Fuzzy Mathematical Programming Research Articles

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.

Optimisasi Portofolio Saham Syariah dengan Pendekatan Fuzzy Goal Programming

This study discusses about solving the problem of stock portfolio optimization. The portfolio optimization problem can be modeled as a multiobjective model with two objective functions, they are maximizing return and minimizing risk. This study uses the mean-variance Markowitz model to model the portfolio. The fuzzy goal programming approach is used to solve stock portfolio problems by converting a multi-objective model into a fuzzy mathematical programming model which is solved using a nonlinear programming method. The results of implementing the model on stocks listed on the Jakarta Islamic Index show that the best investment proportion forms an optimal portfolio according to the level of aspirations. Several different optimal portfolios can be formed using the fuzzy goal programming approach. The difference in the results of these portfolios depends on the level of aspiration of investors.

Malmquist productivity index for two-stage network systems under data uncertainty: A real-world case study.

The measurement of productivity change in decision-making units (DMUs) is crucial for assessing their performance and supporting efficient decision-making processes. In this paper, we propose a new approach for measuring productivity change using the Malmquist productivity index (MPI) within the context of two-stage network data envelopment analysis (TSNDEA) under data uncertainty. The two-stage network structure represents a realistic model for DMUs in various fields, such as insurance companies, bank branches, and mutual funds. However, traditional DEA models do not adequately address the issue of data uncertainty, which can significantly impact the accuracy of productivity measurements. To address this limitation, we integrate the MPI methodology with an uncertain programming framework to tackle data uncertainty in the productivity change measurement process. Our proposed approach enables the evaluation of productivity change by capturing both technical efficiency and technological progress over time. By incorporating fuzzy mathematical programming into the DEA framework, we model the inherent uncertainty in input and output data more effectively, enhancing the robustness and reliability of productivity measurements. The utilization of the proposed approach provides decision-makers with a comprehensive analysis of productivity change in DMUs, allowing for better identification of efficiency improvements or potential areas for enhancement. The findings from our study can enhance the decision-making process and facilitate more informed resource allocation strategies in real-world applications.

Uma Introdução a Metodologias Fuzzy para Otimização Multiobjetivo em Ambiente Incerto

This paper provides an introduction about multiobjective optimization concepts in uncertain environment with the aid of the Fuzzy Mathematical Programming paradigm. The goal is to present methodologies based on Fuzzy Mathematical Programming to solve Multiobjective Programming problems, which model optimization problems with several objective functions and, in many cases, conflicting ones. The article also presents an extensive survey of the classic bibliography in this area, such as the Evolutionary Algorithms for Multi-Objective Optimization (MOEAs), which presents a growing development of algorithms and applications in practical problems since the beginning of this century. Besides, one of the steps in modelling practical problems is to deal with the uncertainty in the real-world data and here we show some proposals that use the Fuzzy Sets Theory for this treatment.

Fuzzy Programming Approach to Solve Multi-Objective Fully Fuzzy Transportation Problem

The aim of this study is presenting the solution methodology of multi-objective fuzzy transportation problem with fuzzy decision variables, where all the input parameters and decisions variables of the programming problems are assumed to be triangular fuzzy number and triangular fuzzy decision variables respectively. Moreover the objectives under considerations are minimization of cost of transportation and minimization of shipping time under fuzzy environment. The fuzziness of the objective functions and the fuzzy constraints of the programming problem are defuzzified using the ranking function and the equality property between two fuzzy numbers, respectively. The consequent crisp multi-objective fuzzy transportation problem is tackled by employing fuzzy mathematical programming approach. Finally fuzzy decision is made after solving the resultant mathematical programming problem using LINGO(Schrage and LINDO Systems (1997)) software. Illustrative numerical example is presented in support of the proposed methodology.

