On optimizing a linear objective function subjected to fuzzy relation inequalities

In this paper, we extend Guo and Xia’s necessary condition which has been presented by Guo and Xia (Fuzzy optimizat Decis Mak 5: 33–47, 2006) in order to study the finitely many constraints of fuzzy relation inequalities and optimize a linear objective function on this region which is defined by the fuzzy max–min operator. The new condition provides a means for removing the unnecessary paths resulting from Guo and Xia’s paths. Also, an algorithm and two numerical examples are offered to abbreviate and illustrate the steps of the resolution process of the problem.

[1]  Cheng-Feng Hu.  Generalized variational inequalities with fuzzy relation , 2002 .

[2]  Zun-Quan Xia,et al.  An Algorithm for Solving Optimization Problems with One Linear Objective Function and Finitely Many Constraints of Fuzzy Relation Inequalities , 2006, Fuzzy Optim. Decis. Mak..

[3]  W. Pedrycz.  Fuzzy relational equations with generalized connectives and their applications , 1983 .

[4]  D. Grant Fisher,et al.  Solution algorithms for fuzzy relational equations with max-product composition , 1998, Fuzzy Sets Syst..

[5]  Amin Ghodousian,et al.  Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition , 2006, Appl. Math. Comput..

[6]  Shu-Cherng Fang,et al.  Solving fuzzy relation equations with a linear objective function , 1999, Fuzzy Sets Syst..

[7]  S. Han,et al.  Fuzzy inequality relation system identification via sign matrix method , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[8]  A. Nola,et al.  Further contributions to the study of finite fuzzy relations equations , 1988 .

[9]  M. Gupta,et al.  Design of fuzzy logic controllers based on generalized T -operators , 1991 .

[10]  W. Pedrycz,et al.  Fuzzy Relation Equations and Their Applications to Knowledge Engineering , 1989, Theory and Decision Library.

[11]  W. Pedrycz,et al.  Control problems in fuzzy systems , 1982 .

[12]  Shu-Cherng Fang,et al.  Linear Optimization and Extensions: Theory and Algorithms , 1993 .

[13]  Shu-Cherng Fang,et al.  Solving nonlinear optimization problems with fuzzy relation equation constraints , 2001, Fuzzy Sets Syst..

[14]  H. T. Zhang,et al.  PROGRAMMING PROBLEM WITH FUZZY RELATION INEQUALITY CONSTRAINTS , 2003 .

[15]  Jiranut Loetamonphong,et al.  Optimization of fuzzy relation equations with max-product composition , 2001, Fuzzy Sets Syst..

[16]  W. Pedrycz,et al.  Fuzzy relation equations on a finite set , 1982 .

[17]  W. Pedrycz.  ON GENERALIZED FUZZY RELATIONAL EQUATIONS AND THEIR APPLICATIONS , 1985 .

[18]  G. Klir,et al.  Resolution of finite fuzzy relation equations , 1984 .

[19]  Pei-Zhuang Wang,et al.  Latticized linear programming and fuzzy relation inequalities , 1991 .

[20]  Klaus-Peter Adlassnig,et al.  Fuzzy Set Theory in Medical Diagnosis , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  M. Prévot.  Algorithm for the solution of fuzzy relations , 1981 .

[22]  Yan-Kuen Wu,et al.  Minimizing a Linear Objective Function with Fuzzy Relation Equation Constraints , 2002, Fuzzy Optim. Decis. Mak..

[23]  P. Wang.  HOW MANY LOWER SOLUTIONS OF FINITE FUZZY RELATION EQUATIONS , 1984 .

[24]  W. Pedrycz.  Processing in relational structures: fuzzy relational equations , 1991 .

[25]  W Pedrycz,et al.  ON IDENTIFICATION IN FUZZY SYSTEMS AND ITS APPLICATIONS IN CONTROL PROBLEM, FUZZY SETS AND SYSTEMS , 1981 .

[26]  Elie Sanchez,et al.  Resolution of Composite Fuzzy Relation Equations , 1976, Inf. Control..

[27]  Jiranut Loetamonphong,et al.  Multi-objective optimization problems with fuzzy relation equation constraints , 2002, Fuzzy Sets Syst..

[28]  A. Nola.  Relational equations in totally ordered lattices and their complete resolution , 1985 .