×

zbMATH — the first resource for mathematics

A survey on fuzzy relational equations. I: Classification and solvability. (English) Zbl 1180.03051
The paper presents a survey of the theory of fuzzy relational equations, their classifcation, and main solution methods. The concepts and results summarized in the paper are classified and discussed. The main attention is focused on the problem of solvability of fuzzy relational equations, and on the analysis of necessary and sufficient conditions. Moreover, the solution sets are characterized. The extensive survey of concepts and results is completed by a rich list (296 items) of references.

MSC:
03E72 Theory of fuzzy sets, etc.
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abbasi Molai, A.; Khorram, E., A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian, Applied Mathematics and Computation,, 190, 1161-1167, (2007) · Zbl 1227.90049
[2] Abbasi Molai, A.; Khorram, E., Another modification from two papers of Ghodousian and Khorram and Ghorram et al, Applied Mathematics and Computation, 197, 559-565, (2008) · Zbl 1141.65045
[3] Abbasi Molai, A.; Khorram, E., An algorithm for solving fuzzy relation equations with max-\(T\) composition operator, Information Sciences, 178, 1293-1308, (2008) · Zbl 1136.03330
[4] Alsina C., Frank M.J., Schweizer B. (2006) Associative functions: Triangular norms and copulas. World Scientific, Singarpore · Zbl 1100.39023
[5] Alsina, C.; Trillas, E., When \((S, N)\)-implications are \((T, T\_{}\{1\})\)-conditional functions?, Fuzzy Sets and Systems, 134, 305-310, (2003) · Zbl 1014.03026
[6] Alsina, C.; Trillas, E.; Valverde, L., On non-distributive logical connectives for fuzzy sets theory, BUSEFAL, 3, 18-29, (1980)
[7] Atanassov, K. T. (1983). Intuitionistic fuzzy sets. In V. Sgurev (Ed.), Seventh scientific session of ITKR, Sofia, June 1983. Deposed in Central Science-Technical Library of Bulgarian Academy of Science, 1697/84 (in Bulgarian).
[8] Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96, (1986) · Zbl 0631.03040
[9] Atanassov K.T. (1999) Intuitionistic fuzzy sets. Physica-Verlag, Heidelberg · Zbl 0939.03057
[10] Atanassov, K. T., Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade’s paper “Terminological difficulties in fuzzy set theory—The case of “Intuitionistic Fuzzy Sets”., Fuzzy Sets and Systems, 156, 496-499, (2005) · Zbl 1098.03060
[11] Atanassov, K. T.; Stoeva, S.; Trappl, R. (ed.), Intuitionistic L-fuzzy sets, 539-540, (1984), Amsterdam
[12] Baccelli B., Cohen G., Olsder G.-J., & Quadrat J.-P. (1992) Synchronization and linearity: An algebra for discrete event systems. John Wiely, Chichester, New York · Zbl 0824.93003
[13] Baczyński, M., Contrapositive symmetry of distributive fuzzy implications, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 10, 135-147, (2002) · Zbl 1057.39023
[14] Baczyński, M.; Jayaram, B., On the characterizations of \((S, N)\)-implications, Fuzzy Sets and Systems, 158, 1713-1727, (2007) · Zbl 1122.03021
[15] Baczyński, M.; Jayaram, B.\(, (S, N)\)- and R-implications: A state-of-the-art survey, Fuzzy Sets and Systems, 159, 1836-1859, (2008) · Zbl 1175.03013
[16] Bandler, W., & Kohout, L. (1980a). Fuzzy relational products as a tool for analysis and synthesis of the behavior of complex natural and artificial systems. In P. Wang & S. Chang (Eds.), Fuzzy sets: Theory and application to policy analysis and information systems (pp. 341-367). Plenum Press.
[17] Bandler, W.; Kohout, L., Semantics of implication operators and fuzzy relational products, International Journal of Man-Machine Studies, 12, 89-116, (1980) · Zbl 0435.68042
[18] Birkhoff, G. (1967). Lattice theory (3rd ed.). American Mathematical Society.
[19] Blyth T.S., Janowitz M.F. (1972) Residuation theory. Pergamon Press, Oxford · Zbl 0301.06001
[20] Bour, L.; Hirsch, G.; Lamotte, M., Opérateur de minimalisation pour la resolution d’équations de relation floue avec la composition inf-conorme, BUSEFAL, 28, 68-77, (1986) · Zbl 0625.04008
[21] Bour, L.; Lamotte, M., Solutions minimales d’équations de relations floues avec la composition max \(t\)-norme, BUSEFAL, 31, 24-31, (1987) · Zbl 0633.04002
[22] Bour, L.; Lamotte, M., Equations de relation floue avec la composition conorme-norme triangulaires, BUSEFAL, 34, 86-94, (1988) · Zbl 0664.04003
[23] Bour, L.; Lamotte, M., Convex combinations of generalized fuzzy relational equations, Fuzzy Sets and Systems, 86, 79-91, (1997) · Zbl 0914.04001
[24] Bourke, M. M.; Fisher, D. G., Convergence, eigen fuzzy sets and stability analysis of relational matrices, Fuzzy Sets and Systems, 81, 227-234, (1996) · Zbl 0885.93038
[25] Buckley, J. J.; Qu, Y., Solving linear and quadratic fuzzy equations, Fuzzy Sets and Systems, 38, 43-59, (1990) · Zbl 0713.04004
[26] Buckley, J. J.; Qu, Y., Solving systems of linear fuzzy equations, Fuzzy Sets and Systems, 43, 33-43, (1991) · Zbl 0741.65023
[27] Buckley, J. J.; Feuring, T.; Hayashi, Y., Solving fuzzy equations using evolutionary algorithms and neural nets, Soft Computing, 6, 116-123, (2002) · Zbl 1001.68102
[28] Bustince, H.; Burillo, P., Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems, 78, 293-303, (1996) · Zbl 0875.04006
[29] Butkovič, P., Strong regularity of matrices—a survey of results, Discrete Applied Mathematics, 48, 45-68, (1994) · Zbl 0804.06017
[30] Butkovič, P., Max-algebra: The linear algebra of combinatorics, Linear Algebra and Its Applications, 367, 313-335, (2003) · Zbl 1022.15017
[31] Butkovič, P.; Cechlárova, K.; & Szabó, P., Strong linear independence in bottleneck algebra, Linear Algebra and Its Applications, 94, 133-155, (1987) · Zbl 0629.90093
[32] Butkovič, P.; Hevery, F., A condition for the strong regularity of matrices in the minimax algebra, Discrete Applied Mathematics, 11, 209-222, (1985) · Zbl 0602.90136
[33] Cao, Z. Q.; Gupta, M. M. (ed.); Sanchez, E. (ed.), The eigen fuzzy sets of a fuzzy matrix, 61-63, (1982), Amsterdam
[34] Cechlárová, K., Strong regularity of matrices in a discrete bottleneck algebra, Linear Algebra and Its Applications, 128, 35-50, (1990) · Zbl 0704.15003
[35] Cechlárová, K., Unique solvability of max-min fuzzy equations and strong regularity of matrices over fuzzy algebra, Fuzzy Sets and Systems, 75, 165-177, (1995) · Zbl 0852.15011
[36] Cechlárová, K. (2001). Solutions of interval linear systems in max-plus algebra. In Proceedings of the 6th international symposium on operational research in Slovenia, Preddvor, Slovenia, pp. 321-326.