A review on aggregate production planning under uncertainty: Insights from a fuzzy programming perspective

It is essential to address uncertainties in different production planning strategies, notably aggregate production planning, which is a critical medium-term strategy. In this context, uncertainties typically appear as vagueness or impreciseness, leading to the prevalent adoption of fuzzy numbers to represent uncertain attributes. However, despite its significance, no dedicated study has exclusively examined aggregate production planning from the perspective of fuzzy mathematical programming. Thus, this review analyzed the published literature on fuzzy aggregate production planning and presented a classification scheme. In this review, various digital databases were explored, yielding a selection of 44 most relevant articles. Furthermore, this study thoroughly analyzed and reported various characteristics such as modelling and solution approaches, objective functions, fuzzy attributes, membership functions, aggregate operators, etc. The review revealed that fuzzy linear programming and fuzzy goal programming were the most utilized modelling approaches, with optimization solvers and metaheuristics standing out as the predominant solution approaches. Additionally, triangular fuzzy numbers emerged as the preferred method for the crisp formulation of fuzzy numbers. This review provides valuable insights into the existing research on fuzzy aggregate production planning and offers guidance to researchers to streamline their future research endeavors.

A novel integrated approach based on best–worst and VIKOR methods for green supplier selection under multi-granularity extended probabilistic linguistic environment

With consideration for the extensive resources consumption and environmental degradation being on the rise today, implementing green development strategy to pursue both socioeconomic growth and the coordinated of environment sustainability, has become an increasingly important issue in modern enterprise supply chain operations management. Hence, the appropriate green supplier selection (GSS), viewed as a core issue in green supply chain management (GSCM), requires continuous research in this field to obtain a complete perception on GSS practices. It can be regarded as a multi-attribute group decision-making (MAGDM) problem that involves many conflict and unmeasurable evaluation criteria. In view of the superiority of multi-granularity extended probabilistic linguistic term sets (MGEPLTSs) in modeling such issues on potential ambiguity, complexity and uncertainty in actual GSS practices, we propose a novel integrated MAGDM methodology for GSS problems, by integrating the BWM (best–worst method) with the VIKOR (VIšekriterijumsko KOmpromisno Rangiranje) technique under the MGEPLTSs environment. First, by introducing the multi-granularity and probabilistic linguistic term sets, the MGEPLTSs are proposed to represent and quantify the decision information of GSCM practitioners. Then, the BWM is introduced to the MGEPLTSs environment to compute the weights of decision-making panels and evaluation attributes in GSS problems, by building the fuzzy mathematical programming model, respectively. Finally, we extend a multi-granularity extended probabilistic linguistic VIKOR method to calculate the compromise measure of alternatives considering the group utility maximization and the individual regret minimization, thereby achieving the full ranking of alternatives. A GSS case is conducted to illustrate the feasibility of the proposed approach, and the sensitivity analysis and comparative analysis with other similar approaches are presented to demonstrate its effectiveness and advantages.

An Investigation of Linear Diophantine Fuzzy Nonlinear Fractional Programming Problems

The linear Diophantine fuzzy set notion is the main foundation of the interactive method of tackling nonlinear fractional programming problems that is presented in this research. When the decision maker (DM) defines the degree α of α level sets, the max-min problem is solved in this interactive technique using Zimmermann’s min operator method. By using the updating technique of degree α, we can solve DM from the set of α-cut optimal solutions based on the membership function and non-membership function. Fuzzy numbers based on α-cut analysis bestowing the degree α given by DM can first be used to classify fuzzy Diophantine inside the coefficients. After this, a crisp multi-objective non-linear fractional programming problem (MONLFPP) is created from a Diophantine fuzzy nonlinear programming problem (DFNLFPP). Additionally, the MONLFPP can be reduced to a single-objective nonlinear programming problem (NLPP) using the idea of fuzzy mathematical programming, which can then be solved using any suitable NLPP algorithm. The suggested approach is demonstrated using a numerical example.

Collaborative emergency decision-making for public health events: An integrated BWM-TODIM approach with multi-granularity extended probabilistic linguistic term sets

Carrying out emergency rescue in coordination with multiple organizations, is of great significance for the effectiveness and timeliness of emergency response. Therefore, this study aims to extend a novel practical tool for distinguishing the optimal combination of different emergency plans in multiple organizations. In a multi-granularity extended probabilistic linguistic term sets (MGEPLTSs) environment, we propose a new collaborative emergency decision-making (CEDM) approach in the inspiration of the best–worst method (BWM) and TOmada de Decisão Iterativa Multicritério (TODIM) method. Firstly, a combined multi-granularity and extended probabilistic linguistic term sets, namely MGEPLTSs, are proposed to quantify the preferences given by decision makers (DMs) to address the issues on potential ambiguity and uncertainty in actual CEDM. Then, the BWM is introduced to the MGEPLTSs environment to compute the index weights of the individual and collaborative performance evaluation for multi-plan combinations, by building the fuzzy mathematical programming model respectively. Finally, we develop the multi-granularity extended probabilistic linguistic TODIM method to calculate the overall dominance of indexes considering the psychological behavior of DMs, thereby achieving the ranking of multi-plan combinations. A CEDM case on COVID-19 epidemic is used to illustrate the feasibility of the proposed approach, and the sensitivity analysis and comparative analysis with other similar approaches are presented to demonstrate its effectiveness and superiority.

