Fuzzy Variables Research Articles

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.

Time-dependent reliability of structures under consideration of fuzzy uncertainty

Time-dependent reliability (TDR) is the possibility that a structure or system under consideration can perform the intended function under specified service conditions over a given time instant under fuzzy uncertainty. This paper is mainly concerned to identify fuzzy variables, generate the membership function of the input variables and output quantities, analyze timedependent performance level, estimate the possibility safety index, and evaluate the TDR of the structures. To evaluate TDR by a possibilistic approach, the fuzzy uncertainty that is characterized by membership function is considered. The type of uncertainty defines the method of reliability analysis, i.e., aleatory uncertainty possesses a probabilistic approach, whereas epistemic uncertainty leads to a possibilistic approach. The TDR analysis of the structures subjected to sustained load and corrosion based on probability theory is well developed. On the contrary, the TDR of structures subjected to combined effects sustained load, corrosion, creep, and shrinkage based on possibility theory lack research. Thus, this paper is significant to evaluate the TDR of structures subjected to the aforementioned effects based on possibility theory. However, it requires a rigorous procedure, a single-loop optimization method (SLOM) is employed to evaluate the TDR of structures involving epistemic uncertainty. To enhance the validation of the proposed approach, several examples are thoroughly carried out.

A Systematic Decision-Making Approach for Quality Function Deployment Based on Hesitant Fuzzy Linguistic Term Sets

As a powerful tool for improving customer satisfaction, quality function deployment (QFD) can convert customer requirements (CRs) into engineering characteristics (ECs) during product development and design. Aiming to address the deficiencies of traditional QFD in expert evaluation, CRs’ weight determination and ECs’ importance ranking, this paper proposes an enhanced QFD model that integrates hesitant fuzzy binary semantic variables, the Best–Worst Method (BWM), and the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS). The objective is to determine the prioritization of product engineering characteristics. Indeed, hesitant fuzzy linguistic term sets (HFLTS) have found extensive application in decision-making problems. Compared to other fuzzy language methods, HFLTS offers greater convenience and flexibility in addressing decision-makers’ hesitations and uncertainties. Initially, the combination of hesitant fuzzy linguistic term sets with interval binary tuple language variables is employed to articulate the uncertainty in the assessment information provided by QFD team members. Subsequently, the improved BWM and TOPSIS methods based on HFLTS are used to improve the accuracy of the importance ranking of engineering characteristics by determining the weights of CRs and prioritizing ECs in two stages. Finally, the feasibility and effectiveness of the proposed method are validated through an illustrative example.

Reliability Allocation in Complex Systems Using Fuzzy Logic Modules

Reliability allocation is critical in the design of complex engineering systems. However, traditional allocation methods rely on precise failure data and have difficulty handling epistemic uncertainty. This paper proposes using fuzzy logic modules for reliability allocation in complex systems. Fuzzy logic can represent imprecise data using membership functions and incorporate expert knowledge through fuzzy rules. The methodology involves developing fuzzy logic modules for each subsystem to allocate reliability based on fuzzy input variables like failure rate and criticality. The outputs are aggregated to obtain the system level allocation. A case study demonstrates the approach and compares results against traditional methods. The fuzzy logic modules are shown to optimize reliability allocation under epistemic uncertainty. This paper demonstrates the advantages of using fuzzy logic for reliability allocation in complex systems with limited failure data. The methodology provides a new tool for reliability engineers to handle imprecise information and optimize designs.

Handling Four DOF Robot to Move Objects Based on Color and Weight using Fuzzy Logic Control

Manipulators are increasingly used in industry to improve efficiency in jobs that require precision, long duration, and repetitive work. This research was conducted on a laboratory scale to control manipulators on a pick-and-place system in the product storage and packing area. The object of this research is a four-degree-of-freedom (4-DOF) manipulator controlled using a fuzzy logic system. The hardware used is a conveyor machine to model the product delivery process, Dobot Magician as a 4-DOF manipulator, HX711 load cell serves as a weight sensor, TCS-3200 serves as a color sensor, and Arduino Mega 2560 as a controller. The software used is Dobot Studio as the main program to control the movement of the robot and Matlab to develop the Fuzzy Logic Control (FLC) function, which is embedded in the Arduino. Fuzzy logic control processes weight variables and color variables read by sensors as information data to control the movement of the manipulator. The results showed that the manipulator was able to pick up and place objects according to the path-planning coordinates. The testing data states that the precision and accuracy of the average coordinates of product pick and place against the path planning has an error deviation of 1.8%.