[37] Cechlárová, K.; Cuninghame-Green, R. A., Interval systems of max-separable linear equations, Linear Algebra and its Applications, 340, 215-224, (2002) · Zbl 1004.15009
[38] Cechlárová, K.; Kolesár, K., Strong regularity of matrices in a discrete bounded bottleneck algebra, Linear Algebra and Its Applications, 256, 141-152, (1997) · Zbl 0877.15018
[39] Cechlárová, K.; Plávka, J., Linear independence in bottleneck algebras, Fuzzy Sets and Systems, 77, 337-348, (1996) · Zbl 0877.15017
[40] Chen, L.; Wang, P. P., Fuzzy relation equations (I): The general and specialized solving algorithms, Soft Computing, 6, 428-435, (2002) · Zbl 1024.03520
[41] Cheng, L.; Peng, B., The fuzzy relation equation with union or intersection preserving operator, Fuzzy Sets and Systems, 25, 191-204, (1988) · Zbl 0651.04005
[42] Cornelis, C., Deschrijver, G., De Cock, M., & Kerre, E. E. (2002). Intuitionistic fuzzy relational calculus: An overview. In Proceedings of IS’2002. First international IEEE symposium intelligent systems (Vol. I, pp. 340-345).
[43] Crawley P., Dilworth R.P. (1973) Algebraic theory of lattices. Englewood Cliffs, NJ: Prentice-Hall · Zbl 0494.06001
[44] Cuninghame-Green R.A. (1979) Minimax algebra. Lecture notes in economics and mathematical systems (Vol. 166). Springer, Berlin
[45] Cuninghame-Green, R. A., Minimax algebra and applications, Fuzzy Sets and Systems, 41, 251-267, (1991) · Zbl 0739.90073
[46] Cuninghame-Green, R. A., Minimax algebra and applications, Advances in Imaging and Electron Physics, 90, 1-121, (1995)
[47] Cuninghame-Green, R. A.; Cechlárová, K., Residuation in fuzzy algebra and some applications, Fuzzy Sets and Systems, 71, 227-239, (1995) · Zbl 0845.04007
[48] Czogała, E.; Drewiak, J.; Pedrycz, W., Fuzzy relation equations on a finite set, Fuzzy Sets and Systems, 7, 89-101, (1982) · Zbl 0483.04001
[49] Davey B.A., Priestley H.A. (2002) Introduction to lattices and order (2nd ed). Cambridge University Press, Cambridge UK · Zbl 1002.06001
[50] Baets, B.; Ruan, D. (ed.), An order-theoretic approach to solving sup-\({\mathcal{T}}\) equations, 67-87, (1995), Dordrecht · Zbl 0874.04005
[51] De Baets B. (1995b) Oplossen van vaagrelationele vergelijkingen: een ordetheoretische benadering, Ph.D. University of Gent, Dissertation
[52] De Baets, B. (1995c). Residual operators of implicators. In H.-J. Zimmermann (Ed.), Proceedings of the third European congress on intelligent techniques and soft computing, Aachen, Germany (Vol. 1, ELITE, pp. 136-140).
[53] De Baets, B. (1995d). Model implicators and their characterization. In N. Steele (Ed.), Proceedings of the first ICSC international symposium on fuzzy logic (pp. A42-A49). ICSC Academic Press.
[54] De Baets, B. (1996). Disjunctive and conjunctive fuzzy modelling. In Proceedings of symposium on qualitative system modelling, qualitative fault diagnosis and fuzzy logic and control, Budapest and Balatonfüred, Hungary, pp. 63-70.
[55] Baets, B., Coimplicators, the forgotten connectives, Tatra Mountains Mathematical Publications, 12, 229-240, (1997) · Zbl 0954.03029
[56] Baets, B.; Kaynak, O. (ed.); et al. (ed.), Sup-\({\mathcal{T}}\) equations: State of the art, 80-93, (1998), Berlin
[57] Baets, B.; Dubois, D. (ed.); Prade, H. (ed.), Analytical solution methods for fuzzy relational equations, 291-340, (2000), Dordrecht · Zbl 0970.03044
[58] Baets, B.; Kerre, E., A primer on solving fuzzy relational equations on the unit interval, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2, 205-225, (1994) · Zbl 1232.03039
[59] Baets, B.; Kerre, E.; Trappl, R. (ed.), A representation of solution sets of fuzzy relational equations, 281-310, (1994), World Scientific Publishing, Singapore
[60] Cooman, G.; Kerre, E., Order norms on bounded partially ordered sets, Journal of Fuzzy Mathematics, 2, 281-310, (1994) · Zbl 0814.04005
[61] Demirli, K.; Baetes, B., Basic properties of implicators in a residual framework, Tatra Mountains Mathematical Publications, 16, 31-46, (1999) · Zbl 0949.03025
[62] Denecke, K., Erné, M., Wismath, S.L. (eds) (2004) Galois connections and applications. Kluwer, Dordrecht · Zbl 1050.06001
[63] Deschrijver, G.; Kerre, E., On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems, 133, 227-235, (2003) · Zbl 1013.03065
[64] Deschrijver, G.; Kerre, E., On the composition of intuitionistic fuzzy relations, Fuzzy Sets and Systems, 136, 333-361, (2003) · Zbl 1028.03047
[65] Deschrijver, G.; Cornelis, C.; Kerre, E., On the representation of intuitionistic fuzzy \(t\)-norms and \(t\)-conorms, IEEE Transactions on Fuzzy Systems, 12, 45-61, (2004) · Zbl 1230.03082
[66] Nola, A., On functionals measuring the fuzziness of solutions in relational equations, Fuzzy Sets and Systems, 14, 249-258, (1984) · Zbl 0559.04002
[67] Nola, A., An algorithm of calculation of lower solutions of fuzzy relation equation, Stochastica, 3, 33-40, (1984) · Zbl 0593.04005
[68] Nola, A., Relational equations in totally ordered lattices and their complete resolution, Journal of Mathematical Analysis and Applications, 107, 148-155, (1985) · Zbl 0588.04006
