Fuzzy Linear Programming Research Articles

A Multi-objective Method for Solving Fuzzy Linear Programming Based on Semi-infinite Model

ABSTRACTIn this paper, we present a new method to solve a fuzzy linear programming problem with fuzzy coefficients in the constraints and the objective function based on solving an associated multi-objective model. In particular, we present a weighted method for linear semi-infinite programming (LSIP) model to solve the original problem. Finally, a numerical example is included to illustrate the suggested solving process.

A PROMETHEE-FLP Method for Heterogeneous Multi-Attributes Group Decision Making

Heterogeneous multi-attribute group decision-making (MAGDM), which is an extension of the MAGDM problems, deals with heterogeneous information formats. In this paper, a new method is proposed for heterogeneous MAGDM in which five kinds of information formats, involving intuitionistic fuzzy sets, triangular intuitionistic fuzzy numbers, trapezoidal intuitionistic fuzzy numbers, intervals, and real numbers, are used to represent the assessments of alternatives, the attribute weight information is incomplete and the decision-makers’ weights are unknown. First, based on preference ranking organization method for enrichment evaluation (PROMETHEE), the net flows of alternatives are obtained. The attribute weights are determined reasonably through constructing a multi-objective program which is transformed into a single objective program to resolve. A conversion formula is defined to transform the net flows into the individual priorities. Then, the complete fuzzy preference relation for each DM is generated. The group priorities of alternatives are derived by a fuzzy linear programming (FLP) model. Therefore, an effect index is defined to obtain the weights of DMs, which can be used to adjust the group priorities. The ranking order of alternatives is derived by the adjusted group priority. Therefore, a new PROMETHEE-FLP method is put forward for heterogeneous MAGDM. Finally, a bank recruitment case is analyzed to demonstrate the effectiveness and application of the proposed method.

Solution of Fuzzy Multi-Objective Fractional Linear Programming Problem Using Fuzzy Programming Technique based on Exponential Membership Function

Solution of Fuzzy Multi-Objective Fractional Linear Programming Problem Using Fuzzy Programming Technique based on Exponential Membership Function

On optimisation over the integer efficient set in fuzzy linear multicriteria programming

The problem of optimising a linear function over the efficient set of a multiobjective linear programming problem is an important field of research and has some applications in multiple objective decision making. The main difficulty of this problem is that its feasible domain is non-convex and not described explicitly. The main purpose of this paper is to describe an efficient and finite new algorithm which provides a global R-optimal solution of the problem of optimising a fuzzy linear function over the efficient set of a fuzzy multiobjective integer linear programming (FMOILP) problem without having to search all integer R-efficient solutions. All the parameters of the considered problem are characterised by trapezoidal fuzzy numbers. The proposed approach is based first on the concept of comparison of fuzzy numbers by using ranking function and on an extension of Jorge's algorithm onto fuzzy numbers. Finally a numerical illustration is included for illustration.

Application of Interval Valued Fuzzy Linear Programming for Stock Portfolio Optimization

In this paper, based on existing results, decision making about portfolio investment schemes is discussed, ordering method of fuzzy numbers of interval value is shown, corresponding auxiliary models are established and solutions are provided with theories of fuzzy mathematics, optimization theory and numerical calculation, etc. Then it applies software programming to solve the portfolio investment situation between investors in savings and four securities according to the established models. The result shows that investors can choose the risk coefficient that they can bear to reach the maximum value of expected returns. The greater the risk coefficient, the greater the income, the smaller the risk coefficient and the smaller the income. Investors can determine their own portfolio strategy according to their own conditions in order to meet their own interests.

Fuzzy optimal solution of electric tomography imaging: Modelling and application

In this paper, efforts are made to find the fuzzy optimal solutions for electric tomography imaging (ETI) process. Most of the conventional ETI methods depend on an optimization process with a deterministic objective function and constraint conditions. The effective application of these methods requires the availability of measured data. However, in practical ETI possess, the assessable data are uncertain, imprecise, incomplete, and characterized by fuzziness. In this paper, the fuzzy characteristics hidden in the ETI process are extracted, and a new model of fuzzy optimization is built up, whose optimal solution is obtained by using fuzzy linear programming (FLP). The FLP model can provide a robust methodology to boost the ETI spatial resolution. Thus it creates a new and promising research direction for the optimization of the ETI process. Experimental results prove that compared with other existing ETI algorithms, the proposed method is more effective in reconstructing complex and discretely distributed objects.

A proposed model for solving fuzzy linear fractional programming problem: Numerical Point of View

In solving real life fractional programming problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To overcome these limitations, the fuzzy logic approach is applied to this problem. In this paper, we propose the concepts of simple ranking approach between two triangular fuzzy numbers. We also formulate an equivalent tri-objective linear fractional programming problem to calculate the upper, middle and lower bounds of the Fuzzy Linear Fractional Programming (FLFP) problem. Furthermore, from the obtained upper, middle and lower bounds, we construct the optimal values numerically. Finally, the effectiveness of the proposed procedure is illustrated through numerical and real life examples.

