • Fuzzy relational equation with defuzzification-algorithm for the largest solution
    • Kagei S. Fuzzy relational equation with defuzzification-algorithm for the largest solution. Fuzzy Sets and Systems 123 (2001) 119-127
    • (2001) Fuzzy Sets and Systems , vol.123 , pp. 119-127
    • Kagei, S.1
  • 29
    • 0032166590 scopus 로고    scopus 로고
    • Composite fuzzy relational equations with non-commutative conjunctions
    • Kawaguchi M.F., and Miyakoshi M. Composite fuzzy relational equations with non-commutative conjunctions. Information Sciences 110 (1998) 113-125
    • (1998) Information Sciences , vol.110 , pp. 113-125
    • Kawaguchi, M.F.1    Miyakoshi, M.2
  • 31
    • 0000386859 scopus 로고    scopus 로고
    • Unattainable solutions of a fuzzy relation equation
    • Imai H., Kikuchi K., and Miyakoshi M. Unattainable solutions of a fuzzy relation equation. Fuzzy Sets and Systems 99 (1998) 193-196
    • (1998) Fuzzy Sets and Systems , vol.99 , pp. 193-196
    • Imai, H.1    Kikuchi, K.2    Miyakoshi, M.3
  • 32
  • 33
    • 0033131022 scopus 로고    scopus 로고
    • Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations: Part II
    • Li X., and Ruan D. Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations: Part II. Fuzzy Sets and Systems 103 (1999) 473-486
    • (1999) Fuzzy Sets and Systems , vol.103 , pp. 473-486
    • Li, X.1    Ruan, D.2
  • 34
    • 0001666681 scopus 로고    scopus 로고
    • Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations: Part III
    • Li X., and Ruan D. Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations: Part III. Fuzzy Sets and Systems 109 (2000) 355-362
    • (2000) Fuzzy Sets and Systems , vol.109 , pp. 355-362
    • Li, X.1    Ruan, D.2
  • 35
    • 0025403690 scopus 로고
    • On some systems of simultaneous equations in a completely distributive lattice
    • Liu W.-J. On some systems of simultaneous equations in a completely distributive lattice. Information Sciences 50 (1990) 185-196
    • (1990) Information Sciences , vol.50 , pp. 185-196
    • Liu, W.-J.1
  • 36
    • 0035284131 scopus 로고    scopus 로고
    • Optimization of fuzzy relational equations with max-product Composition
    • Loetamonphong J., and Fang S.-C. Optimization of fuzzy relational equations with max-product Composition. Fuzzy Sets and Systems 118 (2001) 509-517
    • (2001) Fuzzy Sets and Systems , vol.118 , pp. 509-517
    • Loetamonphong, J.1    Fang, S.-C.2
  • 37
    • 0037117666 scopus 로고    scopus 로고
    • Multi-objective optimization problems with fuzzy relation equation constraints
    • Loetamonphong J., Fang S.-C., and Young R.E. Multi-objective optimization problems with fuzzy relation equation constraints. Fuzzy Sets and Systems 127 (2002) 141-164
    • (2002) Fuzzy Sets and Systems , vol.127 , pp. 141-164
    • Loetamonphong, J.1    Fang, S.-C.2    Young, R.E.3
  • 38
    • 13544263233 scopus 로고    scopus 로고
    • Fuzzy relation equations for coding/decoding processes of images and videos
    • Loia V., and Sessa S. Fuzzy relation equations for coding/decoding processes of images and videos. Information Sciences 171 (2005) 145-172
    • (2005) Information Sciences , vol.171 , pp. 145-172
    • Loia, V.1    Sessa, S.2
  • 39
    • 0035314248 scopus 로고    scopus 로고
    • Solving nonlinear optimization problems with fuzzy relation equation constraints
    • Lu J., and Fang S.-C. Solving nonlinear optimization problems with fuzzy relation equation constraints. Fuzzy Sets and Systems 119 (2001) 1-20
    • (2001) Fuzzy Sets and Systems , vol.119 , pp. 1-20
    • Lu, J.1    Fang, S.-C.2
  • 40
    • 5644270178 scopus 로고    scopus 로고
    • Decomposition and resolution of min-implication fuzzy relation equations based on S-implications
