Fuzzy Linear Fractional Programming Problem Research Articles

A Survey on Generalized Fuzzy Parameter-Based Fractional Programming Problem

In fuzzy sets, the elements of a universal set may belong to that set completely, may not belong to that set, or may belong partially. Therefore, fuzzy sets are called generalizations of crisp sets. Due to the diverse nature of problems in real-world situations, fuzzy set theory is found to be unable to address some of the other features of ambiguity. Therefore, researchers extended fuzzy sets to picture fuzzy sets, orthopair, intuitionistic, Pythagorean, Fermatean, neutrosophic, spherical fuzzy sets, etc. Real-world problems can be solved using the method of fractional programming. Decision-makers are trying to get good results using generalized fuzzy numbers in fractional programming problems; hence, this review paper provides a specific framework for generalized fuzzy sets and generalized fuzzy fractional programming problems. Furthermore, it is a platform for researchers who want to work on generalized fuzzy parameter-based fractional programming problems. This research paper summarizes all the basic concepts and prior research on fractional programming and generalized fuzzy linear fractional programming problems.

Fuzzy Mathematical Approach for Solving Multi-Objective Fuzzy Linear Fractional Programming Problem with Trapezoidal Fuzzy Numbers

Fuzzy Mathematical Approach for Solving Multi-Objective Fuzzy Linear Fractional Programming Problem with Trapezoidal Fuzzy Numbers

An iterative approach for the solution of fully fuzzy linear fractional programming problems via fuzzy multi-objective optimization

<abstract><p>The primary goal of optimization theory is to formulate solutions for real-life challenges that play a fundamental role in our daily lives. One of the most significant issues within this framework is the Linear Fractional Programming Problem (LFrPP). In practical situations, such as production planning and financial decision-making, it is often feasible to express objectives as a ratio of two distinct objectives. To enhance the efficacy of these problems in representing real-world scenarios, it is reasonable to utilize fuzzy sets for expressing variables and parameters. In this research, we have worked on the Fully Fuzzy Linear Fractional Linear Programming Problem (FFLFrLPP). In our approach to problem-solving, we simplified the intricate structure of the FFLFrLPP into a crisp Linear Programming Problem (LPP) while accommodating the inherent fuzziness. Notably, unlike literature, our proposed technique avoided variable transformation, which is highly competitive in addressing fuzzy-based problems. Our methodology also distinguishes itself from the literature in preserving fuzziness throughout the process, from problem formulation to solution. In this study, we conducted a rigorous evaluation of our proposed methodology by applying it to a selection of numerical examples and production problems sourced from the existing literature. Our findings revealed significant improvements in performance when compared to established solution approaches. Additionally, we presented comprehensive statistical analyses showcasing the robustness and effectiveness of our algorithms when addressing large-scale problem instances. This research underscores the innovative contributions of our methods to the field, further advancing the state-of-the-art in problem-solving techniques.</p></abstract>

Fully fuzzy DEA: a novel additive slacks-based measure model

AbstractThe subject of assessing the relative efficiency of Decision-Making Units (DMUs) has been explored extensively in the literature on Data Envelopment Analysis (DEA). While typical DEA models require exact and conclusive data, the observed values of the inputs and outputs in real-world problems may be inaccurate or ambiguous. This paper presents a novel fully fuzzy DEA (FFDEA) model based on the additive slacks-based measure (ASBM). FFDEA models imply that all inputs, outputs, and variables, are fuzzy. It is demonstrated how fuzzy ranking and fuzzy arithmetic approaches can be used to handle the trapezoidal fuzzy number assumptions. To solve the fuzzy ASBM model under variable returns-to-scale assumptions, we proposed two different methods, first method use of lexicographic method for solving multi-objective linear programming (MOLP) approach, which provides an efficiency measure and a fuzzy goal operating point for each DMU under assessment. In alternative method, we convert the fuzzy linear fractional programming problems to an equivalent MOLP problem. A case study is provided to illustrate the applicability of the proposed approach for selecting sustainable suppliers, we compare the results with other fuzzy DEA approaches, while shedding light on future research venues.