Modified Method for Solving Fully Fuzzy Linear Programming Problem with Triangular Fuzzy Numbers

The Fuzzy Linear Programming problem has been used as an important planning tool for the different disciplines such as engineering, business, finance, economics, etc. In this paper, we proposed a modified algorithm to find the fuzzy optimal solution of fully fuzzy linear programming problems with equality constraints. Recently, Ezzati et al. (Applied Mathematical Modelling, 39 (2015) 3183-3193) suggested a new algorithm to solve fully fuzzy linear programming problems. In this paper, we modified this algorithm and compare it with other existing methods. Furthermore, for illustration, some numerical examples and one real problem are used to demonstrate the correctness and usefulness of the proposed method.

OPTIMAL PLANNING WITH FUZZY LINEAR PROGRAMMING METHOD: APPLICATION IN A BUSINESS WHICH RECYCLES FOOD AND AGRICULTURAL PRODUCTS WASTES

OPTIMAL PLANNING WITH FUZZY LINEAR PROGRAMMING METHOD: APPLICATION IN A BUSINESS WHICH RECYCLES FOOD AND AGRICULTURAL PRODUCTS WASTES

A MOLFP Method for Solving Linear Fractional Programming Under Fuzzy Environment

In this paper, a solution procedure is proposed to solve Fully Fuzzy Linear Fractional Programming (FFLFP) problem where all the variables and parameters are triangular fuzzy numbers. Here, FFLFP problem transformed into an equivalent Multi- Objective Linear Fractional Programming (MOLFP) problem. Then MOLFP converted into an equivalent multi objective linear programming problem by using mathematical programming approach. The proposed solution illustrated through numerical examples and compared with existing methods.

A method for solving equally spread symmetric fuzzy assignment problems using branch and bound technique

The fuzzy assignment model depicts a special case of fuzzy linear programming problem (F.L.P.P) in which the objective is to assign the number of origins to the same number of destinations at minimum total cost. The fuzzy assignment should be framed on one-to-one basis. In this research article it is developed a method using the Branch and Bound Technique has been developed for symmetric fuzzy assignment (equally spread) of jobs. Also in this method fuzzy optimal solution has been obtained without converting the symmetric fuzzy assignment problem (equally spread) as a crisp.

A New Method for Solving Fully Fuzzy Multi Objective Supplier Selection Problem

Supplier selection is one of the most critical activities of purchasing management in a supply chain. Because selecting right suppliers helps reduce purchasing costs, improve quality of final products and services, etc. In a real situation, for a supplier selection problem, most of the input information is not known precisely, since decision making deal with human judgment and comprehension and its nature includes ambiguity. In fact, on the one hand, deterministic models cannot easily take this vagueness into account. In these cases, the theory of fuzzy sets is one of the best tools to handle uncertainty. On the other hand, Kumar et al. proposed a new approach to find the fuzzy optimal solution of fully fuzzy linear programming problem. So, using this approach in this paper, we present a new mixed integer multi objective linear programming model for supplier selection problem. Due to uncertainty of the data, in continuation, we present a new method to solve multi objective fully fuzzy mixed integer linear programming and implement the method to supplier selection problem. Computational results present the application of the method and the proposal solving method.

New approach to the resolution of triangular fuzzy linear programs: MOMA-plus method.

In this paper, we propose a new approach to the resolution of linear programs, whose coefficients are fuzzy triangular numbers. This new approach is an adaptation from the method MOMA-plus (Multi-Objective Metaheuristic based on Alienor method) [1] to the resolution of fuzzy linear programs. First of all it consists in using of a new procedure proposed here to the converting of the fuzzy linear program into a deterministic multi-objective linear program, secondly of the using of the MOMA-plus procedure for resolution. Finally, three numerical examples are given to explain the procedures and highlight the performances of this new approach.

Lean Policies in Route Planning and Scheduling of Waste Collection with Fuzzy Demand

This study addresses a household waste collection routing problem with a heterogeneous fleet. The collection fleet includes hand carts and vehicles to transport wastes from houses to disposal sites. The authors attempt to enhance the system efficiency considering lean policies, which leads to minimizing the fleet size and the collection time concurrently. In reality, uncertainty of some parameters stems from environmental and living conditions. Hence, a bi-objective fuzzy possibilistic mixed integer linear programming model is developed to design an optimal collection network. To solve the model, a hybrid solution approach is applied, which combines fuzzy possibilistic programming and fuzzy multi-objective programming. Finally, several numerical examples are tested to illustrate validation of the proposed model and applicability of the applied solution approach.