[69] Nola, A., On solving relational equations in Brouwerian lattices, Fuzzy Sets and Systems, 34, 365-376, (1990) · Zbl 0701.04003
[70] Nola, A.; Kołodziejczyk, W.; Sessa, S.; Bouchon-Meunier, B. (ed.); Yager, R. R. (ed.); Zadeh, L. A. (ed.), Transitive solutions of relational equations on finite sets and linear lattices, 173-182, (1991), Berlin
[71] Nola, A.; & Lettieri, A., Relation equations in residuated lattices, Rendiconti del Circolo Matematico di Palermo, 38, 246-256, (1989) · Zbl 0691.06002
[72] Nola, A.; Martini, G.; Sessa, S., Convergence of powers of a class of transitive matrices and related matrix equations, Simon Stevin, 66, 214-256, (1992) · Zbl 0785.15002
[73] Nola, A.; Pedrycz, W., Entropy and energy measure characterization of resolution of some fuzzy relational equations, BUSEFAL, 10, 44-53, (1982) · Zbl 0525.04002
[74] Nola, A.; Pedrycz, W.; Sessa, S., On solution of fuzzy relational equations and their characterization, BUSEFAL, 12, 60-71, (1982) · Zbl 0525.04003
[75] Nola, A.; Pedrycz, W.; Sessa, S., On measures of fuzziness of fuzzy relation equations with generalized connectives, Journal of Mathematical Analysis and Applications, 106, 443-453, (1985) · Zbl 0593.03011
[76] Nola, A.; Pedrycz, W.; Sessa, S., When is a fuzzy relation decomposable in two fuzzy sets?, Fuzzy Sets and Systems, 16, 87-90, (1985) · Zbl 0576.08001
[77] Nola, A.; Pedrycz, W.; Sessa, S.; Gupta, M. M. (ed.); etal., Fuzzy relation equations and algorithms of inference mechanism in expert systems, 355-367, (1985), Amsterdam
[78] Nola, A.; Pedrycz, W.; Sessa, S., Fuzzy relation equations under LSC and USC \(t\)-norms and their Boolean solutions, Stochastica, 11, 151-183, (1987) · Zbl 0673.04003
[79] Nola, A.; Pedrycz, W.; Sessa, S., Fuzzy relation equations with equality and difference composition operators, Fuzzy Sets and Systems, 25, 205-215, (1988) · Zbl 0645.04004
[80] Nola, A.; Pedrycz, W.; Sessa, S., Fuzzy relational structures: The state-of-art, Fuzzy Sets and Systems, 75, 241-262, (1995) · Zbl 0852.04008
[81] Nola, A.; Pedrycz, W.; Sessa, S.; Sanchez, E., Fuzzy relation equations theory as a basis of fuzzy modelling: An overview, Fuzzy Sets and Systems, 40, 415-429, (1991) · Zbl 0727.04005
[82] Nola, A.; Pedrycz, W.; Sessa, S.; Wang, P. Z., Fuzzy relation equations under triangular norms: A survey and new results, Stochastica, 8, 99-145, (1984) · Zbl 0581.04002
[83] Nola, A.; Sessa, S., On the set of solutions of composite fuzzy relation equations, Fuzzy Sets and Systems, 9, 275-286, (1983) · Zbl 0514.94027
[84] Nola, A.; Sessa, S., On the fuzziness of solutions of \(σ\)-fuzzy relation equations on finite spaces, Fuzzy Sets and Systems, 11, 65-77, (1983) · Zbl 0523.04002
[85] Di Nola, A., & Sessa, S. (1983c). On measures of fuzziness of solutions of composite fuzzy relation equations. In Proceedings of the fourth IFAC symposium, Marseille, France, pp. 277-281. · Zbl 0526.04003
[86] Nola, A.; Sessa, S.; Pedrycz, W., Decomposition problem of fuzzy relations, International Journal of General Systems, 10, 123-133, (1985) · Zbl 0559.04004
[87] Nola, A.; Sessa, S.; Pedrycz, W., On some finite fuzzy relation equations, Information Sciences, 50, 93-109, (1990) · Zbl 0688.90002
[88] Nola, A.; Sessa, S.; Pedrycz, W.; Higashi, M., Minimal and maximal solutions of a decomposition problem of fuzzy relations, International Journal of General Systems, 11, 103-116, (1985)
[89] Di Nola A., Sessa S., Pedrycz W., Sanchez E. (1989) Fuzzy relation equations and their applications to knowledge engineering. Kluwer, Dordrecht · Zbl 0694.94025
[90] Nola, A.; Ventre, A., On Booleanity of relational equation in Brouwerian lattices, Bollettino della Unione Matematica Italiana, Sezione B, 3, 871-882, (1984) · Zbl 0562.04003
[91] Drewniak, J., System of equations in a linear lattice, BUSEFAL, 15, 88-96, (1983) · Zbl 0523.04001
[92] Drewniak, J., Fuzzy relation equations and inequalities, Fuzzy Sets and Systems, 14, 237-247, (1984) · Zbl 0553.04003
[93] Drewniak J. (1989) Fuzzy relation calculus. Universitet Slaski, Katowice, Poland · Zbl 0701.04002
[94] Drewniak, J., Equations in classes of fuzzy relations, Fuzzy Sets and Systems, 75, 215-228, (1995) · Zbl 0856.04005
[95] Drewniak, J.; Sitek, A., Eigen subspace for fuzzy relation, BUSEFAL, 41, 41-48, (1989)
[96] Dubois, D.; Gottwald, S.; Hajek, P.; Kacprzyk, J.; Prade, H., Terminological difficulties in fuzzy set theory—The case of “Intuitionistic Fuzzy Sets”, Fuzzy Sets and Systems, 156, 485-491, (2005) · Zbl 1098.03061
[97] Dubois, D.; Hüllermeier, E.; Prade, H., A systematic approach to the assessment of fuzzy association rules, Data Mining and Knowledge Discovery, 13, 167-192, (2006)
[98] Dubois, D., Levrat, E., Lamotte, M., & Brémont, J. (1992). Solving a system of fuzzy relation equations by using a hierarchical process. In Proceedings of the IEEE international conference of fuzzy systems, San Diego, USA, pp. 679-686.