    • Luo Y., and Li Y. Decomposition and resolution of min-implication fuzzy relation equations based on S-implications. Fuzzy Sets and Systems 148 (2004) 305-317
    • (2004) Fuzzy Sets and Systems , vol.148 , pp. 305-317
    • Luo, Y.1    Li, Y.2
  • 42
    • 38249041067 scopus 로고
    • Lower solutions of systems of fuzzy equations
    • Miyakoshi M., and Shimbo M. Lower solutions of systems of fuzzy equations. Fuzzy Sets and Systems 19 (1986) 37-46
    • (1986) Fuzzy Sets and Systems , vol.19 , pp. 37-46
    • Miyakoshi, M.1    Shimbo, M.2
  • 43
    • 0022060286 scopus 로고
    • Solutions of composite fuzzy relational equations with triangular norms
    • Miyakoshi M., and Shimbo M. Solutions of composite fuzzy relational equations with triangular norms. Fuzzy Sets and Systems 16 (1985) 53-63
    • (1985) Fuzzy Sets and Systems , vol.16 , pp. 53-63
    • Miyakoshi, M.1    Shimbo, M.2
  • 44
    • 33745992937 scopus 로고    scopus 로고
    • On various eigen fuzzy sets and their application to image reconstruction
    • Nobuhara H., Bede B., and Hirota K. On various eigen fuzzy sets and their application to image reconstruction. Information Sciences 176 (2006) 2988-3010
    • (2006) Information Sciences , vol.176 , pp. 2988-3010
    • Nobuhara, H.1    Bede, B.2    Hirota, K.3
  • 45
    • 0023854730 scopus 로고
    • Convexly combined fuzzy relational equations and several aspects of their application to fuzzy information processing
    • Ohsato A., and Sekiguchi T. Convexly combined fuzzy relational equations and several aspects of their application to fuzzy information processing. Information Sciences 45 (1988) 275-313
    • (1988) Information Sciences , vol.45 , pp. 275-313
    • Ohsato, A.1    Sekiguchi, T.2
  • 46
    • 0347169302 scopus 로고
    • Fuzzy relational equations with triangular norms and their resolution
    • Pedrycz W. Fuzzy relational equations with triangular norms and their resolution. BUSEFAL 11 (1982) 24-32
    • (1982) BUSEFAL , vol.11 , pp. 24-32
    • Pedrycz, W.1
  • 47
    • 0346837453 scopus 로고
    • Numerical and applicational aspects of fuzzy relational equations
    • Pedrycz W. Numerical and applicational aspects of fuzzy relational equations. Fuzzy Sets and Systems 11 (1983) 1-18
    • (1983) Fuzzy Sets and Systems , vol.11 , pp. 1-18
    • Pedrycz, W.1
  • 48
    • 0022054643 scopus 로고
    • On generalized fuzzy relational equations and their applications
    • Pedrycz W. On generalized fuzzy relational equations and their applications. J. Math. Anal. Appl. 107 (1985) 520-536
    • (1985) J. Math. Anal. Appl. , vol.107 , pp. 520-536
    • Pedrycz, W.1
  • 49
    • 0022093877 scopus 로고
    • Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data
    • Pedrycz W. Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data. Fuzzy Sets and Systems 16 (1985) 163-175
    • (1985) Fuzzy Sets and Systems , vol.16 , pp. 163-175
    • Pedrycz, W.1
  • 50
    • 38249026779 scopus 로고
    • Approximate solutions of fuzzy relational equations
    • Pedrycz W. Approximate solutions of fuzzy relational equations. Fuzzy Sets and Systems 28 (1988) 183-202
    • (1988) Fuzzy Sets and Systems , vol.28 , pp. 183-202
    • Pedrycz, W.1
  • 51
    • 38249017803 scopus 로고
    • Algorithms for solving fuzzy relational equations in a probabilistic setting
    • Pedrycz W. Algorithms for solving fuzzy relational equations in a probabilistic setting. Fuzzy Sets and Systems 38 (1990) 313-327
    • (1990) Fuzzy Sets and Systems , vol.38 , pp. 313-327
    • Pedrycz, W.1
  • 52
    • 4544227117 scopus 로고    scopus 로고
    • Fuzzy function as an approximate solution to a system of fuzzy relation equations