Solving Triangular Fuzzy Linear Fractional Programming Problem

Solving Triangular Fuzzy Linear Fractional Programming Problem

On optimistic, pessimistic and mixed fuzzy-programming based approaches to solve multi-objective fully intuitionistic fuzzy linear fractional programming problems

On optimistic, pessimistic and mixed fuzzy-programming based approaches to solve multi-objective fully intuitionistic fuzzy linear fractional programming problems

On Fuzzy Linear Fractional Programming Problems via α-Cut-Based Method with Application in Transportation Sector

The article provides an α-cut-based method that solves linear fractional programming problems with fuzzy variables and unrestricted parameters. The parameters and variables are considered as asymmetric triangular fuzzy numbers, which is a generalization of the symmetric case. The problem is solved by using α-cut of fuzzy numbers wherein the α- and r-cut are applied to the objective function and constraints, respectively. This reduces the problem into an equivalent biobjective model which leads to the upper and lower bounds of the given problem. Afterwards, the membership functions corresponding to various values of r∈(0,1] are obtained using the optimal values of the biobjective model. The proposed method is illustrated by taking an example from the literature to highlight the fallacy of an existing approach. Finally, a fuzzy linear fractional transportation problem is modelled and solved using the aforementioned technique.

Solving Triangular Fully Fuzzy Linear Fractional Programming Problem via Parametric Approach

Solving Triangular Fully Fuzzy Linear Fractional Programming Problem via Parametric Approach

Modify Symmetric Fuzzy Approach to Solve the Multi-Objective Linear Fractional Programming Problem

The property of fuzzy sets is approached as an instrument for the construction and finding of the value of the multi-objective linear fractional programming problem (MOLFPP), which is one of the systems of decision problems that are covered by fuzzy dealings. The paper introduces an approach to convert and solve such a problem by modifying the symmetric fuzzy approach, suggesting an algorithm, and demonstrating how the fuzzy linear fractional programming problem (FLFPP) can be answered without raising the arithmetic potency. Also, it introduces a technique that uses an optimal mean to convert MOLFPP to a single LFPP by modifying the symmetric fuzzy approach. A numeric sample is provided to clarify the qualification of the suggested approach and compare the results with other techniques, which are solved by using a computer application to test the algorithm of the above method, indicating that the results obtained by the fuzzy environment are promising.

Efficient Ranking Function Methods for Fully Fuzzy Linear Fractional Programming problems via Life Problems

In this paper, we propose two new ranking function algorithms to solve fully fuzzy linear fractional programming (FFLFP) problems, where the coefficients of the objective function and constraints are considered to be triangular fuzzy numbers (TrFN) s. The notion of a ranking function is an efficient approach when you want to work on TrFNs. The fuzzy values are converted to crisp values by using the suggested ranking function procedure. Charnes and Cooper’s method transforms linear fractional programming (LFP) problems into linear programming (LP) problems. The suggested ranking functions methods' applicability to actual problems of daily life, which take data from a company as an example, is shown, and it presents decision-making and exact error with the main value problem. The study aims to find an efficient solution to the FFLFP problem, and the simplex method is employed to determine the efficient optimal solution to the original FFLFP problem.

Mehar approach to solve fuzzy linear fractional minimal cost flow problems

To the best of author’s knowledge, only one approach is proposed in the literature to solve fuzzy linear fractional minimal cost flow problems (minimal cost flow problems in which each known arc cost is represented either by a triangular fuzzy number or a trapezoidal fuzzy number). In this paper, the mathematical incorrect assumptions, considered in the existing approach to solve fuzzy linear fractional minimal cost flow problems, are pointed out. Also, by generalizing an existing approach for solving fuzzy linear fractional programming problems, an approach (named as Mehar approach) is proposed to solve fuzzy linear fractional minimal cost flow problems. Furthermore, two numerical examples are solved to illustrate the proposed Mehar approach.

An Efficient Algorithm for Fuzzy Linear Fractional Programming Problems via Ranking Function

In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler and easier calculations as well as shortening in the procedures. The fuzzy fractional programming problem is the first reduced to a fractional programming problem and then solved with the technique to obtain the optimal solution. It has a power to give a best solution for supporting the solution theory proposed in this work, some numerical fuzzy fractional programming problem are included to ensure the advantage, efficiency and accuracy of the suggested algorithm. In addition, this research paper describes a comparison between our optimal solutions with other existing solutions for inequalities constrains fuzzy fractional program.