[99] Dubois, D.; Prade, H., Upper and lower images of a fuzzy set induced by a fuzzy relation: Applications to fuzzy inference and diagnosis, Information Sciences, 64, 203-232, (1992) · Zbl 0755.94026
[100] Fernández, M. J.; Suárez, F.; Gil, P., T-eigen fuzzy sets, Information Sciences, 75, 63-80, (1993) · Zbl 0803.04006
[101] Flondor, P.; Georgescu, G.; Iorgulescu, A., Pseudo-t-norms and pseudo-BL algebras, Soft Computing, 5, 355-371, (2001) · Zbl 0995.03048
[102] Fodor, J. C., On fuzzy implication operators, Fuzzy Sets and Systems, 42, 293-300, (1991) · Zbl 0736.03006
[103] Fodor, J. C., Strict preference relations based on weak \(t\)-norms, Fuzzy Sets and Systems, 43, 327-336, (1991) · Zbl 0756.90006
[104] Fodor, J. C., A new look at fuzzy connectives, Fuzzy Sets and Systems, 57, 141-148, (1993) · Zbl 0795.04008
[105] Fodor, J. C., Contrapositive symmetry of fuzzy implications, Fuzzy Sets and Systems, 69, 141-156, (1995) · Zbl 0845.03007
[106] Fodor, J. C.; Keresztfalvi, K., Nonstandard conjunctions and implications in fuzzy logic, International Journal of Approximate Reasoning, 12, 69-84, (1995) · Zbl 0815.03017
[107] García, J. G.; Rodabaugh, S. E., Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval valued “intuitionistic ” sets, “intuitionistic” fuzzy sets and topologies, Fuzzy Sets and Systems, 156, 445-484, (2005) · Zbl 1084.03042
[108] Gaubert S. (1998) Algèbres Max-Plus et applications en informatique et automatique, 26ème école de printemps d’informatique théorique. Noirmoutier, France
[109] Gavalec, M.; Plávka, J., Strong regularity of matrices in general max-min algebra, Linear Algebra and its Applications, 371, 241-254, (2003) · Zbl 1030.15016
[110] Ghodousian, A.; Khorram, E., Solving a linear programming problem with the convex combination of the max-min and the max-average fuzzy relation equations, Applied Mathematics and Computation, 180, 411-418, (2006) · Zbl 1102.90036
[111] Goetschel, R.; Voxman, W., Eigen fuzzy number sets, Fuzzy Sets and Systems, 16, 75-85, (1985) · Zbl 0581.04007
[112] Goguen, J. A., L-Fuzzy sets, Journal of Mathematical Analysis and Applications, 18, 145-174, (1967) · Zbl 0145.24404
[113] Gondran, M.; Minoux, M., L’indépendence linéaire dans les dioîdes, Bulletin de la Direction des Études et Recherches, Série C (Mathématiques, Informatique), 1, 67-90, (1978)
[114] Gondran, M.; Minoux, M., Linear algebra of dioids: A survey of recent results, Annals of Discrete Mathematics, 19, 147-164, (1984) · Zbl 0568.08001
[115] Gondran, M.; Minoux, M., Dioids and semirings: Links to fuzzy sets and other applications, Fuzzy Sets and Systems, 158, 1273-1294, (2007) · Zbl 1117.06010
[116] Gondran M., Minoux M. (2008) Graphs, dioids and semirings: New models and algorithms. Springer, New York · Zbl 1201.16038
[117] Gottwald, S., On the existence of solutions of systems of fuzzy equations, Fuzzy Sets and Systems, 12, 301-302, (1984) · Zbl 0556.04002
[118] Gottwald, S.; Wechsung, G. (ed.), T-normen und \({\phi} \)-operatoren als Wahrheitswertfunktionen mehrtiger junktoren, 121-128, (1984), Berlin
[119] Gottwald, S., Generalized solvability criteria for fuzzy equations, Fuzzy Sets and Systems, 17, 285-296, (1985) · Zbl 0607.03015
[120] Gottwald, S., Characterizations of the solvability of fuzzy equations, Elektron. Informationsverarb. Kybernet., 22, 67-91, (1986) · Zbl 0607.03016
[121] Gottwald S. (1993) fuzzy sets and fuzzy logic: The foundations of application-from a mathematical point of view. Wiesbaden, Vieweg · Zbl 0782.94025
[122] Gottwald, S., Approximately solving fuzzy relation equations: Some mathematical results and some heuristic proposals, Fuzzy Sets and Systems, 66, 175-193, (1994) · Zbl 0842.04010
[123] Gottwald, S.; Novák, V. (ed.); Perfilieva, I. (ed.), Generalized solvability behaviour for systems of fuzzy equations, 401-430, (2000), Heidelberg · Zbl 1006.03033
[124] Gottwald S. (2001) A treatise on many-valued logic, studies in logic and computation. Research Studies Press, Baldock
[125] Gottwald, S., Mathematical fuzzy control, A survey of some recent results. Logic Journal of the IGPL, 13, 525-541, (2005) · Zbl 1161.93319
[126] Gottwald, S.; Pedrycz, W.; Gupta, M. (ed.); Yamakawa, T. (ed.), On the methodology of solving fuzzy relational equations and its impact on fuzzy modelling, 197-210, (1988), Amsterdam
[127] Grzegorzewski, P.; Mrówka, E., Some notes on (Atanassov’s) intuitionistic fuzzy sets, Fuzzy Sets and Systems, 156, 492-495, (2005) · Zbl 1098.03062
[128] Guo, S. Z.; Wang, P. Z.; Nola, A.; Sessa, S., Further contributions to the study of finite fuzzy relation equations, Fuzzy Sets and Systems, 26, 93-104, (1988) · Zbl 0645.04003
[129] Han, S. C.; Li, H. X., Note 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, 289-294, (2005) · Zbl 1086.03019
[130] Han, S. C.; Li, H. X.; Wang, J. Y., Resolution of finite fuzzy relation equations based on strong pseudo-\(t\)-norms, Applied Mathematics Letters, 19, 752-757, (2006) · Zbl 1121.03075
[131] Han, S. C.; Li, H. X.; Wang, J. Y., Resolution of matrix equations over arbitrary Brouwerian lattices, Fuzzy Sets and Systems, 159, 40-46, (2008) · Zbl 1176.03032
[132] Higashi, M.; Klir, G. J., Resolution of finite fuzzy relation equations, Fuzzy Sets and Systems, 13, 65-82, (1984) · Zbl 0553.04006
[133] Imai, H.; Kikuchi, K.; Miyakoshi, M., Unattainable solutions of a fuzzy relation equation, Fuzzy Sets and Systems, 99, 193-196, (1998) · Zbl 0938.03081
[134] Imai, H.; Miyakoshi, M.; Da-Te, T., Some properties of minimal solutions for a fuzzy relation equation, Fuzzy Sets and Systems, 90, 335-340, (1997) · Zbl 0919.04008
[135] Izumi, K.; Hideo, T.; Asai, K., Adjointness of fuzzy systems, Fuzzy Sets and Systems, 20, 211-221, (1986) · Zbl 0633.03014
[136] Izumi, K.; Tanaka, H.; Asai, K., Resolution of composite fuzzy relational equations of type 2, Transaction of the Institute of Electronics and Communication Engineers of Japan, J66D, 1107-1113, (1983)
[137] Kahraman C. (2006) Fuzzy applications in industrial engineering. Springer, Berlin
[138] Karaçal, F.; Khadjiev, D., ∨-Distributive and infinitely ∨-distributive t-norms on complete lattices, Fuzzy Sets and Systems, 151, 341-352, (2005) · Zbl 1062.06007
[139] Kawaguchi, M. F., & Da-Te, T. (1993). A calculation method for solving fuzzy arithmetic equations with triangular norms. In Proceedings of the second IEEE international conference on fuzzy systems, San Francisco, USA (Vol. I, pp. 470-476).
