Programming Problems In Fuzzy Environment Research Articles

The Composite Approach for Linear Fractional Programming Problem in Fuzzy Environment

The Composite Approach for Linear Fractional Programming Problem in Fuzzy Environment

Solving Fuzzy Bi-Criteria Fixed Charge Transportation Problem Using a New Fuzzy Algorithm

The bi-criteria fixed charge transportation problem is an extension of the classical transportation problem. The bi-criteria fixed charge transportation problem in a crisp environment is, often, not effective in dealing with imprecision or vagueness in the values of the problem parameters. To deal with such situations, it has been proposed that the parameters should be represented as fuzzy numbers. Hence, bi-criteria fixed charge transportation problem in fuzzy environment is considered here. In existing approaches, the programming problems in fuzzy environment are solved by converting them into crisp environment by choosing appropriate membership functions and thus, the solutions are also crisp numbers. However, in this paper, a new algorithm is proposed to solve the above said problem using a linear ranking function, without converting it into crisp environment and the solutions derived are fuzzy numbers. The algorithm is suitably illustrated with a numerical example. Numerical results are compared for both fuzzy and crisp versions of the problem.

Fractile criterion iterative-interactive optimisation process for multi-objective stochastic linear programming problems in fuzzy environment

Present article focuses on one general fractile criterion iterative-interactive optimisation process in order to obtain the preferable Pareto optimal solution, subject to specified main objective function to multi-objective stochastic linear programming problems in fuzzy environment. This asks the managers to identify the main objective function among all objective functions without specifying any weights or utility functions. Unlike existing articles, the reference membership levels to conflicting objective functions are analytically determined by employing the trade-off ratios among objective functions in this process. Moreover, the necessity of only very few interactions with decision-makers saves the precious time and money of organisations. Numerical applications demonstrate the efficiency of proposed process. Finally, conclusions are drawn.

Fractile criterion iterative-interactive optimization process for multi-objective stochastic linear programming problems in fuzzy environment

Present article focuses on one general fractile criterion iterative-interactive optimisation process in order to obtain the preferable Pareto optimal solution, subject to specified main objective function to multi-objective stochastic linear programming problems in fuzzy environment. This asks the managers to identify the main objective function among all objective functions without specifying any weights or utility functions. Unlike existing articles, the reference membership levels to conflicting objective functions are analytically determined by employing the trade-off ratios among objective functions in this process. Moreover, the necessity of only very few interactions with decision-makers saves the precious time and money of organisations. Numerical applications demonstrate the efficiency of proposed process. Finally, conclusions are drawn.

On solving fuzzy linear fractional programming in material aspects

In this paper a method is present solving fractional linear programming problems in fuzzy environment by ranging methods, where parameters are fuzzy numbers with uncertain coefficients in the objective function. Here we constitute the crisp relationship between the objective function and the decision variables to solve the resulting programming problem to find a fair optimal solution to the material related problem, illustrated with an example.

Duality theory in Atanassov’s intuitionistic fuzzy mathematical programming problems: Optimistic, pessimistic and mixed approaches

Linear programming problems in fuzzy environment have been investigated by many researchers in the recent years. Some researchers have solved these problems by using primal-dual method with linear and exponential membership functions. These membership functions are particular form of the reference functions. In this paper, we introduce a pair of primal-dual PPs in Atanassov’s intuitionistic fuzzy environment (AIFE) in which the membership and non-membership functions are taken in the form of the reference functions and prove duality results in AIFE by using an aspiration level approach with different view points, viz., optimistic, pessimistic and mixed. Since fuzzy and AIF environments cause duality gap, we propose to investigate the impact of membership functions governed by reference functions on duality gap. This is specially meaningful for fuzzy and AIF programming problems, when the primal and dual objective values may not be bounded. Finally, the duality gap obtained by the approach has been compared with the duality gap obtained by existing approaches.

Solution approach to a special class of full fuzzy linear programming problems

A wide variety of solution approaches to linear programming problems in fuzzy environment are proposed in the recent literature. For this study we consider a linear programming problem with fuzzy inequality constraints, and both coefficients and decision variables described by trapezoidal fuzzy numbers. Our solution approach takes into consideration decision maker’s acceptance degree of the violated fuzzy constraints.We use the interval expectation of the trapezoidal fuzzy numbers to transform the original problem into an interval optimization problem. Then, using an order relation to rank the intervals; and handling the acceptance degree of the violated fuzzy constraints as a parameter in the optimization model, we analyze the Pareto optimal solutions to a parametric bi-objective linear programming problem. For a fixed value of the acceptance degree provided by the decision maker, but after a parametric analysis with respect to the parameter used for aggregating the two objectives, the decision maker becomes better informed about the nature of the problem he has to complete.We illustrate our new solution approach using numerical examples found in the literature, and emphasize its advantages.

Goal Programming for Solving Fractional Programming Problem in Fuzzy Environment

This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.

A study on Nonlinear Programming Problem in Fuzzy Environment

In that paper, the fuzzy nonlinear programming problem is discussed. In order to obtain more accurate solution, the properties of fuzzy set and fuzzy number with linear membership function and fuzzy maximum decision maker is utilized to fuzzifying the crisp problem. In the illustration, we have given a refinement to obtain this solution.

Some Duality Results for Fuzzy Nonlinear Programming Problem

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.

Redefining chance-constrained programming in fuzzy environment

This paper presents an alternative definition of probability of fuzzy event. In analogy to probability of nonfuzzy event we view probability of fuzzy event in terms of cumulative distribution of a random variable. A multi-objective imprecise-chance constrained programming problem has been defined here which is an extension of classical chance-constrained programming problem in fuzzy environment. An illustrative numerical example is given.