    • Perfilieva I. Fuzzy function as an approximate solution to a system of fuzzy relation equations. Fuzzy Sets and Systems 147 (2004) 363-383
    • (2004) Fuzzy Sets and Systems , vol.147 , pp. 363-383
    • Perfilieva, I.1
  • 53
    • 34249302022 scopus 로고    scopus 로고
    • System of fuzzy relation equations as a continuous model of IF-THEN rules
    • Perfilieva I., and Novak V. System of fuzzy relation equations as a continuous model of IF-THEN rules. Information Sciences 177 (2007) 3218-3227
    • (2007) Information Sciences , vol.177 , pp. 3218-3227
    • Perfilieva, I.1    Novak, V.2
  • 54
    • 0009013651 scopus 로고    scopus 로고
    • About simple fuzzy control and fuzzy control based on fuzzy relational equations
    • Pavlica V., and Petrovacki D. About simple fuzzy control and fuzzy control based on fuzzy relational equations. Fuzzy Sets and Systems 101 (1999) 41-47
    • (1999) Fuzzy Sets and Systems , vol.101 , pp. 41-47
    • Pavlica, V.1    Petrovacki, D.2
  • 55
    • 0021405479 scopus 로고
    • Solutions of fuzzy equations with extended operations
    • Sanchez E. Solutions of fuzzy equations with extended operations. Fuzzy Sets and Systems 12 (1984) 237-248
    • (1984) Fuzzy Sets and Systems , vol.12 , pp. 237-248
    • Sanchez, E.1
  • 56
    • 0016900196 scopus 로고
    • Resolution of composite fuzzy relation equations
    • Sanchez E. Resolution of composite fuzzy relation equations. Information and Control 30 (1976) 38-48
    • (1976) Information and Control , vol.30 , pp. 38-48
    • Sanchez, E.1
  • 57
    • 34447337502 scopus 로고    scopus 로고
    • Solutions of fuzzy relation equations based on continuous t-norms
    • Shieh B.-S. Solutions of fuzzy relation equations based on continuous t-norms. Information Sciences 177 (2007) 4208-4215
    • (2007) Information Sciences , vol.177 , pp. 4208-4215
    • Shieh, B.-S.1
  • 58
    • 0035371744 scopus 로고    scopus 로고
    • Resolution of composite fuzzy relation equations based on Archimedean triangular norms
    • Stamou G.B., and Tzafestas S.G. Resolution of composite fuzzy relation equations based on Archimedean triangular norms. Fuzzy Sets and Systems 120 (2001) 395-407
    • (2001) Fuzzy Sets and Systems , vol.120 , pp. 395-407
    • Stamou, G.B.1    Tzafestas, S.G.2
  • 60
    • 37249025943 scopus 로고
    • On generalized fuzzy relation equations: necessary and sufficient conditions for the existence of solutions
    • Turunen E. On generalized fuzzy relation equations: necessary and sufficient conditions for the existence of solutions. Acta Univ. Carolinae Math. Phys. 28 (1987) 33-37
    • (1987) Acta Univ. Carolinae Math. Phys. , vol.28 , pp. 33-37
    • Turunen, E.1
  • 61
    • 38249039891 scopus 로고
    • The complementary process of fuzzy medical diagnosis and its properties
    • Umeyama S. The complementary process of fuzzy medical diagnosis and its properties. Information Sciences 38 (1986) 229-242
    • (1986) Information Sciences , vol.38 , pp. 229-242
    • Umeyama, S.1
  • 62
    • 37249010863 scopus 로고    scopus 로고
    • W.B. Vasantha Kandasamy, F. Smarandache, Fuzzy relational maps and neutrosophic relational maps, hexis church rock (2004) (see chapters one and two) at: http://mat.iitm.ac.in/~wbv/book13.htm.
  • 63
    • 33646063237 scopus 로고
    • On direct and inverse problems for fuzzy equation systems with tolerances
    • Wagenknecht M., and Hartmann K. On direct and inverse problems for fuzzy equation systems with tolerances. Fuzzy Sets and Systems 24 (1987) 93-102
    • (1987) Fuzzy Sets and Systems , vol.24 , pp. 93-102
    • Wagenknecht, M.1    Hartmann, K.2
  • 64
    • 37249038339 scopus 로고    scopus 로고
    • H.-F. Wang, An algorithm for solving iterated composite relation equations, in: Proc. NAFIPS, 1988, pp. 242-249.