[140] Kawaguchi, M. F., Da-Te, T., & Nonaka, H. (1994). A necessary condition for solvability of fuzzy arithmetic equations with triangular norms. In Proceedings of the Third IEEE international conference on fuzzy systems, Orlando, USA (Vol. II, pp. 1148-1152).
[141] Kawaguchi, M. F.; Miyakoshi, M., Composite fuzzy relational equations with non-commutative conjunctions, Information Sciences, 110, 113-125, (1998) · Zbl 0930.03074
[142] Kerre, E. E. (2007). An overview of fuzzy relational calculus and its applications. In V. Torra, Y. Narukawa, & Y. Yoshida (Eds.), Proceedings of the fourth international conference on modeling decisions for artificial intelligence, Kitakyushu, Japan. Lecture notes in artificial intelligence (Vol. 4617, pp. 1-13). · Zbl 1181.03054
[143] Kerre E.E., Nachtegael M. (2000) Fuzzy techniques in image processing: Techniques and applications. Physica-Verlag, Heidelberg · Zbl 0956.68152
[144] Khorram, E.; Ghodousian, A., Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Applied Mathematics and Computation, 173, 872-886, (2006) · Zbl 1091.65057
[145] Khorram, E.; Ghodousian, A.; Abbasi Molai, A., Solving linear optimization problems with max-star composition equation constraints, Applied Mathematics and Computation, 179, 654-661, (2006) · Zbl 1103.65067
[146] Kickert, W. J.M., Towards an analysis of linguistic modelling, Fuzzy Sets and Systems, 2, 293-307, (1979) · Zbl 0413.68089
[147] Kitainik, L. M., Cut technique in valued relational systems: Mainsprings and applications, Fuzzy Sets and Systems, 75, 143-164, (1995) · Zbl 0852.04010
[148] Klement, E.P., Mesiar, R. (eds) (2005) Logical, algebraic, analytic and probabilistic aspects of triangular norms. Elsevier, Amsterdam · Zbl 1063.03003
[149] Klement E.P., Mesiar R., Pap E. (2000) Triangular Norms. Kluwer, Dordrecht · Zbl 0972.03002
[150] Klir G.J., Folger T.A (1988) Fuzzy sets, uncertainty, and information. Prentice Hall, Englewood Cliffs, NJ · Zbl 0675.94025
[151] Klir G.J., Yuan B. (1995) Fuzzy sets and fuzzy logic: Theory and applications. Prentice Hall, Upper Saddle River, NJ · Zbl 0915.03001
[152] Kohout, L. J., Theory of fuzzy generalized morphisms and relational inequalities, International Journal of General Systems, 33, 339-360, (2004) · Zbl 1063.03042
[153] Kołodziejczyk, W., Orlovsky’s concept of decision-making with fuzzy preference relation—further results, Fuzzy Sets and Systems, 19, 11-20, (1986) · Zbl 0597.90004
[154] Kołodziejczyk, W., Canonical form of a strongly transitive fuzzy matrix, Fuzzy Sets and Systems, 22, 297-302, (1987) · Zbl 0623.15019
[155] Kołodziejczyk, W., Decomposition problem of fuzzy relation—further results, International Journal of General Systems, 14, 307-315, (1988) · Zbl 1200.03040
[156] Kołodziejczyk, W., To what extent does “decomposable” mean “transitive” for a fuzzy relation?, Fuzzy Sets and Systems, 32, 125-128, (1989) · Zbl 0673.04002
[157] Kołodziejczyk, W., On transitive solutions of \(σ\)-fuzzy relation equations describing fuzzy systems, International Journal of General Systems, 17, 277-288, (1990) · Zbl 0718.93038
[158] Kundu, S., The min-max composition rule and its superiority over the usual max-min composition rule, Fuzzy Sets and Systems, 93, 319-329, (1998) · Zbl 0927.03079
[159] Levrat, E., Dubois, G., Bombardier, V., & Lamotte, M. (1993) Generalisation of the resolution of a fuzzy relational equation. In Proceedings of the second IEEE conference on fuzzy systems, San Francisco, USA (Vol. 2, pp. 1414-1418).