МЕТОД АВТОМАТИЗОВАНОЇ КЛАСИФІКАЦІЇ НАДЗВИЧАЙНИХ СИТУАЦІЙ ІЗ СУДНОМ В АКВАТОРІЇ МОРСЬКОГО ПОРТУ

The aim of the study is to develop a method that allows to improve the accuracy of classification of emergencies with a ship in the seaport area. To achieve the research objective, an improved method for automated classification of ship emergencies in the seaport area under conditions of deterministic uncertainty is proposed. The method consists of methods for formalising and processing knowledge on determining the classes of ship emergencies. The method of knowledge formalisation is based on the formation of a set of factors influencing the classification of ship emergencies in the seaport water area based on fuzzy binary relations of non-strict preference. The method of knowledge processing is based on the formation of productive rules for classifying emergencies with a ship in the seaport area according to the predicted or current values of the desired factors in a fuzzy formulation. The determination of the membership functions of several fuzzy variables to linguistic variables is based on the processing of expert data represented by a matrix of binary relations of the values of the membership function of the elements of the domain of determining linguistic variables. A comparative assessment of the classes of recognisable emergencies with a vessel in the seaport water area involves solving a multi-criteria optimisation problem using the hierarchy analysis method. As a mathematical model for determining the classes of emergency situations with a vessel in the seaport waters, the article substantiates a logical-linguistic productive hierarchical model. The process of determining the classes of emergency is described with the help of an algebraic model, which is closest to the linguistic description. In case of inexpediency of synthesis of products, it is proposed to use the method of fuzzy identification to reduce the number of product rules. The proposed method allows to improve the accuracy of classification of emergencies with a ship in the seaport area under conditions of deterministic uncertainty. Keywords: classification, maritime port, hierarchy analysis, fuzzy identification, logicallinguistic production hierarchical model, vessel, class of emergency situations, fuzzy variable, linguistic variable

Model and solution of sustainable bi-level emergency commodity allocation based on type-2 fuzzy theory

The allocation of emergency commodities is very important for efficient emergency response after a disaster. In this study, a sustainable multi-objective bi-level emergency commodity allocation model is established, providing a practical emergency commodity allocation strategy for humanitarian supply chains. First, type-2 fuzzy variables are used to describe uncertain transportation costs and handle them based on the conditional value-at-risk (CVaR) theory of type-2 fuzzy variables. Second, Karush-Kuhn–Tucker (KKT) conditions with complementary constraints are used, auxiliary variables are introduced, and global criteria are applied to achieve the equivalent transformation of the model. Finally, with the Wenchuan earthquake in China in 2008 as an example, we prove the necessity of introducing the CVaR for risk measurement and the practicability of using type-2 fuzzy variables to describe uncertain parameters by comparing this scenario with a risk-neutral situation and the proposed model with a model based on type-1 fuzzy theory. The novelties of this study include considering both the government and suppliers are decision-makers, exploiting CVaR to measure tail risk and using type-2 fuzzy theory to transform uncertain parameters. The contributions of this study include considering sustainability during the rescue process and proposing a CVaR formula based on type-2 theory.

A multi-period optimization model for medicine supply chains using modified interactive multi-objective fuzzy programming

The research on multi-period optimization using modified interactive multi-objective fuzzy programming for product complaints in pharmaceutical supply chains is new and evolving. This study proposes and develops an integrated multi-period, multi-objective medicine supply chain model in healthcare. The study considers an unknown number of drug manufacturer complaints. The business triad is a term used to describe the combination of the three objectives: time, quality, and cost. The process starts with developing a mathematical model for the business triad. A modified interactive multi-objective fuzzy programming is then proposed for the optimization of the business triad, has been proposed. The proposed method blends expert opinion and experience using fuzzy linguistic variables and a triangle membership function. A numerical example demonstrates the practical application of the proposed model. This study considers a model for fuzzy inventory pharmaceutical products with a two-tier supply chain. This supply chain model aids healthcare decision-makers in acquiring medications that meet the necessary time, quality, and cost standards.

