linear objective function optimization with fuzzy relation equation constraints regarding max av composition in this paper an optimization model with a linear objective function subject to a system of the fuzzy relation equations with max av composition is presented the solution set of such a fuzzy relation equations is a non convex set in this paper firstly we discuss the feasible solution set with two schemes and secondly study relationship between maximum and minimum points and also the feasible points as well furthermore an algorithm and few concrete examples are presented in order to optimize linear objective function

linear optimization with an arbitrary fuzzy relational inequality in this paper optimization of a linear objective function with fuzzy relational inequality constraints is investigated whereby an arbitrary function is considered as fuzzy composition the feasible solution set is determined and compared with some common results in the literature a necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem it is shown that in general a lower bound is always attainable for the optimal objective value moreover we prove that the optimal solution of the problem is obtained if the problem is defined by a non decreasing or non increasing function an algorithm is presented to summarize the process and an example is described to illustrate the algorithm

some results on the resolution of fuzzy relation equations abstract in this paper two special cases of the solution of the inverse problem are investigated the necessary and sufficient conditions for the existence of a solution such that the upper bound is the unit vector and for a unique solution of the inverse problem equal to the unit vector are presented an algorithmic approach which derives the output vector and the state matrix in each one of these cases is also proposed

multi objective optimization with a max t norm fuzzy relational equation constraint in this paper we consider minimizing multiple linear objective functions under a max t norm fuzzy relational equation constraint since the feasible domain of a max archimedean t norm relational equation constraint is generally nonconvex traditional mathematical programming techniques may have difficulty in yielding efficient solutions for such problems in this paper we apply the two phase approach utilizing the min operator and the average operator to aggregate those objectives to yield an efficient solution a numerical example is provided to illustrate the procedure

relational equations in totally ordered lattices and their complete resolution abstract the set of all solutions of a composite fuzzy relation equation of sanchez inform and control 30 1976 defined on finite spaces is studied by determining and characterizing all the lower solutions of such an equation

an algorithm for solving optimization problems with fuzzy relational inequality constraints an algorithm for solving a kind of optimization problems with fuzzy relational inequalities was proposed by guo and xia 6 however it is too expensive to verify the optimal condition in this paper some rules for reducing these problems are proposed and the relationship between minimal solutions and fri paths is also given these lead to a new algorithm for solving this kind of problems numerical experiments are presented for illustrating the efficiency of the proposed algorithm

virtual element method for fourth order problems l 2 estimates abstract we analyse the family of c 1 virtual elements introduced in brezzi and marini 2013 for fourth order problems and prove optimal estimates in l 2 and in h 1 via classical duality arguments

minimizing a linear objective function under a fuzzy max t norm relation equation constraint the work examines the feasibility of minimizing a linear objective function subject to a max t fuzzy relation equation constraint where t is a continuous archimedean t norm conventional methods for solving this problem are significantly improved by first separating the problem into two sub problems according to the availability of positive coefficients this decomposition is thus more easily handled than in previous literature next based on use of the maximum solution of the constraint equation the sub problem with non positive coefficients is solved and the size of the sub problem with positive coefficients reduced as well this step is unique among conventional methods owing to its ability to determine as many optimal variables as possible additionally several rules are developed for simplifying the remaining problem finally those undecided optimal variables are obtained using the covering problem rather than the branch and bound methods three illustrative examples demonstrate that the proposed approach outperforms conventional schemes its potential applications are discussed as well

solving fuzzy relation equations with a linear objective function abstract 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

optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined by dubois prade family of t norms abstract in this paper optimization of a linear objective function with fuzzy relational inequality constraints is investigated in doing so the feasible region is formed by the intersection of two inequality fuzzy systems and dubois prade family of t norms which are considered as fuzzy composition the most well known continuous t norms are archimedean such as frank yager hamacher sugeno weber and schweizer sklar family an interesting family of t norms that is not archimedean has been introduced by dubois and prade in this paper the resolution of the feasible region of the problem is initialy investigated when it is defined with max duboise prade composition a necessary and sufficient condition along with three other necessary conditions are derived for determining the feasibility of the problem moreover two procedures have also been presented with the aim of simplifying the current linear problems a method is proposed to generate random feasible max dubois prade fuzzy relational inequalities and an algorithm is accordingly presented to solve the problem finally an example is described to illustrate this algorithm