[160] Li, G.; Fang, S.-C., Solving interval-valued fuzzy relation Equations, IEEE Transactions on Fuzzy Systems, 6, 321-324, (1998)
[161] Li, H. X.; Miao, Z. H.; Han, S. C.; Wang, J. Y., A new kind of fuzzy relation equations based on inner transformation, Computers and Mathematics with Applications, 50, 623-636, (2005) · Zbl 1085.03043
[162] Li, J.-X., A new algorithm for the greatest solution of fuzzy bilinear equations, Fuzzy Sets and Systems, 46, 193-210, (1992) · Zbl 0756.65067
[163] Li, P.; Fang, S.-C., On the resolution and optimization of a system of fuzzy relational equations with sup-\(T\) composition, Fuzzy Optimization and Decision Making, 7, 169-214, (2008) · Zbl 1169.90493
[164] Li, P., & Fang, S.-C. (2008b). A note on solution sets of interval-valued fuzzy relational equations. Fuzzy Optimization and Decision Making, 8. doi:10.1007/s10700-009-9055-4
[165] Li, Y.-M; Wang, X.-P., Necessary and sufficient conditions for existence of maximal solutions for inf-α composite fuzzy relational equations, Computers and Mathematics with Applications, 55, 1961-1973, (2008) · Zbl 1138.03322
[166] Ling, C.-H., Representation of associative functions, Publicationes Mathematicae Debrecen, 12, 189-212, (1965) · Zbl 0137.26401
[167] Luo, Y., Resolution of fuzzy relation equations (I) based on boolean-type implications, Computers and Mathematics with Applications, 52, 421-428, (2006) · Zbl 1136.03329
[168] Luo, Y.; Li, Y., Decomposition and resolution of min-implication fuzzy relation equations based on S-implication, Fuzzy Sets and Systems, 148, 305-317, (2004) · Zbl 1060.03077
[169] Luo, Y., Yang, C., Li, Y., & Pi, D. (2005). Decomposition and resolution of fuzzy relation equations (II) based on Boolean-type implication. In Proceedings of the 18th Australian joint conference on artificial intelligence, Sydney, Australia. Lecture notes in computer science (pp. 308-317). Berlin: Springer. · Zbl 1154.68468
[170] Mas, M.; Monserrat, M.; Torrens, J.; Trillas, E., A survey on fuzzy implication functions, IEEE Transactions on Fuzzy Systems, 15, 1107-1121, (2007)
[171] Mayor, G.; Torrens, J., On a class of operators for expert Systems, International Journal of Intelligent Systems, 8, 771-778, (1993) · Zbl 0785.68087
[172] Menger, K., Statistical metrics, Proceedings of the National Academy of Sciences of the United States of America, 28, 535-537, (1942) · Zbl 0063.03886
[173] Miyakoshi, M.; Shimbo, M., Solutions of composite fuzzy relational equations with triangular norms, Fuzzy Sets and Systems, 16, 53-63, (1985) · Zbl 0582.94031
[174] Mordeson J.N., Malik D.S. (2002) Fuzzy automata and languages: Theory and applications. Chapman & Hall/CRC, Boca Raton · Zbl 1046.68068
[175] Morsi, N. N.; Roshdy, E. M., Issues on adjointness in multiple-valued logics, Information Sciences, 176, 2886-2909, (2006) · Zbl 1107.03023
[176] Myšková, H., Interval systems of max-separable linear equations, Linear Algebra and its Applications, 403, 263-272, (2005) · Zbl 1077.15004
[177] Myšková, H., Control solvability of interval systems of max-separable linear equations, Linear Algebra and its Applications, 416, 215-223, (2006) · Zbl 1129.15003
[178] Nobuhara, H.; Bede, B.; Hirota, K., On various eigen fuzzy sets and their application to image reconstruction, Information Sciences, 176, 2988-3010, (2006) · Zbl 1102.68697
[179] Nobuhara, H., & Hirota, K. (2003a). Eigen fuzzy sets of various composition and their application to image analysis. In Proceedings of the seventh world multi conference on systemics, cybernetics and informatics SCI’2003, Orlando, USA, (CD Proceedings). · Zbl 1037.68786
[180] Nobuhara, H., & Hirota, K. (2003b). A solution for eigen fuzzy sets of adjoint max-min composition and its application to image analysis. In Proceedings of the IEEE international symposium on intelligent signal processing, WISP’2003, Budapest, Hungary, pp. 27-30.
[181] Nobuhara, H., Iyoda, E. M., Bede, B., & Hirota, K. (2004). A solution for generalized eigen fuzzy sets equations by genetic algorithms and its application to image analysis. In Proceedings of the second IEEE international conference on intelligent systems, Varna, Bulgaria, pp. 208-212.
[182] Nosková, L., Systems of fuzzy relation equation with inf-→ composition: Solvability and solutions, Journal of Electrical Engineering,, 12, 69-72, (2005) · Zbl 1106.68105
[183] Oh, K. W.; Kandel, A., Coimplication and its application to fuzzy expert systems, Information Sciences, 56, 59-73, (1991) · Zbl 0717.68091
[184] Oh, K. W.; Kandel, A., A general purpose fuzzy inference mechanism based on coimplication, Fuzzy Sets and Systems, 39, 247-260, (1991) · Zbl 0713.68092
[185] Ohsato, A., & Sekiguchi, T. (1983). Convexly combined form of fuzzy relational equations and its application to knowledge representation. In Proceedings of the international conference of systems, man and cybernetics, Bombay, 1983/84 (pp. 294-299). Bombay, New Delhi: IEEE India Council.