Fuzzy logic control for watering system

A two-dimensional finite element (FEM) model was developed to simulate water propagation in soil during irrigation. The first dimension was water distribution depth in soil, and the second dimension was time. The developed model was tested by analyzing water distribution in a conventional (clock-controlled) irrigation model. The values in the conventional model were calculated based on the literature. The results were consistent with the results obtained from the model. In the next step, a fuzzy logic model for irrigation control was developed. The input variables were ambient temperature, soil moisture content and time of day (which is related to solar radiation and evapotranspiration), and the output variable was irrigation intensity. The fuzzy logic control (FLC) model was tested by simulating water distribution in soil and comparing water consumption in both models. The study demonstrated that the depth of the soil moisture sensor affected water use in the fuzzy logic-controlled irrigation system relative to the conventional model. Water consumption was reduced by around 12% when the soil moisture sensor was positioned at an optimal depth, but it increased by around 20% when sensor depth was not optimal. The extent to which the distribution of fuzzy variables affects irrigation performance was examined, and the analysis revealed that inadequate distribution of fuzzy variables in the irrigation control system can increase total water consumption by up to 38% relative to the conventional model. It can be concluded that a fuzzy logic-controlled irrigation system can reduce water consumption, but the system’s operating parameters should be always selected based on an analysis of local conditions to avoid an unintended increase in water use. A well-designed FLC can decrease water use in agriculture (thus contributing to rational management of scarce water resources), decrease energy consumption, and reduce the risk of crop pollution with contaminated groundwater.

Deconvolution-based methods to extract uncertainty components

A measurement result is supposed to provide information about the distribution of values that could reasonably be attributed to the measurand. However, in general, it provides the distribution of values returned by the employed measuring system, when the measurand is given as the input quantity to this system. This distribution of values is mathematically given by the convolution of two probability density functions (PDFs): the one representing the actual distribution of values of the measurand and the one representing the uncertainty contribution of the employed measuring system. In principle, if the uncertainty contribution of the measuring system is known, the distribution of values that could reasonably be attributed to the measurand can be obtained by applying a proper deconvolution algorithm: this distribution is, indeed, the one of interest in any industrial measurement process. Similarly, if the PDF representing the distribution of values of the measurand is known, the PDF representing the uncertainty contribution of the measuring system to the resulting distribution of values returned by the instrument can be obtained by applying a proper deconvolution algorithm: this distribution is, indeed, the one of interest when a calibration is performed. In practical situations, deconvolution algorithms provide rather inaccurate results when applied to PDFs, especially when they are experimentally obtained from histograms of collected data. This paper proposes a deconvolution method, based on the use of Fuzzy variables (or Possibility Distributions) to represent distribution of values, which proves to provide much more accurate results. Simulation results, as well as experimental results are discussed to validate the proposed method.

Modified sharp regression discontinuity model to settings with fuzzy variables

ObjectiveThe goal of this study is to develop a Modified Sharp Regression Discontinuity model to predict alcohol consumption in People Living with Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS). Previous studies focused on either fuzzy dependent or fuzzy independent variables separately. However, there is a gap in research that examines the interaction between both types of fuzzy variables thus the model considers both dependent and independent fuzzy variables.MethodsA statistical model was developed to predict the relationship between alcohol consumption and HIV progression. The model equations are solved numerically using parametric estimation.ResultsIn simulation studies, as the sample size expanded, the estimates derived from the modified sharp regression discontinuity model exhibited probabilistic convergence towards the true value, thereby validating the estimator of the Average Causal Effect’s consistency. Counseling has an average causal effect in the sharp Regression Discontinuity Design (RDD) for compliers that is roughly equal to 0.199. This was the variation in Alcohol Use Detective Identification Test (AUDIT) threshold scores or the change in intercept scores when counseling was effective. Following six months of participation in the counseling program, AUDIT scores decreased, leading to an increase in Cluster of Differentiation 4 (CD4) counts and a decrease in viral loads.ConclusionThe Modified Sharp RDD offers a robust approach to handle fuzzy variables in causal inference. Our study contributes to the advancement of RDD methodology and its applicability in real-world settings with uncertain data.

Multiple-factor optimistic value based model and parameter estimation for uncertain portfolio optimization

In the traditional portfolio models, the return rates of risky assets are usually defined as random variables or fuzzy variables. However, when some events such as financial crises or wars occur that can cause instability in financial markets, the results of these assumptions are not always satisfactory. Therefore, some scholars try to use uncertain variables to express the return rates. In this paper, a two-factor uncertain portfolio problem under optimistic value criteria is studied, where we use the optimistic value instead of expected value to describe the investment return and study the impact of economic circumstance factor and corporation’s specificity factor on the return rates. Firstly, a two-factor optimistic value-variance-entropy model with background risk is constructed, in which the total investment return consists of the risky asset return and the background asset return. Then, considering the investors with two kinds of risk preferences, a three-step method is applied to convert the bi-objective optimization model. Moreover, a moment estimation method is used to process the expert-estimated data on the return rates. Finally, a numerical simulation is presented for showing the applicability of our models and solution method.