Research on Railway Emergency Resources Scheduling Model under Multiple Uncertainties

This paper discusses the optimization of emergency resource scheduling for major railway emergencies under multiple uncertainties while considering the uncertainties in demand, reserve, and transportation costs of resources. We introduce a novel approach that integrates stochastic mathematical programming, interval parameter programming, and fuzzy mathematical programming to study uncertain parameter interactions and coupling. A two-stage interval fuzzy credibility-constrained model is established and solved using an interval interactive algorithm. Finally, through a case study on China Railway Nanchang Group Co., Ltd., the novelty and effectiveness of the proposed method for optimizing emergency resource scheduling strategies under multiple uncertainties are demonstrated.

Research on the scheduling scheme of resource storage locations in deep-sea oil and gas exploitation

Crucial components of the exploration and exploitation of deep-sea oil and gas resources include the identification of pre-disaster emergency resource storage locations and the appropriate scheduling of emergency resources. Frequently, integer linear programming or integer nonlinear programming is used to investigate them. Both techniques may result in optimization, but it is difficult to determine the global optimal solution. Consequently, this study presents a two-stage optimization model of emergency resource storage location-scheduling that not only surpasses the limitations of independent research but also applies an intelligent optimization algorithm to discover the global optimal solution. In the first phase of the model, the objective of optimization is to decrease the emergency response time. Uncertainty and unpredictability are incorporated as marine environmental components in the goal function. Using the analytic hierarchy method, the effect of resource storage and location is evaluated, and the genetic algorithm (GA) and immune algorithm (IA) are used to determine the goal model's optimal solution. The objective of the second stage is to optimize resource scheduling satisfaction, and the resource storage locations determined in the first stage are assigned using a fuzzy trigonometric function formula and mathematical programming algorithm. The two-stage optimization methodology is shown using the deep-sea fire explosion incidence as an example. The results suggest that the transit time of resources from the resource storage site selection points to the operation points calculated by GA is 50% less than that obtained by IA, and the 4 time of IA is at least 5 times that of GA. The overall resource scheduling time is lowered by 41.1% compared to conventional shore-based terminals, the economic cost of an accident is minimized, and the life safety of on-site operators is improved. Throughout 1000 different seasons, the objective ideal value and average value of GA and IA are compared. GA has a slower convergence rate than IA, but its convergence quality is much higher. The quantity of emergency supplies given by each resource storage site may meet the resource need of the operational point. We believe that the model proposed in this study can guarantee the accuracy of prediction results in situations of small sample sizes, and its validity and applicability have been validated.

Fuzzy Mathematical Programming Approach for Transportation Problem with Flexible Constraints

Fuzzy Mathematical Programming Approach for Transportation Problem with Flexible Constraints

RETRACTED: Selecting and balancing market portfolio using artificial intelligence and fuzzy multiobjective decision-making model

Most enterprises focus on product portfolio management (PPM) and exclude market portfolio management, and individual markets are selected solely based on financial performance which may not be appropriate because other factors may dictate the outcome of the market selection. This study proposes a market portfolio model that considers market share, market growth, market competition, market risk, and market cost to maximize overall profit. A three-stage approach is proposed to identify potential product markets using an AI algorithm. A set of the most promising market is then determined based on the results of Stage 1 using a fuzzy multi-objective mathematical programming model by concurrently maximizing the total market share and market growth, and minimizing the market competition and market risk. A single-objective mathematical programming model is then used to determine a market portfolio to maximize the total profit using the results for Stage 2. The single-objective model is tested using two sets of threshold constraints. The balance of the market portfolio is discussed and the results are compared. The novelty of the article: (1) the first study involves a product market portfolio, (2) the decision of market selection is scientific (using AI instead of personal judgment), holistic (factors include market share, growth, competition, risk, cost, and profit) and optimized (using mathematical optimization), and (3) the market portfolio maximizes total profit. (4) the proposed method produces a portfolio with a higher profit than the TOPSIS method.