[186] Ohsato, A.; Sekiguchi, T., Convexly combined fuzzy relational equations and several aspects of their application to fuzzy information processing, Information Sciences, 45, 275-313, (1988) · Zbl 0664.68112
[187] Pedrycz, W. (1982a). Fuzzy control and fuzzy systems. Technical report 82 14, Department of Mathematics, Delft University of Technology. · Zbl 0506.93039
[188] Pedrycz, W., Fuzzy relational equations with triangular norms and their resolutions, BUSEFAL, 11, 24-32, (1982) · Zbl 0498.04004
[189] Pedrycz, W., Fuzzy relational equations with generalized connectives and their applications, Fuzzy Sets and Systems, 10, 185-201, (1983) · Zbl 0525.04004
[190] Pedrycz, W., On generalized fuzzy relational equations and their applications, Journal of Mathematical Analysis and Applications, 107, 520-536, (1985) · Zbl 0581.04003
[191] Pedrycz, W., Processing in relational structures: Fuzzy relational equations, Fuzzy Sets and Systems, 40, 77-106, (1991) · Zbl 0721.94030
[192] Pedrycz, W., s-t Fuzzy relational equations, Fuzzy Sets and Systems, 59, 189-195, (1993)
[193] Pedrycz, W., Fuzzy relational equations: Bridging theory, methodolody and practice, International Journal of General Systems, 29, 529-554, (2000) · Zbl 0965.03066
[194] Peeva, K., Fuzzy linear systems, Fuzzy Sets and Systems, 49, 339-355, (1992) · Zbl 0805.04005
[195] Peeva, K., Resolution of composite intuitionistic fuzzy relational equations, Notes on Intuitionistic Fuzzy Sets, 6, 15-24, (2000) · Zbl 1182.03096
[196] Peeva, K.; Cheshankov, B. (ed.); Todorov, M. (ed.), Min-max fuzzy linear systems of equations, 254-259, (2001), Sofia
[197] Peeva, K., Direct and inverse problem resolution in intuitionistic fuzzy relational calculus, Notes on Intuitionistic Fuzzy Sets, 8, 37-42, (2002) · Zbl 1230.03086
[198] Peeva K., Kyosev Y. (2004) Fuzzy relational calculus: Theory, applications and software. World Scientific, New Jersey · Zbl 1083.03048
[199] Perfiliva, I., Applications of the theory of fuzzy sets, Journal of Mathematical Sciences, 58, 148-194, (1992)
[200] Perfiliva, I.; Nosková, L., System of fuzzy relation equations with inf-→ composition: Complete set of solutions, Fuzzy Sets and Systems, 159, 2256-2271, (2008) · Zbl 1183.03053
[201] Portilla, M. I.; Burillo, P., Compositions of fuzzy relations based on aggregation operator and its pseudocomplement, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 8, 691-699, (2000) · Zbl 0989.03062
[202] Prade, H., Unions et intersections d’ensembles flous, BUSEFAL, 3, 58-62, (1980)
[203] Prévot, M., Algorithm for the solution of fuzzy relations, Fuzzy Sets and Systems, 5, 319-322, (1981) · Zbl 0451.04004
[204] Qu, X. B.; Wang, X. P., Some properties of infinite fuzzy relational equations on complete Brouwerian lattices, Fuzzy Sets and Systems, 158, 1327-1339, (2007) · Zbl 1120.03041
[205] Rudeanu S. (1974) Boolean functions and equations. North Holland, Amsterdam · Zbl 0321.06013
[206] Rudeanu S. (2001) Lattice functions and equations. Springer, London · Zbl 0984.06001
[207] Sanchez, E. (1974). Equations de relation floues, Thèse de Doctorat, Faculté de Médecine de Marseille.
[208] Sanchez, E., Resolution of composite fuzzy relation equation, Information and Control, 30, 38-48, (1976) · Zbl 0326.02048
[209] Sanchez, E.; Gupta, M. M. (ed.); Saridis, G. N. (ed.); Gaines, B. R. (ed.), Solutions in composite fuzzy relation equations: Application to medical diagnosis in Brouwerian logic, 221-234, (1977), Amsterdam
[210] Sanchez, E., Solution of eigen fuzzy sets equations, Fuzzy Sets and Systems, 1, 69-74, (1978) · Zbl 0366.04001
[211] Sanchez, E., Eigen fuzzy sets and fuzzy relations, Journal of Mathematical Analysis and Applications, 81, 399-421, (1981) · Zbl 0466.04003
[212] Sanchez, E., Solution of fuzzy equations with extended operations, Fuzzy Sets and Systems, 12, 237-248, (1984) · Zbl 0556.04001
[213] Sanchez, E., Truth-qualification and fuzzy relations in natural languages, application to medical diagnosis, Fuzzy Sets and Systems, 84, 155-167, (1996) · Zbl 0905.03010
[214] Sanchez, E.; Nikravesh, M. (ed.); Zadeh, L. A. (ed.); Korotkikh, V. (ed.), Decomposition of fuzzy relations and functional Relations, 251-266, (2004), Berlin · Zbl 1060.03078
[215] Sander, W.; Calvo, T. (ed.); Mayor, G. (ed.); Mesiar, R. (ed.), Associative aggregation operators, 124-158, (2002), Heidelberg · Zbl 1025.03054
[216] Sessa, S., Characterizing the Boolean solutions of relational equations in Brouwerian lattices, Bollettino della Unione Matematica Italiana, Sezione B, 5, 39-49, (1986) · Zbl 0599.06012
[217] Schweizer B., Sklar A. (1983) Probabilistic metric spaces. Amsterdam, North-Holland · Zbl 0546.60010
[218] Shi, Y.; Gassea, B.; Ruan, D.; Kerre, E. E., On the first place antitonicity in QL-implications, Fuzzy Sets and Systems, 159, 2988-3013, (2008) · Zbl 1178.03037
[219] Shieh, B.-S., Infinite fuzzy relation equations with continuous \(t\)-norms, Information Sciences, 178, 1961-1967, (2008) · Zbl 1135.03346
[220] Suárez García, F.; Gil Álvarez, P., Two families of fuzzy integrals, Fuzzy Sets and Systems, 18, 67-81, (1986) · Zbl 0595.28011
[221] Szczepaniak P.S., Lisboa P.J.G, Kacprzyk J. (2000) Fuzzy Systems in Medicine. Physica-Verlag, Heidelberg · Zbl 0934.00011
[222] Tang, F., Fuzzy bilinar equations, Fuzzy Sets and Systems, 28, 217-226, (1988) · Zbl 0664.15005
[223] Trillas, E., Sobre functions de negación en la teoría de conjuntas difusos, Stochastica, 3, 47-60, (1979)
[224] Trillas, E., & Valverde, L. (1981). On some functionally expressable implications for fuzzy set theory. In Proceedings of the 3rd international seminar on fuzzy set theory, Linz, Austria, pp. 173-190. · Zbl 0498.03015
[225] Trillas, E.; Valverde, L.; KacprzykJ. Yager, R. (ed.), On implication and indistinguishability in the setting of fuzzy logic, 198-212, (1985), Köln
[226] Vrba, J., General decomposition problem of fuzzy relations, Fuzzy Sets and Systems, 54, 69-79, (1993) · Zbl 0793.04008
[227] Wagenknecht, M., On transitive solutions of fuzzy equations, inequalities and lower approximations of fuzzy relations, Fuzzy Sets and Systems, 75, 229-240, (1995) · Zbl 0856.04007
[228] Wagenknecht, M.; Hartmann, K., On the construction of fuzzy eigen solutions in given regions, Fuzzy Sets and Systems, 20, 55-65, (1986) · Zbl 0602.15010
[229] Wagenknecht, M.; Hartmann, K., Fuzzy modelling with tolerances, Fuzzy Sets and Systems, 20, 325-332, (1986) · Zbl 0613.93003
[230] Wagenknecht, M.; Hartmann, K., On direct and inverse problems for fuzzy equation systems with tolerances, Fuzzy Sets and Systems, 24, 93-102, (1987) · Zbl 0633.04001
[231] Wagenknecht, M.; Hartmann, K., Application of fuzzy sets of type 2 to the solution of fuzzy equations systems, Fuzzy Sets and Systems, 25, 183-190, (1988) · Zbl 0651.04006
[232] Wagenknecht, M.; Hartmann, K., On the existence of minimal solutions for fuzzy equations with tolerances, Fuzzy Sets and Systems, 34, 237-244, (1990) · Zbl 0687.90094
[233] Walker, C. L.; Walker, E. A., The algebra of fuzzy truth values, Fuzzy Sets and Systems, 149, 309-347, (2005) · Zbl 1064.03020
[234] Wang, G. J.; He, Y. Y., Intuitionistic fuzzy sets and L-fuzzy sets, Fuzzy Sets and Systems, 110, 271-274, (2000) · Zbl 0944.03051
[235] Wang, H. F.; Chang, Y. C., Resolution of composite interval-valued fuzzy relation equations, Fuzzy Sets and Systems, 44, 227-240, (1991) · Zbl 0738.04003
[236] Wang, P. Z., & Meng, Y. (1980). Relation equations and relation inequalities. Selected papers on fuzzy subsets, Beijing Normal University, pp. 20-31.
