Linear Objective Function Optimization with the Max-product Fuzzy Relation Inequality Constraints

bibitem{AdPa:Srrfre}
G. I. Adamopoulos and C. P. Pappis, {it Some results on the resolution of fuzzy relation equations}, Fuzzy Sets and Systems, {bf 60} (1993), 83--88.
bibitem{Ad:Fstmd}
 K. P. Adlassnig, {it Fuzzy set theory in medical diagnosis}, IEEE Trans. Systems Man Cybernet., {bf 16} (1986), 260--265.
bibitem{BoFi:Safremc}
 M. M. Bourke and D. G. Fisher, {it Solution algorithms for fuzzy relational equations with max-product composition}, Fuzzy Sets and Systems, {bf 94} (1998), 61--69.
bibitem{CzDrPe:Frefs}
 E. Czogala, J. Drewniak and W. Pedrycz, {it Fuzzy relation equations on a finite set}, Fuzzy Sets and Systems, {bf 7} (1982), 89--101.
bibitem{CzPe:Ifsacp}
 E. Czogala and W. Pedrycz, {it On Identification in Fuzzy Systems and its applications in control problem}, Fuzzy Sets and Systems, {bf 6} (1981), 73--83.
bibitem{Di:Retolcr}
 A. Di Nola, {it Relational equations in totally ordered lattices and their complete resolution}, J. Math. Anal. Appl., {bf 107} (1985), 148--155.
bibitem{DuPr:Nrpsfso}
 D. Dubois and H. Prade, {it New results about properties and semantics of fuzzy set-theoretic operators}, In: P. P.Wang, S. K. Chang, eds., Fuzzy Sets, Plenum Press, New York, (1986), 59--75.
bibitem{FaLi:Sfrelof}
 S. C. Fang and G. Li, {it Solving fuzzy relation equations with a linear objective function}, Fuzzy Sets and Systems, {bf 103} (1999), 107--113.
bibitem{GuWaDiSe:Fcsffre}
 S. Z. Guo, P. Z. Wang, A. Di Nola and S. Sessa, {it Further contributions to the study of finite fuzzy relation equations}, Fuzzy Sets and Systems, {bf 26} (1988), 93--104.
bibitem{GuXi:Asoploffmcfri}
 F. F. Guo and Z. Q. Xia, {it An algorithm for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities}, Fuzzy optim. Decis. Making, {bf 5} (2006), 33--47.
bibitem{GuWu:Mloffrec}
 S. M. Guu and Y. K. Wu, {it Minimizing a linear objective function with fuzzy relation equation constraints}, Fuzzy Optim. Decis. Making, {bf 12} (2002), 1568--4539.
bibitem{HaSoSe:Firsismm}
 S. Z. Han, A. H. Song and T. Sekiguchi, {it Fuzzy inequality relation system identification via sign matrix method}, Proceeding of 1995 IEEE International Conference 3, (1995), 1375--1382.
bibitem{HiKl:Rffre}
 M. Higashi and G. J. Klir, {it Resolution of finite fuzzy relation equations}, Fuzzy Sets and Systems, {bf 13} (1984), 65--82.

bibitem{Ho:Opdl}
 M. Hosseinyazdi, {it The optimization problem over a distributive lattice}, J. Glob. Optim., {bf 41} (2008), 283--298.
bibitem{Hu:Gvifr}
 C. F. Hu, {it Generalized variational inequalities with fuzzy relation}, J. Comput. Appl. Math., {bf 146} (1998), 198--203.
bibitem{KaSm:Frmnrm}
 W. B. V. Kandasamy and F. Smarandache, {it Fuzzy relational maps and neutrosophic relational maps}, hexis church rock, 2004.

bibitem{LiFa:Rosfresc}
 P. Li and S. C. Fang, {it On the resolution and optimization of a system of fuzzy relational equations with sup-T composition}, Fuzzy Optim. Decis. Making, {bf 7} (2008), 169--214.
bibitem{LiFa:Rffre}
 G. Li and S. C. Fang, {it On the resolution of finite fuzzy relation equations}, OR Report No. 322, North Carolina State University, Raleigh, North Carolina, May 1996.
bibitem{LoFa:Ofremc}
 J. Loetamonphong and S. C. Fang, {it Optimization of fuzzy relation equations with max-product composition}, Fuzzy Sets and Systems, {bf 118}  (2001), 509--517.
bibitem{LoFaYo:Mopfrec}
 J. Loetamonphong, S. C. Fang and R. E. Young, {it Multi-objective optimization problems with Fuzzy Relation Equation constraints}, Fuzzy Sets and Systems, {bf 127} (2002), 141--164.
bibitem{Pe:Prsfre}
 W. Pedrycz, {it Proceeding in relational structures: fuzzy relational equations}, Fuzzy Sets and Systems, {bf40} (1991), 77--106.
bibitem{PeKy:Frctas}
 K. Peeva and Y. Kyosev, {it Fuzzy relational calculus: theory, applications and software}, World Scientific, New Jersey, 2004.
bibitem{Pr:Asfr}
 M. Prevot, {it Algorithm for the solution of fuzzy relations}, Fuzzy Sets and Systems, {bf 5} (1981), 319--322.
bibitem{Sa:Rcfre}
E. Sanchez, {it Resolution of composite fuzzy relation equations}, Information and Control, {bf 30} (1976), 38--48.

bibitem{ThZiZy:Smpoi}
 U. Thole, H. J. Zimmermann and P. Zysno, {it On the suitability of minimum and product operators for intersection of fuzzy sets}, Fuzzy Sets and Systems, {bf 2} (1979), 167--180.
bibitem{Wa:Hmlsffre}
 P. Z. Wang, {it How many lower solutions of finite fuzzy relation equations}, Fuzzy Mathematics (Chinese), {bf 4} (1984), 67--73.
bibitem{WaZhSaLe:Llpfri}
 P. Z. Wang, D. Z. Zhang, E. Sanchez and E. S. Lee, {it Lattecized linear programming and fuzzy relation inequities}, J. Math. Anal. Appl., {bf 159} (1991), 72--87.
bibitem{ZhDoRe:Ppfric}
 H. T. Zhang, H. M. Dong and R. H. Ren, {it Programming problem with fuzzy relation inequality constraints}, J. Liaon. Nor. Univ., {bf 3} (2003), 231--233.
bibitem{ZiZy:Lchd}
 H. J. Zimmermann and P. Zysno, {it Latent connectives in human decision-making}, Fuzzy Sets and Systems, {bf 4} (1980), 37--51.