NEW IMPROVED METHOD FOR SOLVING THE FUZZY LINEAR PROGRAMMING PROBLEMS WITH VARIABLES GIVEN AS FUZZY NUMBERS

The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random numerical examples has been solved using the proposed approach.

A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers

Recently, new methods have been recommended to solve fully fuzzy linear programming (FFLP) issues. Likewise, the present study examines a new approach to solve FFLP issues through fuzzy decision parameters and variables using triangular fuzzy numbers. The strategy, which is based on alpha-cut theory and modified triangular fuzzy numbers, is suggested to obtain the optimal fully fuzzy solution for real-world problems. In this method, the problem is considered as a fully fuzzy problem and then is solved by applying the new definition presented for the triangular fuzzy number to optimize decision variables and the objective function. Several numerical examples are solved to illustrate the above method.

Type 2 Fully Fuzzy Linear Programming

Since its inception, fuzzy linear programming (FLP) has proved to be a more powerful tool than classical linear programming to optimize real-life problems dealing with uncertainty. However, the proposed models are partially fuzzy; in other words, they suppose that only some aspects can be uncertain, while others have to be crisp. Furthermore, the few methods that deal with fully fuzzy problems use Type 1 fuzzy membership function, while Type 2 fuzzy logic captures the uncertainty in a more suitable way. This work presents a fully fuzzy linear programming approach in which all parameters are represented by unrestricted Interval Type 2 fuzzy numbers (IT2FN) and variables by positive IT2FN. The treated comparative results show that the proposed achieves a better optimized function while permitting consideration of both equality and inequality constraints.

Exploring the Optimal Allocation Decision-Making of Expenditure Budget in Hospitals Under Multi-Objective Constraints: Evidence from Urban Public Hospitals, China

Hospitals in many countries face the need for balancing different categories of expenditures to achieve multiple goals within a limited budget. This study established a two-stage fuzzy linear programming (FLP) estimation model to explore the optimal allocation decision-making of expenditure budget under the multi-objective constraints. Taking all urban public hospitals in Henan province of China as a sample, the optimal allocation decision-making of total expenditure budget was tested with the human resources expenditures (HE) as the dependent variable. And the outcome was compared with the actual expenditure data of these hospitals between 2010 and 2016. The study found that when the HE achieves the maximum and minimum feasible scale, the expenditure scales of the budget allocation categories including pharmaceutical expenditures, medical supplies expenditures, and other expenditures were all within a reasonable range. Among them, the observed promoting space for HE was 3.78 billion yuan. The results show that the FLP method can help urban public hospitals to make better total expenditure budget allocation decisions, which can maintain their reasonable expenditure structure under the hospitals’ development goals and the government’s regulatory requirements.

Solving fully fuzzy linear programming problems by controlling the variation range of variables

This paper deals with a fully fuzzy linear programming problem (FFLP) in which the coefficients of decision variables, the right-hand coefficients and variables are characterized by fuzzy numbers. A method of obtaining optimal fuzzy solutions is proposed by controlling the left and right sides of the fuzzy variables according to the fuzzy parameters. By using fuzzy controlled solutions, we avoid unexpected answers. Finally, two numerical examples are solved to demonstrate how the proposed model can provide a better optimal solution than that of other methods using several ranking functions.

Truck dispatching in surface mines -Application of fuzzy linear programming

Material handling in surface mines accounts for around 50% of the operational cost. Optimum truck dispatching plays a critical role in the reduction of this operational cost in truck and shovel surface mines. Researchers in this field have presented several mathematical models to solve the truck dispatching problem optimally. However, a critical survey of the literature has shown that three significant drawbacks exist in the available truck dispatching models. The published models underestimate the importance of the interaction between truck fleet, shovel fleet, and the processing plants. They also disregard goals set by strategic-level plans. Moreover, none of the available models account for the uncertainty associated with the input parameters. In this paper we present a new truck dispatching model that covers all of these drawbacks, using a fuzzy linear programming method. The performance of the developed model was evaluated through implementatin in an active surface mining operation. The results show a significant improvement in production and fleet utilization.

Wetland Restoration Planning Approach Based on Interval Fuzzy Linear Programming under Uncertainty

When planning wetland restoration projects, the planting area allocation and the costs of the restoration measures are two major issues faced by decision makers. In this study, a framework based on the interval fuzzy linear programming (IFLP) method is introduced for the first time to plan wetland restoration projects. The proposed framework can not only effectively deal with interval and fuzzy uncertainties that exist in the planning process of wetland restorations but also handle trade-offs between ecological environment benefits and economic cost. This framework was applied to a real-world wetland restoration planning problem in the northeast of China to verify its validity and examine the credibility of the constraints. The optimized results obtained from the framework that we have developed indicate that higher ecological and social benefits can be obtained with optimal restoration costs after using the wetland restoration decision-making framework. The optimal restoration measure allocation schemes obtained by IFLP under different credibility levels can help decision makers generate a range of alternatives, which can also provide decision suggestions to local managers to generate a satisfactory decision-making plan. Furthermore, a comparison was made between the IFLP model and ILP model in this study. The comparison results indicate that the IFLP model provides more information regarding ecological environment and economic trade-offs between the system objective, certainty, and reliability. This framework provides managers with an effective way to plan wetland restoration projects, while transference of the model may help solve similar problems.

A new approach to solve fully intuitionistic fuzzy linear programming problem with unrestricted decision variables

In many real-world problems, one may encounter uncertainty in the input data. The fuzzy set theory fits well to handle such situations. However, it is not always possible to determine with full satisfaction the membership and non-membership degrees associated with an element of the fuzzy set. The intuitionistic fuzzy sets play a key role in dealing with the hesitation factor along-with the uncertainity involved in the problem and hence, provides more flexibility in the decision-making process. In this article, we introduce a new ordering on the set of intuitionistic fuzzy numbers and propose a simple approach for solving the fully intuitionistic fuzzy linear programming problems with mixed constraints and unrestricted variables where the parameters and decision variables of the problem are represented by intuitionistic fuzzy numbers. The proposed method converts the problem into a crisp non-linear programming problem and further finds the intuitionistic fuzzy optimal solution to the problem. Some of the key significance of the proposed study are also pointed out along-with the limitations of the existing studies. The approach is illustrated step-by-step with the help of a numerical example and further, a production planning problem is also demonstrated to show the applicability of the study in practical situations. Finally, the efficiency of the proposed algorithm is analyzed with the existing studies based on various computational parameters.

FUZZY LINEAR PROGRAMMING PROBLEM AND APPLYING NEURAL NETWORKS TO ITS SOLUTION

In present paper consider one economical problem- optimal planning of manufacture. In space of pair of fuzzy numbers this problem formulated as linear programming problem. Applying the certain techniques this problem reduced to classical linear programming problem. Obtained problem solved applying neural networks.