Solving fuzzy quadratic programming problems based on ABS algorithm

Extrapolation parameters in Refinement of Jacobi over Relation method in solving fuzzy linear systems were hypothesized to influence the rate of convergence. This paper aims to investigate the relationship between extrapolation parameters and approximate solutions of fuzzy linear systems when solved using Refinement of Jacobi over Relaxation method. The Algorithms of Refinement of Jacobi over Relaxation method are proposed based on the Jacobi method that specifically used in solving the system. A five by five fuzzy linear system is given to investigate the convergence to exact solution with three different values of extrapolation parameters. The numerical results show that there is a positive correlation between extrapolation parameter and convergence to exact solution. The three extrapolation parameters suggest that convergence to exact solution can be increased in line with the increase in the values of extrapolation parameters.

Mathematical models have great significance with respect to their applicability in many fields of medical research. This paper targets to examine the better approximate solution of the system of linear differential equation using Runge Kutta method of order four. In the numerical examples we find the capability of the method by comparison with the exact solution of fuzzy linear systems on glucose-insulin regulatory model. It is found that solution obtained by the proposed method is closer to the exact solution.

In this paper, the triangular fuzzy bilevel programming problem (TFBLPP) is investigated. We transformed TBFLPP to interval fuzzy bilevel linear programming problem by using nearest interval approximation. In the next step, three problem were obtained that by solving them solution TBFLPP obtained.

The difficulty in solving either multi-objective linear programming (MOLP) problems or fuzzy multi-objective linear programming (FMOLP) problems is the trade-off among objectives. To deal with this difficulty, we proposed a new algorithm for solving FMOLP problems by using zero-sum game. First, FMOLP problem given is converted to a crisp MOLP problem by using ranking function, and then a payoff matrix is constructed to find the weights of each objective function of the MOLP problem. After that, each weight is multiplied with the corresponding objective function, a single-objective LP problem is obtained and thus, FMOLP problem is solved. The proposed algorithm is illustrated by numerical examples for the FMLOP problems having fuzzy constraints or not.

Branch-and-price algorithm for fuzzy integer programming problems with block angular structure

An interactive approach based on a genetic algorithm for a type of quadratic programming problems with fuzzy objective and resources

In many fuzzy programming problems, the objectives and constraints may consist of some expected values of prescribed fuzzy variables. Therefore, analyzing the properties of those expected values is helpful to solving the problems. The objective of this paper is to deal with some analytical properties of expected values of fuzzy variables with parameters. First, some continuity theorems are derived for the properties of continuity and semicontinuity of the expected values. Then, a differentiation formula of the expected value with respect to the parameter is established. The results obtained in this paper are useful in fuzzy programming models.

This paper presents a new method for steady state hierarchical optimizing control of large-scale industrial processes. Several classical steady state coordination mechanisms are applied to the case in which the model coefficients of each subprocess of a large-scale industrial process are replaced by fuzzy numbers. Hence, each subprocess model is converted into a fuzzy form and then the original crisp programming problem with equality and inequality constraints is transformed into the fuzzy programming problem with fuzzy equality and crisp inequality constraints in each local decision unit. The final solutions are obtained by solving the general mathematical programming problem after the fuzzy equality constraints are converted into crisp inequality constraints. The developed method is mainly used to deal with the model-reality difference caused by either the model coefficients of the subprocess not being known accurately or the model slowly varying during normal operation. Three main types of coordination for processes with fuzzy parameters are derived in this paper: interaction balance method (IBM), interaction prediction method (IPM), and mixed method (MM). Simulation results of two examples show that 1) the proposed method can deal with model-reality difference efficiently, 2) the convergence speed of the on-line coordination for fuzzy parameter processes is faster than that of corresponding coordination for crisp parameter processes, and 3) the objective function of real processes can be improved by using the proposed method compared with the classical case. Furthermore, the studies show that the interaction balance method with global feedback (IBMF) based on a double iterative technique for processes with fuzzy parameters is the coordination algorithm that requires the fewest number of on-line iterations so far.

Probabilistic Fuzzy Goal Programming Problems Involving Pareto Distribution: Some Additive Approaches

Fuzzy programming is a well-known optimization problem in resource allocation, optimization decision etc. In this paper, by analyzing the essential characteristic of fuzzy programming and the deficiencies of the existing methods, we propose the concept of synthesizing effect function for processing the objective function and constraints, and further we give an axiomatic system for synthesizing effect function. Finally, we establish a general solution model based on synthesizing effect function for fuzzy programming problem, and analyze the model through three examples. All the results indicate that our method not only includes the existing methods for fuzzy programming, but also effectively merge the decision preferences into the solution, so it can be widely used in many fields such as complicated system optimization and artificial intelligence.

The concept of duality plays an important role in optimization theory. This paper discusses some relations between primal and dual nonlinear programming problems in fuzzy environment. Here, fuzzy feasible region for a general fuzzy nonlinear programming is formed and the concept of fuzzy feasible solution is defined. First order dual relation for fuzzy nonlinear programming problem is studied.

Fuzzy programming approach has wide application in many fields such as project management, multi-attribute decision making, and comprehensive evaluation. Its solving methods have attracted many attentions. In this paper we present a new approach, based on the genetic algorithm, for dealing with a programming problem with fuzzy-valued objective function and constraints. Firstly, we propose the concept of generalized equilibrium value of fuzzy number, and analyze the properties, further give the operation rules; secondly, we establish a generalized equilibrium value-based fuzzy programming method combined with genetic algorithm; finally, we analyze the characteristic of the above mentioned method through a nonlinear fuzzy programming problems.

<p>There exist several methods for solving fuzzy linear or nonlinear programming problems under positivity fuzzy variables and restricted fuzzy coefficients. Due to the limitation of these methods, they can’t be applied for solving fully fuzzy linear or non- linear programming problems with unrestricted fuzzy coefficients and fuzzy variables. In this paper an efficient method to find the fuzzy optimal solution for fully fuzzy quadratic programming (FFQP) problem with unrestricted variables and parameters has been proposed. All the coefficients and decision variables of both objective functions and the constraints are triangular fuzzy numbers. The proposed method is based on converted FFQP problem into crisp quadratic programming (CQP) problem. Finally an illustrative numerical example has been given to clarify the proposed solution method.</p>

This paper investigates a kind of bilevel programming with fuzzy random variable coefficients in both objective functions and the right hand side of constraints. On the basis of the notion of Er-expected value of fuzzy random variable, the upper and lower level objective functions can be replaced with their corresponding Er-expected values. In terms of probability over defuzzified operator, fuzzy stochastic constraints can be converted into the equivalent forms. Based on these, the fuzzy random bilevel programming problem can be transformed into its deterministic one. Then we suggest differential evolution algorithm to solve the final crisp problem. Finally, a numerical example is given to illustrate the proposed method.

This paper presents a fuzzy goal programming approach for modelling and solving multi-objective decision making problem having fuzzy random variables and fuzzy numbers associated with the system constraints. In the model formulation process, the problem is converted into an equivalent fuzzy programming problem by using chance constrained programming technique. The problem is then decomposed into sub problems by considering the tolerance limits of fuzzy numbers relating to the system constraints. The individual optimal solution of each objective is found to construct the membership goals. A two-phase fuzzy goal programming model is developed to achieve the highest degree of each of the defined membership goals of the objectives to the extent possible by minimising under deviational variables and thereby obtaining most satisfactory solution in the decision making environment. A numerical example is solved to illustrate the proposed approach and the achieved solutions are compared with other existing methodologies.