Optimal Water Resources Allocation in the Yinma River Basin in Jilin Province, China, Using Fuzzy Programming

Being one of the most important sources of water in the Jilin Province in China, the Yinma River Basin (YRB) is facing problems of water scarcity in low economic areas and low utilization in richer areas mainly caused by the irrational allocation of water, excessive pursuit of economic benefits, and neglect of environmental problems. Restricting watershed development involves potential decision-making risks. Some scholars have used the interval two-stage stochastic planning method to adjust water resource allocation in the Drinking Horse River Basin, but the method uses historical statistics for projection and does not take into account the ambiguity and uncertainty in real planning situations. Therefore, this study addresses the problems prevalent in the allocation of water resources in the YRB through optimization using stochastic programming methods, interval and two-stage, and introduces the fuzzy mathematical programming method, with the aim of coordinating the water balance of various water-consuming sectors in the YRB, so as to reconfigure the water allocation. The goal is to solve the existing problems of irrational water allocation, reduce system risks posed by excessive economic development, mitigate water shortages in the water-consuming sectors, and alleviate potential decision-making risks and vague uncertainties associated with the allocation of water resources. Additionally, optimization of the pollution-holding capacity improvement project was carried out. The interval fuzzy two-stage model simulation developed in this study shows that the distribution of water across the different administrative regions can be reduced by up to 30% compared with the original model, effectively reducing the problem of water wastage. Post-optimization, the impact of water shortage in the water resources allocation scheme is alleviated to a significant degree, and there is no water shortage in some areas. At the same time, the eco-environmental sector has gradually taken the leading role in the distribution of water reuse among the different water-consuming sectors. The pollution-holding capacity has been enhanced, and the discharge and river entry chemical oxygen demand (COD) and ammonia nitrogen, two typical pollutants, have been reduced. The membership interval in the interval fuzzy two-stage model reflects the relationship between the possible level of the target value and the risk level. This study provides a guideline for decision makers for balancing the relationship between benefits and risks and proposes a planning scheme that is more conducive to the development of the river basin.

Green Design of Regional Wheat Supply Chains under Uncertainty

This study presents a fuzzy mathematical programming model to optimize regional wheat hub center in Iran with the aim of achieving sustainable self-sufficiency, swap and export of wheat to neighboring countries. The proposed model is developed for a 10-year planning horizon with real-world assumptions under uncertainty. By the proposed model, the optimal decisions are made on the amount of wheat cultivation areas in different provinces, capacity of silos, amount of import, swap and export of wheat, transportation mode and storage amount of wheat in different periods. Two objective functions including economic and environmental goals are optimized by the proposed model. The proposed model is examined under uncertainty conditions and the possibilistic programming approach is used to deal with the uncertainty of parameters. Finally, the presented model is validated through investigating a real case study in Iran. The results show the efficiency of the model for making optimal strategic and tactical decisions in wheat supply chains.

A Fuzzy Multi-Objective Mixed Integer Linear Programming Model for End of Life Use

One of the main challenges of designing the effective reverse logistic network is to predict the amount of product which reach end of their useful life. Thus, in this study, we propose fuzzy multi-objective mixed integer linear programming (Fuzzy-MOMILP) model which the amount of returned product is considered as an uncertain parameter. In order to solve the proposed multi objective fuzzy mathematical programming model, a fuzzy solution approach is applied. The proposed Fuzzy-MOMILP model seeks to minimize the total reverse logistic network cost and minimize the total carbon emissions related to the transportation and processing of used products. To validate the model, a case study is examined. The results of this study indicate that the proposed model can be used to design a sustainable reverse logistic network for end-of-life (EOL) products.

Optimization of Ecological Water Replenishment Scheme Based on the Interval Fuzzy Two-Stage Stochastic Programming Method: Boluo Lake National Nature Reserve, Jilin Province, China.

