Abstract
This note discusses three types of solutions for a system of interval-valued fuzzy relational equations with max-T composition and illustrates their relations to the solutions of a system of fuzzy relational inequalities with max-T composition. It validates the major claims appeared in Fuzzy Optimization and Decision Making, 2 (2003) 41–60; 4 (2005) 331–349.
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References
De Baets B. (2000) Analytical solution methods for fuzzy relational equations. In: Dubois D., Prade H. (eds) Fundamentals of fuzzy sets, The handbooks of fuzzy sets series, (Vol. 1). Kluwer, Dordrecht, pp 291–340
Klement E.P., Mesiar R., Pap E. (2000) Triangular norms. Kluwer, Dordrecht
Klir, G., & Yuan, B. (1995). Fuzzy sets and fuzzy logic: Theory and applications. Upper Saddle River, NJ: Prentice Hall.
Kreinovich V., Lakeyev A., Rohn J., Kahl P. (1998) Computational complexity and feasibility of data processing and interval computations. Kluwer, Dordrecht
Li G., Fang S.-C. (1998) Solving interval-valued fuzzy relation equations. IEEE Transactions on Fuzzy Systems 6: 321–324
Li P., Fang S.-C. (2008) On the resolution and optimization of a system of fuzzy relational equations with sup-T composition. Fuzzy Optimization and Decision Making 7: 169–214
Peeva K., Kyosev Y. (2004) Fuzzy relational calculus: Theory, applications and software. World Scientific, New Jersey
Sanchez E. (1976) Resolution of composite fuzzy relation equation. Information and Control 30: 38–48
Sanchez E. (1977) Solutions in composite fuzzy relation equations: Application to medical diagnosis in Brouwerian logic. In: Gupta M.M., Saridis G.N., Gaines B.R. (eds) Fuzzy automata and decision processes. North-Holland, Amsterdam, pp 221–234
Wang H.-F., Chang Y.-C. (1991) Resolution of composite interval-valued fuzzy relation equations. Fuzzy Sets and Systems 44: 227–240
Wang P.Z., Zhang D.Z., Sanchez E., Lee E.S. (1991) Latticized linear programming and fuzzy relation inequalities. Journal of Mathematical Analysis and Applications 159: 72–87
Wang S., Fang S.-C., Nuttle H.L.W. (2003) Solution sets of interval-valued fuzzy relational equations. Fuzzy Optimization and Decision Making 2: 41–60
Wang S., Fang S.-C., Nuttle H. L. W. (2005) Solution sets of interval-valued min-s-norm fuzzy relational equations. Fuzzy Optimization and Decision Making 4: 331–349
Wang S., Fang S.-C., Nuttle H.L.W. (2007) Errata. Fuzzy Optimization and Decision Making 6: 297
Zimmermann K. (2000) Generalized fuzzy relational inequalities and related problems. International Journal of General Systems 29: 637–644
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Li, P., Fang, SC. A note on solution sets of interval-valued fuzzy relational equations. Fuzzy Optim Decis Making 8, 115–121 (2009). https://doi.org/10.1007/s10700-009-9055-4
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DOI: https://doi.org/10.1007/s10700-009-9055-4