Fuzzy Linear Programming Problems Research Articles

Fuzzy linear programming with the intuitionistic polygonal fuzzy numbers

In real world applications, data are subject to ambiguity due to several factors; fuzzy sets and fuzzy numbers propose a great tool to model such ambiguity. In case of hesitation, the complement of a membership value in fuzzy numbers can be different from the non-membership value, in which case we can model using intuitionistic fuzzy numbers as they provide flexibility by defining both a membership and a non-membership functions. In this article, we consider the intuitionistic fuzzy linear programming problem with intuitionistic polygonal fuzzy numbers, which is a generalization of the previous polygonal fuzzy numbers found in the literature. We present a modification of the simplex method that can be used to solve any general intuitionistic fuzzy linear programming problem after approximating the problem by an intuitionistic polygonal fuzzy number with n edges. This method is given in a simple tableau formulation, and then applied on numerical examples for clarity.

Формирование оптимального кредитного портфеля с использованием нечётко-множественного подхода

The problem of profit maximization from lending to a financial organization is considered. A set of loan con-tracts forms a loan portfolio, which makes it possible to use the portfolio theory in the study of the designated problem. We will consider the formation of a loan portfolio as the formation of an investment portfolio. The problem arises of redistributing the funds of the investment portfolio in order to minimize its possible risk and maximize profitability. This problem in classical formulation can be solved according to Markowitz risk diversification. Thus, the problem of risk minimization and profitability maximization from lending to a financial institu-tion can be represented as a fuzzy mathematical programming problem, and more specifically, as a fuzzy linear programming problem. The resulting problem is solved by considering discrete α-levels and is reduced to a set of linear programming problems constructed for each of them. A clear expected optimal solution can be obtained by applying the defuzzification method, which allows you to convert a fuzzy set into a crisp number.

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.

An Alternative Method for Finding the Critical Path of the Network in Fuzzy Time Cost Trade off Problem

Background : The critical path approach is used to determine the network's longest path, according to historical records. This study examines a different approach to determining the construction network's longest path. Method: Here, the network is viewed as a directed acyclic graph, and the critical path of the network is found using the longest path algorithm of the network. To find the best answer for a building project, the longest path that was found was integrated into a linear programming issue. The triangle fuzzy variable defines all of the project's inputs. The 992 square foot building area is incorporated, and three project manager’s quotes are used as a triangular fuzzy variable. Findings : This work has the options of getting quotation from the project managers, convert them as the fuzzy variables such as triangular fuzzy variable, Trapezoidal fuzzy variable and pentagonal fuzzy variable. After the network is converted into a linear programming problem using the fully fuzzy mathematical model, the best possible solution is found. Novelty and applications : Alternative method for critical path of the network has been incorporated. It has been found that the proposed method reduces the time to find the critical path of the larger networks. Keywords: Directed Acyclic Graph, Longest Path Algorithm, Triangular Fuzzy Variable, Fuzzy Linear Programming Problem, Fully Fuzzy Mathematical Model

New methods for fuzzy linear programming problem based on heptadecagonal fuzzy number

New methods for fuzzy linear programming problem based on heptadecagonal fuzzy number

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>

Employing Novel Ranking Function for Solving Fully Fuzzy Fractional Linear Programming Problems

Fuzzy programming is especially useful in cases where the coefficients are ambiguous. Because of this feature, in recent years, numerous techniques have emerged for addressing uncertainty. This paper proposes a novel ranking function technique with variables of type decagonal fuzzy numbers for solving fully fuzzy fractional linear programming (FFFLP) problems. This technique is dependent on introducing a new membership function for a decagonal fuzzy number and using a fully fuzzy simplex method. After converting the FFFLP problem to the fully fuzzy linear programming (FFLP) problem by a complementary method, then solved with the fully fuzzy simplex tables, in which all the values are fuzzy decagonal numbers. With the aid of the arithmetic operations of decagonal numbers, the new iteration of the simplex table is reached. Steps are repeated until the optimal fuzzy solution is reached. To demonstrate the proposed method a numerical example is provided to illustrate the steps of finding an optimal fuzzy solution to the problem.

Triangular Intuitionistic Fuzzy Linear Programming Problem with a New Ranking Method based on Correlation Coefficient

Triangular Intuitionistic Fuzzy Linear Programming Problem with a New Ranking Method based on Correlation Coefficient

Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized “min” Operator

Solving optimization problems in a fuzzy environment is an area widely addressed in the recent literature. De-fuzzification of data, construction of crisp more or less equivalent problems, unification of multiple objectives, and solving a single crisp optimization problem are the general descriptions of many procedures that approach fuzzy optimization problems. Such procedures are misleading (since relevant information is lost through de-fuzzyfication and aggregation of more objectives into a single one), but they are still dominant in the literature due to their simplicity. In this paper, we address the full fuzzy linear programming problem, and provide solutions in full accordance with the extension principle. The main contribution of this paper is in modeling the conjunction of the fuzzy sets using the “product” operator instead of “min” within the definition of the solution concept. Our theoretical findings show that using a generalized “min” operator within the extension principle assures thinner shapes to the derived fuzzy solutions compared to those available in the literature. Thinner shapes are always desirable, since such solutions provide the decision maker with more significant information.

Multidimensional solution of fuzzy linear programming

There are several approaches to address fuzzy linear programming problems (FLPP). However, due to using standard interval arithmetic (SIA), these methods have some limitations and are not complete solutions. This article establishes a new approach to fuzzy linear programming via the theory of horizontal membership functions and the multidimensional relative-distance-measure fuzzy interval arithmetic. Furthermore, we propose a multidimensional solution based on the primal Simplex approach that satisfies any equivalent form of FLPP. The new solutions of FLPP are also compared with the results of existing methods. Some numerical examples have been illustrated to show the efficiency of the proposed method.

An optimization method to solve a fully intuitionistic fuzzy non-linear separable programming problem

This paper presents an optimization method to solve a non-linear separable programming problem with coefficients and variables as generalized trapezoidal intuitionistic fuzzy numbers. Such optimization problems are known as fully intuitionistic fuzzy non-linear separable programming problems. The optimization method is based on the linear approximation of fully intuitionistic fuzzy non-linear separable functions. The concept of an intuitionistic fuzzy line segment between two intuitionistic fuzzy points is introduced to find the required linear approximation. In this way, a fully intuitionistic fuzzy non-linear programming problem is converted into an intuitionistic fuzzy linear programming problem. The defuzzification and component-wise comparison techniques are then used to convert the fully intuitionistic fuzzy linear programming problem to a linear programming problem with crisp coefficients which can then be solved by using traditional optimization techniques. The application of the proposed approach in an investment problem faced by a businessman has been presented.

Optimal Solution for Fully Spherical Fuzzy Linear Programming Problem

Optimal Solution for Fully Spherical Fuzzy Linear Programming Problem

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.

Mehar approach to solve hesitant fuzzy linear programming problems

Mehar approach to solve hesitant fuzzy linear programming problems

Study of Fuzzy Integer Linear Programming Problems (IFLPP) and Simplex Method

In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear programming problems with triangular fuzzy numbers. A computational method for solving fully fuzzy linear programming problems (FFLPP) is proposed, based upon the new Ranking function. The proposed method is very easy to understand and to apply for fully fuzzy linear programming problems occurring in real life situations as compared to the existing methods. To illustrate the proposed method numerical examples are solved.

Developing solution algorithm for LR-type fully interval-valued intuitionistic fuzzy linear programming problems using lexicographic-ranking method

Developing solution algorithm for LR-type fully interval-valued intuitionistic fuzzy linear programming problems using lexicographic-ranking method

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.