Fuzzy Linear Programming Research Articles

Comparative Study of R Programming and Lingo Software in Fully Fuzzy Linear Programming Problems

Authors: The paper begins with an introduction to the concept of fuzzy optimization, providing an in-depth explanation of its significance and applications. It then proceeds to define two distinct ranking functions that is Yager’s and vR – ranking functions within the context of fuzzy optimization along with the properties of vR- ranking function. Following this, a comprehensive overview of Lingo software and R programming is presented, delving into their respective features and capabilities. This paper further delves into a detailed comparison of Lingo and R programming, offering a thorough exploration of their strengths and limitations through the use of example problems. These examples illustrate the process of computing optimal solutions for fully fuzzy linear programming problems using both Lingo and R programming, providing a comprehensive and practical comparison of their effectiveness in this context.

Addressing Fuzzy Linear Programming Problems Through Ranking Functions

In contemporary decision-making, reliance on information is paramount, yet much of it is fraught with uncertainty, making logical decision-making challenging. To tackle this uncertainty, various methods, including the use of fuzzy numbers, have been employed. This paper specifically delves into addressing linear programming (LP) problems characterized by fuzzy coefficients in the objective function, fuzzy values in the right-hand side, and fuzzy coefficients of constraints. The proposed approach involves employing linear ranking functions such as Maleki, Campos, Yager’s F1 and Yager linear ranking functions to solve these fuzzy linear programming (FLP) problems and attain optimal solutions. Furthermore, the paper elucidates the resolution steps through the presentation of numerical examples, in this study, a comprehensive methodology is presented for effectively addressing a wide range of linear programming problems.

Parametric Optimization for Fully Fuzzy Linear Programming Problems with Triangular Fuzzy Numbers

This paper presents a new approach for solving FFLP problems using a double parametric form (DPF), which is critical in decision-making scenarios characterized by uncertainty and imprecision. Traditional linear programming methods often fall short in handling the inherent vagueness in real-world problems. To address this gap, an innovative method has been proposed which incorporates fuzzy logic to model the uncertain parameters as TFNs, allowing for a more realistic and flexible representation of the problem space. The proposed method stands out due to its integration of fuzzy arithmetic into the optimization process, enabling the handling of fuzzy constraints and objectives directly. Unlike conventional techniques that rely on crisp approximations or the defuzzification process, the proposed approach maintains the fuzziness throughout the computation, ensuring that the solutions retain their fuzzy characteristics and better reflect the uncertainties present in the input data. In summary, the proposed method has the ability to directly incorporate fuzzy parameters into the optimization framework, providing a more comprehensive solution to FFLP problems. The main findings of this study underscore the method’s effectiveness and its potential for broader application in various fields where decision-making under uncertainty is crucial.

A fuzzy multi-criteria decision-making for optimizing supply chain aggregate production planning based on cost reduction and risk mitigation

In an increasingly complex and uncertain business environment, decision makers require robust strategies for supply chain aggregate production planning that account for the interdependencies and coordination across multiple echelons of the supply chain network. Traditional approaches often inadequately address the uncertainties and risks inherent in supply chain operations, leading to suboptimal performance and increased costs. This study introduces a business model incorporating open innovation dynamics to achieve cost-effectiveness and resilient supply chain performance in the face of uncertainties. A Multi-Objective Fuzzy Linear Programming model was proposed by integrating the Chance-Constraint Programming and Zimmermann’s approach designed to assist decision makers in optimizing the production plan, material flows and resource allocation across the entire supply chain network. The model focuses on both cost and risk minimization based on unsymmetrical triangular fuzzy numbers. Specifically, it targets the downside risk of uncertainty, aiming to reduce the likelihood of negative outcomes or financial losses due to fluctuations, unpredictability, and unforeseen circumstances, which can drive-up supply chain operation costs. The efficacy of the model is demonstrated through a case study. It highlights various imprecise factors such as costs, customer demands, and machine operating hours. The findings underscore the model's capability to provide decision makers with a comprehensive supply chain aggregate production plan that not only optimizes the supply chain network and enhances operational efficiency and reliability but also significantly reduces costs and mitigates unsymmetrical skewness of risks associated with operational uncertainties.