optimization of fuzzy relation equations with max product composition abstract an optimization problem with a linear objective function subject to a system of fuzzy relation equations using max product composition is considered since the feasible domain is non convex traditional linear programming methods cannot be applied we study this problem and capture some special characteristics of its feasible domain and the optimal solutions some procedures for reducing the original problem are presented the problem is transformed into a 0 1 integer program which is then solved by the branch and bound method for illustration purpose an example of the procedures is provided

latticized linear optimization on the unit interval this paper considers the latticized linear optimization llo problem and its variants which are a special class of optimization problems constrained by fuzzy relational equations or inequalities we show that an optimal solution to such a problem can be obtained in polynomial time as long as the objective function is a max separable function with continuous monotone components we further show that the set of all optimal solutions is fully determined by one maximum optimal solution and a finite number of minimal optimal solutions the maximum optimal solution can be constructed in polynomial time once the optimal objective value is known while the detection of all minimal optimal solutions in an efficient manner remains as a challenging problem the relation between llo and max separable optimization and related issues are also investigated

resolution of finite fuzzy relation equations abstract general schemes for solving fuzzy relation equations with finite sets are derived in this paper the relationship between the results derived here and those of previous publications regarding this subject is also discussed

normal linearization and transition map near a saddle connection with symmetric resonances abstract we consider a heteroclinic connection in a planar system between two symmetric hyperbolic saddles of which the eigenvalues are resonant starting with a c normal form defined globally near the connection we normally linearize the vector field by using finitely smooth tags of logarithmic form we furthermore define an asymptotic entry exit relation and we discuss on two examples how to deal with counting limit cycles near a limit periodic set involving such a connection

a fixed charge model with fuzzy inequality constraints composed by max product operator abstract a fixed charge model subject to a system of fuzzy relation inequalities with max product composite operator is presented the feasible domain of the model is first investiged of which the necessary and sufficient condition is proposed if it is infeasible a minimum calibration procedure is provided to have at least one solution due to the nonconvexity of its feasible domain a solution procedure is designed to have a minimum objective value of which the initial cost is considered an illustrative example is presented

further contributions to the study of finite fuzzy relations equations abstract an interesting property of the schein rank of a fuzzy matrix stressed by k h kim and f w roush is formalized as definition of the basis of a set of fuzzy vectors defined over a commutative semiring with respect to another set of fuzzy vectors we apply this definition and another related concept in the setting of finite fuzzy relation equations in particular we give a sufficient condition for the existence of the smallest solution of a max min fuzzy equation

a modified algorithm for solving the proposed models by ghodousian and khorram and khorram and ghodousian abstract in this paper we focus on the proposed algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition that it has been proposed by ghodousian and khorram a ghodousian e khorram an algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition appl math comput 178 2006 502 509 firstly we show that the algorithm may not lead to the optimal solution in some cases secondly we propose a new algorithm for solving the presented model by ghodousian and khorram 2006 as mentioned above in fact it modifies the presented algorithm in the ghodousian and khorram s paper also this algorithm is extended to the presented model by khorram and ghodousian e khorram a ghodousian linear objective function optimization with fuzzy relation equation constraints regarding max av composition appl math comput 173 2006 872 886 with max av composition finally some numerical examples are given for illustrating the purposes

solving nonlinear optimization problems with fuzzy relation equation constraints abstract an optimization model with a nonlinear objective function subject to a system of fuzzy relation equations is presented since the solution set of the fuzzy relation equations is in general a non convex set when it is not empty conventional nonlinear programming methods are not ideal for solving such a problem in this paper a genetic algorithm ga is proposed this ga is designed to be domain specific by taking advantage of the structure of the solution set of fuzzy relation equations the individuals from the initial population are chosen from the feasible solution set and are kept within the feasible region during the mutation and crossover operations the construction of test problems is also developed to evaluate the performance of the proposed algorithm

fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

posynomial geometric programming problem subject to max min fuzzy relation equations we discuss a class of posynomial geometric programming problem pgpf aimed at minimizing a posynomial subject to fuzzy relational equations with max min composition by introducing auxiliary variables we convert the pgpf into an equivalent programming problem whose objective function is a non decreasing function with an auxiliary variable we show that an optimal solution consists of a maximum feasible solution and one of the minimal feasible solutions by an equivalent programming problem in addition we introduce some rules for simplifying the problem then by using a branch and bound method and fuzzy relational equations fre path we present an algorithm to obtain an optimal solution to the pgpf finally numerical examples are provided to illustrate the steps of the procedure