[237] Wang, S.; Fang, S.-C.; Nuttle, H. L.W., Solution sets of interval-valued fuzzy relational equations, Fuzzy Optimization and Decision Making, 2, 41-60, (2003) · Zbl 1178.03071
[238] Wang, S.; Fang, S.-C.; Nuttle, H. L.W., Solution sets of interval-valued min-s-norm fuzzy relational equations, Fuzzy Optimization and Decision Making, 4, 331-349, (2005) · Zbl 1139.93020
[239] Wang, X. P., Method of solution to fuzzy relation equations in a complete Brouwerian lattice, Fuzzy Sets and Systems, 120, 409-414, (2001) · Zbl 0981.03055
[240] Wang, X. P., Infinite fuzzy relational equations on a complete Brouwerian lattice, Fuzzy Sets and Systems, 138, 657-666, (2003) · Zbl 1075.03026
[241] Wang, X. P.; Xiong, Q. Q., The solution set of a fuzzy relational equation with sup-conjunctor composition in a complete lattice, Fuzzy Sets and Systems, 153, 249-260, (2005) · Zbl 1073.03539
[242] Wang, Z.; Yu, Y., Pseudo-\(t\)-norms and implication operators on a complete Brouwerian lattice, Fuzzy Sets and Systems, 132, 113-124, (2002) · Zbl 1013.03020
[243] Wang, Z.; Yu, Y., Pseudo-\(t\)-norms and implication operators: Direct products and direct product decompositions, Fuzzy Sets and Systems, 139, 673-683, (2003) · Zbl 1032.03023
[244] Winter, M. (2007). Goguen categories: A categorical approach to L-fuzzy relations, Springer. · Zbl 1261.03154
[245] Wolter, F., On logics with coimplication, Journal of Philosophical Logic, 27, 353-387, (1998) · Zbl 0976.03020
[246] Wu, W., Fuzzy reasoning and fuzzy relational equations, Fuzzy Sets and Systems, 20, 67-78, (1986) · Zbl 0629.94031
[247] Wu, Y.-K., Optimization of fuzzy relational equations with max-av composition, Information Sciences, 177, 4216-4229, (2007) · Zbl 1140.90523
[248] Xiong, Q. Q.; Wang, X. P., Some properties of sup-min fuzzy relational equations on infinite domains, Fuzzy Sets and Systems, 151, 393-402, (2005) · Zbl 1062.03053
[249] Xiong, Q. Q.; Wang, X. P., Solution sets of inf-\({\alpha_{\mathcal{T}}}\) fuzzy relational equations on complete Brouwerian lattices, Information Sciences, 177, 4757-4767, (2007) · Zbl 1129.03032
[250] Yang, Y.; Wang, X. P., The general α-decomposition problem of fuzzy relations, Information Sciences, 117, 4922-4933, (2007) · Zbl 1131.03028
[251] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353, (1965) · Zbl 0139.24606
[252] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning—I, Information Sciences, 8, 199-249, (1975) · Zbl 0397.68071
[253] Zadeh L.A., Desoer C.A. (1963) Linear system theory. McGraw-Hill, New York · Zbl 1145.93303
[254] Zhang, K. L., On fuzzy bilinear equations, Fuzzy Sets and Systems, 76, 91-96, (1995) · Zbl 0860.15014
[255] Zhang, K. L.; Li, D. H.; Song, L. X., On finite relation equations with sup-conjunctor composition over a complete lattice, Fuzzy Sets and Systems, 160, 119-128, (2008) · Zbl 1183.03060
[256] Zhao, C. K., On matrix equations in a class of complete and completely distributive lattice, Fuzzy Sets and Systems, 22, 303-320, (1987) · Zbl 0621.06006
[257] Zhao, R.; Govind, R., Solutions of algebraic equations involving generalized fuzzy numbers, Information Sciences, 56, 199-243, (1991) · Zbl 0726.65048
[258] Zhu, J. S.; Cheng, R. Z., Some properties of fuzzy eigen set, BUSEFAL, 30, 51-57, (1987) · Zbl 0626.15012
[259] Zimmermann, K. (1976). Extremální Algebra (in Czech), Výzkumná Publikace Ekonomicko-Matematické Laboratoře při Ekonomickém Ústavě ČSAV, 46, Praha.
[260] Zimmermann, K., On max-separable optimization problems, Annals of Discrete Mathematics, 19, 357-362, (1984) · Zbl 0551.90098
[261] Zimmermann, K., Generalized fuzzy relational inequalities and related problems, International Journal of General Systems, 29, 637-644, (2000) · Zbl 0955.03063
[262] Zimmermann, K., Disjunctive optimization, max-separable problems and extremal algebras, Theoretical Computer Science, 293, 45-54, (2003) · Zbl 1031.90046
[263] Zimmermann, K.; Fiedler, M. (ed.); Nedoma, J. (ed.); Ramik, J. (ed.); Rohn, J. (ed.); Zimmermann, K. (ed.), Interval linear systems and optimization problems over max-algebras, 165-193, (2006), New York
[264] Zimmermann, K., A note on a paper by E, Khorram and A. Ghodousian. Applied Mathematics and Computation, 188, 244-245, (2007) · Zbl 1118.65066
[265] Zimmermann, U. (1981). Linear and combinatorial optimization in ordered algebraic structures. Annals of discrete mathematics (Vol. 10). Amsterdam: North-Holland.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.