Load shedding in islanded microgrid using fuzzy linear programming

Load shedding in islanded microgrid using fuzzy linear programming

Sensitivity Analysis for Fuzzy Linear Programming Problem by Mehar Method

Numerous manufacturing companies face significant financial setbacks due to excessive raw material costs, low profits, and no taxes on imported goods. The production companies also suffer from uncertainty concerning expenses, production levels, sales figures, and the accessibility of raw materials. Therefore, in our study, we developed an innovative method to design a fuzzy linear programming model customised for the Doura Refinery of the Middle Refineries Company. We emphasised five essential products: white oil, naphtha, light puffs, heavy Jet, and liquid gas. The main goal of our approach was to achieve optimal decision-making by identifying the most favourable production quantities and evaluating the corresponding net income derived from product sales. Following the Mehar method, we employed a methodology that converts the fuzzy linear programming problem into a standard linear programming problem. Subsequently, we conducted a sensitivity analysis, focusing only on the impact of fuzzy cost changes, and successfully derived optimal solutions for this case. Therefore, we aim to resolve the challenges of fuzzy linear programming and explore how

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

البرمجة الضبابية مفيدة بشكل خاص في الحالات التي تكون فيها المعاملات غامضة. بسبب هذه الميزة ، في السنوات الأخيرة ، ظهرت العديد من التقنيات لمعالجة عدم اليقين. يقترح هذا البحث تقنية دالة ترتيب جديدة مع متغيرات من نوع الأرقام الضبابية العشرية لحل مشاكل البرمجة الخطية الكسرية الضبابية التامة (FFFLP). تعتمد هذه التقنية على إدخال دالة رتبية جديدة لرقم ضبابي عشري ، واستخدام الطريقة المبسطة الضبابية التامة. بعد تحويل مشكلة FFFLP إلى مشكلة البرمجة الخطية الضبابية التامة (FFLP) باستخدام الطريقة التكميلية ، ثم يتم حلها باستخدام الجداول المبسطة الضبابية التامة ، والتي تكون فيها جميع القيم أرقامًا عشرية ضبابية. بمساعدة العمليات الحسابية للأرقام العشرية ، يتم الوصول إلى التكرار الجديد للجدول البسيط. يتم تكرار الخطوات لحين الوصول إلى الحل الضبابي الأمثل. ولبيان الطريقة المقترحة، يتم تقديم مثال عددي يوضح خطوات ايجاد الحل الضبابي الأمثل للمشكلة.

A Methodology for Solving Fuzzy Linear Programming Problem as a Fuzzy Linear Complementarity Problem

A Methodology for Solving Fuzzy Linear Programming Problem as a Fuzzy Linear Complementarity Problem

Multi‐objective interval type‐2 fuzzy linear programming problem with vagueness in coefficient

AbstractOne of the most widely used fuzzy linear programming models is the multi‐objective interval type‐2 fuzzy linear programming (IT2FLP) model, which is of particular importance due to the simultaneous integration of multiple criteria and objectives in a single problem, the fuzzy nature of this type of problems, and thus, its closer similarity to real‐world problems. So far, many studies have been done for the IT2FLP problem with uncertainties of the vagueness type. However, not enough studies have been done regarding the multi‐objective interval type‐2 fuzzy linear programming (MOIT2FLP) problem with uncertainties of the vagueness type. As an innovation, this study investigates the MOIT2FLP problem with vagueness‐type uncertainties, which are represented by membership functions (MFs) in the problem. Depending on the localisation of vagueness in the problem, that is, vagueness in the objective function vector, vagueness in the technological coefficients, vagueness in the resources vector, and any possible combination of them, various problems may arise. Furthermore, to solve problems with MOIT2FLP, first, using the weighted sum method as an efficient and effective method, each of the MOIT2FLP problems is converted into a single‐objective problem. In this research, these types of problems are introduced, their MFs are stated, and different solution methods are suggested. For each of the proposed methods, the authors have provided an example and presented the results in the corresponding tables.

An integrated control model (chemical and biological) via fuzzy linear programming for \textit{Spodoptera frugiperda} (Lepidoptera: Noctuidae)

This paper proposes an integrated control model that enables the pesticide use according to the prey density and the insertion of the natural enemy, the predators, by fuzzy linear programming. The fall armyworm Spodoptera frugiperda (Lepidoptera: Noctuidae) is one of the main resistant pests of corn, which can cause damage to the productivity up to 34%. The control is strictly chemical.

