Margit Kovács

Optimality for fuzzified mathematical programming problems: a parametric approach

From a conventional mathematical programming model, and in accordance with which fuzzification is used, several models of fuzzy mathematical programming problems can be obtained. This paper deals with the study of the optimality concept for (g,p)-fuzzified mathematical programming problems. An auxiliary parametric mathematical programming problem is presented which allows the above model to be solved in a straightforward way. In addition, some results about the (g, p)-fuzzified mathematical programming problem are obtained using the parametric mathematical programming problem.

Stable embedding of ill-posted linear equality systems into fuzzified systems

Abstract In this paper the (g, p, d)-fuzzification of linear systems is introduced. It is shown that this type of fuzzification possesses the feature of regularization, i.e. the maximal height solution of the fuzzified problem is stable for a wide class of problems.

Algebraic structure of centered M -fuzzy numbers

Abstract In this paper we discuss the algebraic structure of fuzzy numbers assuming that they are generated by a subset of mappings from R to a lattice ordered monoid, particularly to a positive or a negative cone, and for every fuzzy number there is a center defined. Using a special ordering on the set of fuzzy numbers and introducing special binary fuzzy-algebraic operations we obtain different structural properties of these fuzzy numbers. We study these algebraic structures using different class of generator mappings and establish the isomorphism between the real line and the set of the centered fuzzy numbers.

Flexible linear programs with a restricted overall flexibility level

It is usually supposed that tolerance levels are determined by the decision maker a priori in flexible linear programming (FLP) problems. In this paper, we shall suppose that the decision maker does not care about the particular values of tolerance levels, but he wishes to keep their sum below a predetermined level which we call his overall flexibility level. We also suppose that his overall flexibility level is soft, i.e. it is admissible to exceed it (to a certain extent). This is a new statement of FLP problems, because here the tolerance levels are also treated as variables, and the only restriction on them is that their sum should not exceed very much a given level. In this setup, we shall prove that the consistency level of FLP problems depends continuously on the decision makers overall flexibility level.

Fuzzy Linear Programming Problems with Min— and Max-Extended Algebraic Operations on Centered Fuzzy Numbers

In this paper a new class of fuzzy linear programming will be treated. It is supposed that both coefficients of the objective and constraint functions both the unknown decision variables are centered fuzzy numbers of given basis and the min — and max — extended arithmetic operations on the centered fuzzy numbers are defined as in [3]. Using different combinations of the min — and max — operations 8 different fuzzy linear programming problems can be formulated, the optimality conditions of which will be discussed.

Convergence rate for regularized arrier function methods

In this paper the regularized variants of barrier function methods are discussed. These variants are related to the following regularization methods: Tichonov-function method, method of residuals and method of quasisolutions. .A convergence rate estimation is given for each method if both the original minimization problem and the connected problem of finding R-normal sohlion posses The feature of strong compatibility.

Some convergence theorems on nonstationary minimization processes 1

In this paper the sufficient convergence conditions of the general nonstationary minimization processes are studied. The sensitivity property of these methods is also investigated. It is shown, that the theorems may be applicated to the gradient type SUMT method and to the Tichonov-regularized gradient type SUMT method.

A Multiobjective Linear Programming Algorithm Based on the Dempster-Shafer Composition Rule

In this paper a new algorithm is given to find an efficient solution with maximal commonality for multiobjective linear programming problems. The algorithm is based on the evidence theory.

A Concept of Optimality for Fuzzified Linear Programming Based on Penalty Function

In this paper, an optimality concept is introduced Jor a Juzzijied linear programming problems, where all parameters - including the coefficients of the objective Junction - are Juzzy numbers. This concept is based on the parametric embedding of the original problem into a penalty problem.

Two Types of Fuzzy Linear Programming Problems on Centered Fuzzy Numbers

In the lecture a special class of fuzzy linear programming will be treated. It will be supposed that both the coefficients of the objective and constraints functions and the unknown decision variables are centered fuzzy numbers of given basis. The idea of centered fuzzy numbers and the arithmethic operations on them was introduced in [1] as follows: A centered fuzzy number μ is given by a pair (α, f), where f is a normal fuzzy number such that 0 ∈ ker f and μ(x) = f(x - α) for every x ∈ ℝ. f is the generator function and α is the center of the fuzzy number. We will assume that the subset of generator functions closed for the V, ^ and * fuzzy set-operations and it contains the characteristic function of zero. Furthermore, F will denote the set of all centered fuzzy numbers on a given set of generator functions.