A revisit of the proposed model for solving fuzzy linear fractional programming problem

Linear fractional programming (LFP) problem is used worldwide in solving real world problems. In real life situations the parameters of the problem are imprecise instead of fixed real numbers. So, a procedure for modelling these impreciseness in mathematical form is required. Fuzzy set theory is a best tool to deal with such situations. In this paper LFP problem with fuzzy parameters are studied. A fuzzy linear fractional programming (FLFP) problem is considered by Das et al. (2018) where a simple ranking approach between two triangular fuzzy numbers is provided. Then, in their study a tri-objective LFP problem is formulated to calculate the upper, middle and the lower bounds of the fuzzy optimal value. There are some errors and shortcomings in Das et al. method. Hence, in this study errors and shortcomings of Das et al. method are pointed out. Also, to overcome these errors, a simple method is presented to obtain optimal solution and fuzzy optimal value of the objective function. Moreover, by solving some numerical examples these errors are demonstrated and using the new proposed algorithm the correct optimal solution and the fuzzy optimal value of objective function are obtained.

Empirical (α, β)-acceptable optimal values to full fuzzy linear fractional programming problems

In this paper we aim to provide empirical solutions to a special class of full fuzzy linear fractional programming problems. We use trapezoidal fuzzy numbers to describe the parameters and derive empirical shape of the membership of the goal function optimal values of the problem. Our approach essentially follows the extension principle, and is based on solving crisp quadratic optimization problems. The model we propose treats in different ways, through two independent parameters, the objective function coefficients and coefficients in the constraints. To illustrate our theory, we solve a relevant instance and compare our numerical results with the numerical results recalled from the recent literature.

Interval-Type Fuzzy Linear Fractional Programming Problem in Neutrosophic Environment: A Fuzzy Mathematical Programming Approach

Interval-Type Fuzzy Linear Fractional Programming Problem in Neutrosophic Environment: A Fuzzy Mathematical Programming Approach

Fuzzy solution of fully fuzzy multi-objective linear fractional programming problems

In this study, we present a novel method for solving fully fuzzy multi-objective linear fractional programming problems without transforming to equivalent crisp problems. First, we calculate the fuzzy optimal value for each fractional objective function and then we convert the fully fuzzy multi-objective linear fractional programming problem to a single objective fuzzy linear fractional programming problem and find its fuzzy optimal solution which inturn yields a fuzzy Pareto optimal solution for the given fully fuzzy multi-objective linear fractional programming problem. To demonstrate the proposed strategy, a numerical example is provided.

An approach to optimize the cost of transportation problem based on triangular fuzzy programming problem

In this article, we address a fully fuzzy triangular linear fractional programming (FFLFP) problem under the condition that all the parameters and decision variables are characterized by triangular fuzzy numbers. Utilizing the computation of triangular fuzzy numbers and Lexicographic order (LO), the FFLFP problem is changed over to a multi-objective function. Consequently, the problem is changed into a multi-objective crisp problem. This paper outfits another idea for diminishing the computational complexity, in any case without losing its viability crisp LFP issues. Lead from real-life problems, a couple of mathematical models are considered to survey the legitimacy, usefulness and applicability of our method. Finally, some mathematical analysis along with one case study is given to show the novel strategies are superior to the current techniques.

On Solutions of Fully Fuzzy Linear Fractional Programming Problems Using Close Interval Approximation for Normalized Heptagonal Fuzzy Numbers

On Solutions of Fully Fuzzy Linear Fractional Programming Problems Using Close Interval Approximation for Normalized Heptagonal Fuzzy Numbers

Development of Unrestricted Fuzzy Linear Fractional Programming Problems Applied in Real Case

Purpose: We formulate a linear fractional programming (LFP) problem in which costs of the objective functions and constraints all are taken to be triangular fuzzy numbers. Methodology: The fuzzy LFP problem is transformed into an equivalent crisp line fractional programming (CLFP) problem by using the centroid ranking function. This proposed method is based on crisp LFP and has a simple structure. Findings: To show the efficiency of our proposed method a real life problem has been illustrated. The discussion of the practical problem will help decision makers to realise the usefulness of the CLFP problem. Value: Using centroid ranking function, we overcome the all limitations of our day to day real life problem. Finally, a result analysis is also established for applicability of our method.

Solution of fully Fuzzy Linear Fractional Programming Problem-A Simple Approach

In this paper, we discuss fully fuzzy linear fractional programming (FFLFP) problems under fuzzy nature with triangular fuzzy numbers. We recommend a simple method for the solution of FFLFP problems which preserves the fuzzy nature of the problem. The efficiency of the method proposed is illustrated with an example.