A five-phase combinatorial approach for solving a fuzzy linear programming supply chain production planning problem

A five-phase combinatorial approach for solving a fuzzy linear programming supply chain production planning problem

Mathematical Modeling on Integrated Vehicle Assignment and Rebalancing in Ride-hailing System with Uncertainty Using Fuzzy Linear Programming

The general public frequently uses taxis as local transportation to get from one location to another. Ride-hailing is an innovation in taxi services that lets customers use their smartphones to find drivers, find prices, and submit requests. The two parts of ride-hailing are vehicle assignment and rebalancing. The task of the assignment is to allocate resources as efficiently as possible to fulfil demand. Demand and supply in the area are brought into balance through the rebalancing process. The rebalancing step is frequently carried out independently of the assignment process in ride-hailing pickup systems. However, it can be integrated into a single optimization process to improve system performance. The linear programming approach can integrate assignment and rebalancing. The batch assignment is an assignment algorithm in which each supply and demand is collected within a specific time window. The assignment is done after the vehicles and requests are collected. Fuzzy linear programming is used to deal with environmental uncertainty. Uncertain demand can reduce the reliability of ride-hailing pickup systems in addressing the problem of allocating empty vehicles to areas of high demand. The pickup time may change over time due to traffic conditions. Assignment integration and rebalancing modelling with fuzzy parameters are carried out to obtain a ride-hailing pickup system model that can handle demand uncertainty, pickup travel time, and travel delay times and increase the ride-hailing effectiveness of the pickup system. Numerical simulations were carried out on the assignment and rebalancing integration model without and with uncertainty parameters—numerical simulations based on publicly available taxi travel request data. The model selection for the ride-hailing system can be determined based on the numerical simulation results. This research can potentially advance and expand knowledge, especially in transportation.

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.

Optimization of Production of Cendol Dawet Ice and Doger Ice on Pakde Carts Using Fuzzy Linear Programming

Optimization of Production of Cendol Dawet Ice and Doger Ice on Pakde Carts Using Fuzzy Linear Programming

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.

Synergizing economic growth and carbon emission reduction in China: A path to coupling the MFLP and PLUS models for optimizing the territorial spatial functional pattern

Carbon emissions caused by economic growth are the main cause of global warming, but controlling economic growth to reduce carbon emissions does not meet China's conditions. Therefore, how to synergize economic growth and carbon emission reduction is not only a sustainable development issue for China, but also significant for mitigating global warming. The territorial spatial functional pattern (TSFP) is the spatial carrier for coordinating economic development and carbon emissions, but how to establish the TSFP of synergizing economic growth and carbon emission reduction remains unresolved. We propose a decision framework for optimizing TSFP coupled with the multi-objective fuzzy linear programming and the patch-generating land use simulation model, to provide a new path to synergize economic growth and carbon emission reduction in China. To confirm the reliability, we took Qionglai City as the demonstration. The results found a significant spatiotemporal coupling between TSFP and the synergistic states between economic growth and carbon emission reduction (q ≥ 0.8220), which resolves the theoretical uncertainty about synergizing economic growth and carbon emission reduction through the path of TSFP optimization. The urban space of Qionglai City in 2025 and 2030 obtained by the decision framework was 6497.57 hm2 and 6628.72 hm2 respectively, distributed in the central and eastern regions; the rural space was 60,132.92 hm2 and 56,084.97 hm2, concentrated in the east, with a few located in the west; and the ecological space was 71,072.52 hm2 and 74,998.31 hm2, mainly located in the western and southeastern areas. Compared with the TSFP in 2020, the carbon emission intensity of the TSFP obtained by the decision framework was reduced by 0.7 and 4.7 tons/million yuan, respectively, and realized the synergy between economic growth and carbon emission reduction (decoupling index was 0.25 and 0.21). Further confirming that TSFP optimization is an effective way to synergize economic growth and carbon emission reduction, which can provide policy implications for coordinating economic growth and carbon emissions for China and even similar developing countries.

Forest Carbon Sequestration Based on Time Series Analysis and Fuzzy Linear Programming Model

Forest Carbon Sequestration Based on Time Series Analysis and Fuzzy Linear Programming Model

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