In this paper, a fuzzy mathematical programming method is introduced on the basis of the interval two-stage stochastic programming (ITSP) optimisation model for the wetland ecological water replenishment scheme in Boluo Lake National Nature Reserve. The minimum ecological water supply is taken as the objective function, and the lake bubble water diversion capacity, lake bubble water supply capacity, water diversion sequence, ecological service value, and minimum capacity of the wetland water supply are taken as constraints. The ecological water replenishment schemes of five lakes in the Boluo Lake National Nature Reserve are optimised at the levels of low flow years, normal flow years, and high flow years, and an optimised model for the wetland ecological water replenishment scheme in Boluo Lake National Nature Reserve based on the interval fuzzy two-stage stochastic programming (IFTSP) method is constructed. The model fully considers the waste of water resources and the protection of migratory bird habitat and makes rational allocation of water resources to make full use of flood resources. The IFTSP model proposed herein fully considers the fuzzy and uncertain characteristics of the planning area in the lake bubble area of Boluo Lake National Nature Reserve and improves the decision-making efficiency of decision-makers by providing technical support for smooth implementation of the ecological water replenishment project in nature reserves. The model can also be used as a theoretical guide for ecological recharge projects in other regions of the world.

Fuzzy Multi-Objective Linear Programming Problem Using DM's Perspective

In this paper, a two-stage method has been proposed for solving Fuzzy Multi-objective Linear Programming Problem (FMOLPP) with Interval Type-2 Triangular Fuzzy Numbers (IT2TFNs) as its coefficients. In the first stage of problem solving, the imprecise nature of the problem has been handled. All technological coefficients given by IT2TFNs are first converted to a closed interval and then the objectives are made crisp by reducing a closed interval into a crisp number and constraints are made crisp by using the concept of acceptability index. The amount by which a specific constraint can be relaxed is decided by the decision maker and thus the problem reduces to a crisp multi-objective linear programming problem (MOLPP). In the second stage of problem solving, the multi-objective nature of the problem is handled by using fuzzy mathematical programming approach. In order to explain the methodology, two numerical examples of the proposed methodology in Production planning and Diet planning problems have also been worked out in this paper.

Introducing a trapezoidal interval type-2 fuzzy regression model

The uncertainty is an important attribute about data that can arise from different sources including randomness and fuzziness, therefore in uncertain environments, especially, in modeling, planning, decision-making, and control under uncertainty, most data available contain some degree of fuzziness, randomness, or both, and at the same time, some of this data may be anomalous (outliers). In this regard, the new fuzzy regression approaches by creating a functional relationship between response and explanatory variables can provide efficient tools to explanation, prediction and possibly control of randomness, fuzziness, and outliers in the data obtained from uncertain environments. In the present study, we propose a new two-stage fuzzy linear regression model based on a new interval type-2 (IT2) fuzzy least absolute deviation (FLAD) method so that regression coefficients and dependent variables are trapezoidal IT2 fuzzy numbers and independent variables are crisp. In the first stage, to estimate the IT2 fuzzy regression coefficients and provide an initial model (by original dataset), we introduce two new distance measures for comparison of IT2 fuzzy numbers and propose a novel framework for solving fuzzy mathematical programming problems. In the second stage, we introduce a new procedure to determine the mild and extreme fuzzy outlier cutoffs and apply them to remove the outliers, and then provide the final model based on a clean dataset. Furthermore, to evaluate the performance of the proposed methodology, we introduce and employ suitable goodness of fit indices. Finally, to illustrate the theoretical results of the proposed method and explain how it can be used to derive the regression model with IT2 trapezoidal fuzzy data, as well as compare the performance of the proposed model with some well-known models using training data designed by Tanaka et al. [55], we provide two numerical examples.

A literature review on blood supply chain management focused on uncertainty: an inclusive approach

In the context of Blood Supply Chain Management, blood supply chain network design is one of the most pivotal planning problems. The stages of blood supply chain management comprise of blood collection, production, inventorying and distribution. The main challenges faced by supply channels are related to shortage, out datedness, and supply chain cost which needs to be minimized. In the current scenario, supply chain network design decisions should be flexible enough to operate under complex and uncertain business environments for many years. Decision-making under uncertainty is a crucial phenomenon and a large number of relevant publications have emphasized its importance. This paper makes an attempt towards reviewing the literature in the fields of blood supply chain network design under uncertainty. This study is organized into two phases. In the first phase, a discussion is made on the types of blood products, potential issues, and stages of blood supply chain management whereas in the second phase, an exploration is made on the optimization techniques for dealing with uncertainty such as recourse-based stochastic programming, robust optimization and fuzzy mathematical programming. The scope of the study lies with capturing the unexplored dimensions related to blood supply chain management that will serve as substantial input for upcoming researchers and practitioners in the field of supply chain management.