An Algorithm for Solving Fuzzy Relation Programming with the Max-T Composition Operator

Year 2015, Volume: 5 Issue: 1, 21 - 29, 01.06.2015

A. A. Molai

Abstract

This paper studies the problem of minimizing a linear objective functionsubject to max-T fuzzy relation equation constraints where T is a special class of pseudot-norms. Some sufficient conditions are presented for determination of its optimal solutions. Some procedures are also suggested to simplify the original problem. Somesufficient conditions are given for uniqueness of its optimal solution. Finally, an algorithm is proposed to Şnd its optimal solution

Keywords

Fuzzy relation equations, Max-T composition, Maximum solution, Minimal solution, Fuzzy optimization, Optimal solution.

References

• Abbasi Molai, A. and Khorram, E., (2008), An algorithm for solving fuzzy relation equations with max-T composition operator, Inform. Sci., 178, pp. 1293-1308.
• Czogala, E. and Predrycz, W., (1981), On identiŞcation in fuzzy systems and its applications in control problems, Fuzz. Sets Syst., 6, pp. 73-83.
• Fang, S.C. and Li, G., (1999), Solving fuzzy relation equations with a linear objective function, Fuzz. Sets Syst., 103, pp. 107-113.
• Guu, S.M. and Wu, Y.K., (2002), Minimizing a linear objective function with fuzzy relation equation constraints, Fuzz. Optim. Decis. Mak., 1(4), pp. 347-360.
• Guu, S.M. and Wu, Y.K., (2010), Minimizing a linear objective function under a max-t-norm fuzzy relational equation constraint, Fuzz. Sets Syst., 161, pp. 285-297.
• Han, S.C. and Li, H.X., (2005), Notes on ”Pseudo-t-norms and implication operators on a complete
• Brouwerian lattice” and ”Pseudo-t-norms and implication operators: direct products and decomposi- tions”, Fuzz. Sets Syst., 153, pp. 289-294. Han, S.-C., Li, H.-X. and Wang, J.-Y., (2006), Resolution of Şnite fuzzy relation equations based on strong pseudo-t-norms, Appl. Math. Let., 19, pp. 752-757.
• Klir, G.J. and Folger, T.A., (1988), Fuzzy sets, uncertainty, and information, Prentice Hall, New Jersey.
• Loetamonphong, J. and Fang, S.C., (2001), Optimization of fuzzy relation equations with max-product composition, Fuzz. Sets Syst., 118, pp. 509-517.
• Loia, V. and Sessa, S., (2005), Fuzzy relation equations for coding/decoding processes of images and videos, Inform. Sci., 171, pp. 145-172.
• Pedrycz, W., (1985), On generalized fuzzy relational equations and their applications, J. Math. Anal. Appl., 107, pp. 520-536.
• Sanchez, E., (1976), Resolution of composite fuzzy relation equations, Inform. Contr., 30, pp. 38-48.
• Wang, Z.D. and Yu, Y.D., (2002), Pseudo-t-norms and implication operators on a complete Brouwe- rian lattice, Fuzz. Sets Syst., 132, pp. 113-124.
• Wang, Z.D. and Yu, Y.D., (2003), Pseudo-t-norms and implication operators: direct products and direct product decompositions, Fuzz. Sets Syst., 139, pp. 673-683.
• Wu, Y.K., Guu, S.M. and Liu, J.Y.C., (2002), An accelerated approach for solving fuzzy relation equations with a linear objective function, IEEE Trans. Fuzz. Syst., 10(4), pp. 552-558.
• Wu, Y.K. and Guu, S.M., (2005), Minimizing a linear function under a fuzzy max-min relational equation constraint, Fuzz. Sets Syst., 150, pp. 147-162.
• Wu, Y.K. and Guu, S.M., (2004), A note on fuzzy relation programming problems with max-stric-t- norm composition, Fuzz. Optim. Decis. Mak., 3(3), pp. 271-278
• Vasantha and http://mat.iitm.ac.in/ wbv/book13.htm. Smarandache, hexis rock relational and at: neutrosophic relational maps, church (see chapters one two)Ali Abbasi Molai for the photography and short autobiography, see TWMS J. App. Eng. Math., V.3, N.2.