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Solving fuzzy relation equations with a linear objective function. (English) Zbl 0933.90069
Summary: An optimization model with a linear objective function subject to a system of fuzzy relation equations is presented. Due to the non-convexity of its feasible domain defined by fuzzy relation equations, designing an efficient solution procedure for solving such problems is not a trivial job. In this paper, we first characterize the feasible domain and then convert the problem to an equivalent problem involving 0-1 integer programming with a branch-and-bound solution technique. After presenting our solution procedure, a concrete example is included for illustration purpose.

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
90C09 Boolean programming
Full Text: DOI
[1] Adamopoulos, G.I.; Pappis, C.P., Some results on the resolution of fuzzy relation equations, Fuzzy sets and systems, 60, 83-88, (1993) · Zbl 0794.04005
[2] Adlassnig, K.P., Fuzzy set theory in medical diagnosis, IEEE trans. systems man cybernet., 16, 260-265, (1986)
[3] Czogala, E.; Drewniak, J.; Pedrycz, W., Fuzzy relation equations on a finite set, Fuzzy sets and systems, 7, 89-101, (1982) · Zbl 0483.04001
[4] Di Nola, A., Relational equations in totally ordered lattices and their complete resolution, J. math. appl., 107, 148-155, (1985) · Zbl 0588.04006
[5] Fang, S.-C.; Puthenpura, S., Linear optimization and extensions: theory and algorithm, (1993), Prentice-Hall Englewood Cliffs, NJ
[6] Guo, S.Z.; Wang, P.Z.; Di 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
[7] Higashi, M.; Klir, G.J., Resolution of finite fuzzy relation equations, Fuzzy sets and systems, 13, 65-82, (1984) · Zbl 0553.04006
[8] Li, G.; Fang, S.-C., On the resolution of finite fuzzy relation equations, ()
[9] Prevot, M., Algorithm for the solution of fuzzy relations equations, Fuzzy sets and systems, 5, 319-322, (1985) · Zbl 0451.04004
[10] Sanchez, E., Resolution of composite fuzzy relation equations, Inform. and control, 30, 38-48, (1976) · Zbl 0326.02048
[11] Wang, H.-F., An algorithm for solving iterated composite relation equations, (), 242-249
[12] Wang, P.Z.; Sessa, S.; Di Nola, A.; Pedrycz, W., How many lower solutions does a fuzzy relation equation have?, Bull. pour. sous. ens. flous. appl. (BUSEFAL), 18, 67-74, (1984) · Zbl 0581.04001
[13] Winston, W.L., Introduction to mathematical programming: application and algorithms, (1995), Duxbury Press Belmont, CA · Zbl 0837.90086
[14] Zimmermann, H.-J., Fuzzy set theory and its applications, (1991), Kluwer Academic Publishers Boston/Dordrecht/London · Zbl 0719.04002
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