  • 66
    • 0035371659 scopus 로고    scopus 로고
    • Method of solution to fuzzy relation equations in a complete Brouwerian lattice
    • Wang X.P. Method of solution to fuzzy relation equations in a complete Brouwerian lattice. Fuzzy Sets and Systems 120 (2001) 409-414
    • (2001) Fuzzy Sets and Systems , vol.120 , pp. 409-414
    • Wang, X.P.1
  • 67
    • 18444412020 scopus 로고    scopus 로고
    • The sets of solutions of L-relation equations T(a,x) = b and I(a,x) = b
    • (in Chinese)
    • Wang Z.D., and Dai F.M. The sets of solutions of L-relation equations T(a,x) = b and I(a,x) = b. Journal of Yangzhou University 6 3 (2003) 8-10 (in Chinese)
    • (2003) Journal of Yangzhou University , vol.6 , Issue.3 , pp. 8-10
    • Wang, Z.D.1    Dai, F.M.2
  • 68
    • 0037121224 scopus 로고    scopus 로고
    • Pseudo-t-norms and implication operators on a complete Brouwerian lattice
    • Wang Z.D., and Yu Y.D. Pseudo-t-norms and implication operators on a complete Brouwerian lattice. Fuzzy Sets and Systems 132 (2002) 113-124
    • (2002) Fuzzy Sets and Systems , vol.132 , pp. 113-124
    • Wang, Z.D.1    Yu, Y.D.2
  • 69
    • 0141865535 scopus 로고    scopus 로고
    • Pseudo-t-norms and implication operators: direct products and direct product decompositions
    • Wang Z.D., and Yu Y.D. Pseudo-t-norms and implication operators: direct products and direct product decompositions. Fuzzy Sets and Systems 139 (2003) 673-683
    • (2003) Fuzzy Sets and Systems , vol.139 , pp. 673-683
    • Wang, Z.D.1    Yu, Y.D.2
  • 70
    • 0042121376 scopus 로고    scopus 로고
    • Infinite fuzzy relational equations on a complete Brouwerian lattice
    • Wang X.-P. Infinite fuzzy relational equations on a complete Brouwerian lattice. Fuzzy Sets and Systems 138 (2003) 657-666
    • (2003) Fuzzy Sets and Systems , vol.138 , pp. 657-666
    • Wang, X.-P.1
  • 71
    • 4043096989 scopus 로고    scopus 로고
    • A note on fuzzy relation programming problems with max-strict-t-norm composition
    • Wu Y.-K., and Guu S.-M. A note on fuzzy relation programming problems with max-strict-t-norm composition. Fuzzy Optimization and Decision Making 3 (2004) 271-278
    • (2004) Fuzzy Optimization and Decision Making , vol.3 , pp. 271-278
    • Wu, Y.-K.1    Guu, S.-M.2
  • 72
    • 34447307929 scopus 로고    scopus 로고
    • Optimization of fuzzy relational equations with max-av composition
    • Wu Y.-K. Optimization of fuzzy relational equations with max-av composition. Information Sciences 177 (2007) 4216-4229
    • (2007) Information Sciences , vol.177 , pp. 4216-4229
    • Wu, Y.-K.1
  • 73
    • 13644262815 scopus 로고    scopus 로고
    • Some properties of sup-min fuzzy relational equations on infinite domains
    • Xiong Q.-Q., and Wang X.-P. Some properties of sup-min fuzzy relational equations on infinite domains. Fuzzy Sets and Systems 151 (2005) 393-402
    • (2005) Fuzzy Sets and Systems , vol.151 , pp. 393-402
    • Xiong, Q.-Q.1    Wang, X.-P.2
  • 76
    • 45949117435 scopus 로고
    • On matrix equations in a class of complete and completely distributive lattices
    • Zhao C.K. On matrix equations in a class of complete and completely distributive lattices. Fuzzy Sets and Systems 22 (1987) 303-320
    • (1987) Fuzzy Sets and Systems , vol.22 , pp. 303-320
    • Zhao, C.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.