In this paper, an algorithm is presented to solve fuzzy multi-objective linear fractional programming (FMOLFP) problems through an approach based on superiority and inferiority measures method (SIMM). In the model for...
详细信息
In this paper, an algorithm is presented to solve fuzzy multi-objective linear fractional programming (FMOLFP) problems through an approach based on superiority and inferiority measures method (SIMM). In the model for the proposed approach, each of fuzzy goals defined for the fractionalobjectives and some of constraints have fuzzy numbers. To achieve the highest membership value, SIMM is adopted to deal with fuzzy number in constraints, then a linear goal programming methodology is introduced to solve the problem in which the fractionalobjectives is fuzzy goals. A case of agricultural planting structures optimization problem is solved to illustrate the application of the algorithm. The results show that winter wheat and summer corn acreage should be 38,386.4 ha, and cotton acreage should be 20,669.6 ha. Because of high risk in cotton cultivation at present, the ratio of grain planted area to cotton planted area is unreasonable. An improved support in policy is necessary for the government to enhance the enthusiasm of farmers to plant cotton and sustain the development of cotton market in the long term. (C) 2020 Elsevier Ltd. All rights reserved.
A fuzzy version of Gauss Elimination Approach (GEA) for the solution of fully fuzzy multiobjectivelinearfractionalprogramming (FFMOLFP) problems involving triangular fuzzy numbers (TFNs) is presented in this artic...
详细信息
A fuzzy version of Gauss Elimination Approach (GEA) for the solution of fully fuzzy multiobjectivelinearfractionalprogramming (FFMOLFP) problems involving triangular fuzzy numbers (TFNs) is presented in this article. Fully fuzzy linearfractionalprogramming problem is first reduced to an equivalent fully fuzzy linearprogramming (FFLP) problem by suitable transformation and then the optimum value of each objective function is obtained individually with respect to the same set of constraints. Secondly by using all these objective values, the FFMOLFP problem is then converted to a single objective non fractional FFLP problem and its optimum solution is obtained which in turn provides the Pareto optimum solution the given FFMOLFP problem. To indicate the efficacy of the proposed procedure, a numerical illustration is given.
The multi-objective linear fractional programming is an interesting topic with many applications in different fields. Until now, various algorithms have been proposed in order to solve the multi-objectivelinear fract...
详细信息
The multi-objective linear fractional programming is an interesting topic with many applications in different fields. Until now, various algorithms have been proposed in order to solve the multi-objective linear fractional programming (MOLFP) problem. An important point in most of them is the use of non-linearprogramming with a high computational complexity or the use of linearprogramming with preferences of the objective functions which are assigned by the decision maker. The current paper, through combining goal programming and data envelopment analysis (DEA), proposes an iterative method to solve MOLFP problems using only linearprogramming. Moreover, the proposed method provides an efficient solution which fairly optimizes each objective function when the decision maker has no information about the preferences of the objective functions. In fact, along with normalization of the objective functions, their relative preferences are fairly determined using the DEA. The implementation of the proposed method is demonstrated using numerical examples.
This article proposes to handle multiobjectivelinearfractionalprogramming (MOLFP) problems in fuzzy environment. As a generalized mean value theorem first order Taylor series approach is used to convert multi obje...
详细信息
ISBN:
(纸本)9781509002252
This article proposes to handle multiobjectivelinearfractionalprogramming (MOLFP) problems in fuzzy environment. As a generalized mean value theorem first order Taylor series approach is used to convert multiobjectivelinearfractionalprogramming to multiobjectivelinearprogramming problem by introducing imprecise aspiration level to each objective. Then additive weighted method has been used to get its solution. It has been observed that optimality reached for different weight values of the membership function for the different objective functions. The method has been presented by an algorithm and sensitivity analysis for the fuzzy multiobjectivelinearfractionalprogramming (FMOLFP) problem with respect to aspiration level and tolerance limit are also presented. The present approach is demonstrated with one numerical example.
This study has focused on developing a new method for solving the multi-objectivelinearfractional decentralized bi-level decision-making (MOLF-DBLDM) problem in an intuitionistic fuzzy decision environment. The main...
详细信息
This study has focused on developing a new method for solving the multi-objectivelinearfractional decentralized bi-level decision-making (MOLF-DBLDM) problem in an intuitionistic fuzzy decision environment. The main motivation behind this study is to determine a solution approach algorithm that is effective and simple to apply while taking actual decision-making circumstances into account. Real-world decision-making situations involve a bi-level of several decision-makers who use various decision-making processes such as agree, not certain, and disagree. By considering such real-world conditions here, all uncertain coefficients of objectives, constraint functions, and resources are portrayed as trapezoidal intuitionistic fuzzy numbers, and their crisp form is obtained through the (alpha, beta)-cut (confidence level) concept. In the suggested method, we have transformed the crisp (alpha, beta)-MOLF-DBLDM problem into a single objectivelinear decentralized bi-level decision-making (SOL-DBLDM) model using a modified linearized approach. Additionally, the upper level specified a tolerance region for its decision variables to regulate the lower levels in order to prevent decision lock. Then, the SOL-DBLDM problem is expressed as a single-level model using a new scalar function of membership and non-membership degree for each objective function at all decision-makers and upper level decision control variables. The key advantage of this method over others is that it produces an alternate, preferable compromise solution to the problem of imprecise hierarchical-level optimization. Finally, comparisons to the current methodology and appropriate numerical examples are used to demonstrate the superiority and effectiveness of the suggested method.
Optimizing the sum-of-fractional functions under the bounded feasible space is a very difficult optimization problem in the research area of nonlinear optimization. All the existing solution methods in the literature ...
详细信息
Optimizing the sum-of-fractional functions under the bounded feasible space is a very difficult optimization problem in the research area of nonlinear optimization. All the existing solution methods in the literature are developed to find the solution of single-objective sum-of-fractional optimization problems only. Sum-of-fractionalmulti-objective optimization problem is not attempted to solve much by the researchers even when the fractional functions are linear. In the present article, a duality-based branch and bound computational algorithm is proposed to find a global efficient (non-dominated) solution for the sum-of-linear-fractionalmulti-objective optimization (SOLF-MOP) problem. Charnes-Cooper transformation technique is applied to convert the original problem into non-fractional optimization problem, and equivalence is shown between the original SOLF-MOP and non-fractional MOP. After that, weighted sum method is applied to transform MOP into a single-objective problem. The Lagrange weak duality theorem is used to develop the proposed algorithm. This algorithm is programmed in MATLAB (2016b), and three numerical illustrations are done for the systematic implementation. The non-dominance of obtained solutions is shown by comparison with the existing algorithm and by taking some feasible solution points from the feasible space in the neighborhood of obtained global efficient solution. This shows the superiority of the developed method.
Present research deals with more efficient solution of a multi-objectivelinearfractional (MOLF) optimization problem by using branch and bound method. The MOLF optimization problem is reduced into multi-objective op...
详细信息
Present research deals with more efficient solution of a multi-objectivelinearfractional (MOLF) optimization problem by using branch and bound method. The MOLF optimization problem is reduced into multi-objective optimization problem by a transformation. The reduced multi-objective optimization problem is converted into single objective optimization problem by giving suitable weight for each objective. The equivalency theorems are established. Weak duality concept is used to compute the bounds for each partition and some theoretical results are also established. The proposed method is motivated by the work of Shen et al. (J Comput Appl Math 223:145-158, 2009). Matlab code is designed for the proposed method to run all the simulated results and it is applied on two numerical problems. The efficiency of the method is measured by comparing with earlier established method.
暂无评论