A novel method for solving fully fuzzy linear fractional programming problems

A novel method for solving fully fuzzy linear fractional programming problems

An interval chance-constrained fuzzy modeling approach for supporting land-use planning and eco-environment planning at a watershed level

An interval chance-constrained fuzzy land-use allocation (ICCF-LUA) model is proposed in this study to support solving land resource management problem associated with various environmental and ecological constraints at a watershed level. The ICCF-LUA model is based on the ICCF (interval chance-constrained fuzzy) model which is coupled with interval mathematical model, chance-constrained programming model and fuzzy linear programming model and can be used to deal with uncertainties expressed as intervals, probabilities and fuzzy sets. Therefore, the ICCF-LUA model can reflect the tradeoff between decision makers and land stakeholders, the tradeoff between the economical benefits and eco-environmental demands. The ICCF-LUA model has been applied to the land-use allocation of Wujiang watershed, Guizhou Province, China. The results indicate that under highly land suitable conditions, optimized area of cultivated land, forest land, grass land, construction land, water land, unused land and landfill in Wujiang watershed will be [5015, 5648] hm2, [7841, 7965] hm2, [1980, 2056] hm2, [914, 1423] hm2, [70, 90] hm2, [50, 70] hm2 and [3.2, 4.3] hm2, the corresponding system economic benefit will be between 6831 and 7219 billion yuan. Consequently, the ICCF-LUA model can effectively support optimized land-use allocation problem in various complicated conditions which include uncertainties, risks, economic objective and eco-environmental constraints.

Designing train-speed trajectory with energy efficiency and service quality

ABSTRACTWith the development of automatic train operations, optimal trajectory design is significant to the performance of train operations in railway transportation systems. Considering energy efficiency and service quality, this article formulates a bi-objective train-speed trajectory optimization model to minimize simultaneously the energy consumption and travel time in an inter-station section. This article is distinct from previous studies in that more sophisticated train driving strategies characterized by the acceleration/deceleration gear, the cruising speed, and the speed-shift site are specifically considered. For obtaining an optimal train-speed trajectory which has equal satisfactory degree on both objectives, a fuzzy linear programming approach is applied to reformulate the objectives. In addition, a genetic algorithm is developed to solve the proposed train-speed trajectory optimization problem. Finally, a series of numerical experiments based on a real-world instance of Beijing–Tianjin Intercity Railway are implemented to illustrate the practicability of the proposed model as well as the effectiveness of the solution methodology.

An Integrated Method for Interval Multi-Objective Planning of a Water Resource System in the Eastern Part of Handan

In this study, an integrated solving method is proposed for interval multi-objective planning. The proposed method is based on fuzzy linear programming and an interactive two-step method. It cannot only provide objectively optimal values for multiple objectives at the same time, but also effectively offer a globally optimal interval solution. Meanwhile, the degree of satisfaction related to different objective functions would be obtained. Then, the integrated solving method for interval multi-objective planning is applied to a case study of planning multi-water resources joint scheduling under uncertainty in the eastern part of Handan, China. The solutions obtained are useful for decision makers in easing the contradiction between supply of multi-water resources and demand from different water users. Moreover, it can provide the optimal comprehensive benefits of economy, society, and the environment.

A Hybrid Fuzzy PSO Algorithm for Solving Steelmaking-Continuous Casting Scheduling Problem

In this paper, steelmaking-continuous casting (SCC) scheduling problem is investigated and a mixed integer linear programming model is developed. Since the technical constraints in the mathematical model are not defined exactly, fuzzy sets are used to present them. With using fuzzy constraints, a compromise between different criteria is made based on expert’s ideas in steel industry. Since the mathematical model is suitable only for small size problems, a hybrid algorithm is developed to solve the SCC scheduling problem. The proposed algorithm is based on a combination of particle swarm optimization and fuzzy linear programming (FLP) methods. In this algorithm, the process of generating a solution consists of two phases. In the first phase, assigning and sequencing the charges on machines is done, while in the second phase, a FLP model is applied to determine start time of charges on assigned machines. To evaluate the proposed procedure, it is compared with an algorithm reported in the literature through solving different problems. Numerical results show that the proposed algorithm can obtain very good solutions for SCC scheduling problem. The results also reveal the higher efficiency of the proposed approach in decreasing waiting time of charges between processing.

A group decision-making model based on incomplete comparative expressions with hesitant linguistic terms

As a result of uncertainty and complexity for environments of decision-making, it is more suitable for decision makers to use hesitant fuzzy linguistic information. In this paper, a novel group decision making (GDM) model based on fuzzy linear programming is proposed for incomplete comparative expressions with hesitant fuzzy linguistic term set (HFLTSs). We establish an equivalence theorem of additive consistency between 2-tuple fuzzy linguistic preference relation (FLPR) and corresponding fuzzy preference relation. Based on this framework, a fuzzy linear programming is established to address incomplete comparative expressions with HFLTSs. It is more important that the proposed fuzzy linear programming has a double action, finding the highest consistent incomplete 2-tuple FLPR and increasing inconsistent 2-tuple FLPR to the additive consistent 2-tuple FLPR based on given incomplete comparative expressions with HFLTSs. By this means, a novel GDM model is constructed based on importance induced ordered weighted averaging operator. Finally, an investment decision-making in real-world is solved by the proposed model, which shows the result of GDM is effectiveness.