Optimal decisions for selling on an online group buying platform in a competitive fuzzy game environment

Online group buying platforms (OGBPs) as a new form of e-commerce, offer a new channel for vendors to provide discounts on assorted services through promotion, and attract new customers with the opportunity to experience their services. This paper is conducted based on genuine issues observed in OGBPs where a vendor decides to advertise its service by offering a discount coupon on an OGBP. Accordingly, we propose a fuzzy, dual-channel supply chain, with one OGBP and one vendor who sells her/his service through both offline and online channels. Considering the cognitive uncertainty of parameters in a supply chain, all parameters of the problem are specified as fuzzy variables based on experts’ opinions. This paper develops a demand function of online customers depending on online and offline prices, sales period on the OGBP and vendor's credibility. The vendor's credibility is also affected by service level and advertisements. Furthermore, in the competitive OGB market, two game structures, i.e., a centralized model and a decentralized model called as OGBP-leader Stackelberg, are considered under different refunding and revenue sharing scenarios of unredeemed coupons. By comparing these scenarios, the purpose of this paper is to examine the optimal approach for OGBP’s pricing strategy and vendor’s decisions. Expected value models are developed to evaluate how members decide commission price, online price, service quality, and sales period of a service in each scenario. According to the results, the vendor or OGBP that provide a full refund to the customers maximizes the expected profits compared to No-refund policy; sharing the entire revenue from the coupons sales with the vendor increases the commission price. This increases the online price and reduces the quality, sales period and expected profits; the vendor's generosity, meaning providing a refund to customers and earning revenue from redeemed coupons, is in favor of both the vendor and OGBP; and we investigate the impact of quality and credibility factors under a fuzzy environment on optimal profits.

Statistical inference on quantiles of two independent populations under uncertainty

Statistical inference is the process of drawing conclusions about underlying population(s) using sample data to either confirm or falsify hypotheses. However, the complexity of real-life problems often makes the underlying statistical models inadequate, as information is often imprecise in many respects. To address this common problem, some papers have been published on modifications and extensions of test concepts by employing tools of fuzzy statistics. In this paper, we present a non-parametric test for the difference between quantiles of two independent populations based on fuzzy random variables. For this purpose, we consider the fuzzy quantile function and its estimation based on alpha -values of fuzzy random variables. We then provide a fuzzy test based on the fuzzy empirical distribution function for the difference of fuzzy order statistics from these independent populations. We also suggest a specific degree-based criterion to compare the fuzzy test statistics at a specific significance level to decide whether the underlying fuzzy null hypothesis can be rejected or not. The effectiveness of the proposed two-sample test on quantiles is investigated via numerical examples.

Fuzzy Economic Order Quantity (EOQ) Model Through Fractional Backorder

This paper has analyzed fuzzy EOQ model through fractional back order for inventory system. Here, under function principle, fuzzy entire behavior cost of the model is calculated. The ideal EOQ is derived through median rule. This approach can be very helpful when the precise data of Fuzzy variables is unavailable. In this paper for recommended fuzzy EOQ model, the ideal resolution for the proposed fuzzy EOQ model is slightly greater than the economic order quantity (EOQ) in crisp value because of the scarcity of data. Partial backorder of fuzzy system, Setup and interrelated mechanism for implementation of fuzzy set for inventory system with partial backorder, A numerical example and conclusion are described in different sections.

An application of generalized symmetric type-2 intuitionistic fuzzy variables to a transportation problem with the effect of a new ranking function

The primary objective of this study is to establish and introduce generalized symmetric type-2 intuitionistic fuzzy set, a type-2 fuzzy set extension. The major goal of such an extension is to enable the concept of fuzzy outranking relation which is known as foot print of uncertainty (FOU) to be employed in generalized symmetric type-2 intuitionistic fuzzy number (GST2IFN) for the first time. This is interesting to deal this GST2IFNs and it is complicated to find the equivalent crisp quantities due to this special structure. Hence, we have introduced a new ranking function using the mean level set of membership and non-membership functions. Besides, the arithmetic operations of the GST2IFNs are discussed. To express the effectiveness and application of the proposed GST2IF variables, a transportation problem (TP) is formulated with all cost parameters are GST2IFNs. In addition, few different algorithmic approaches are applied to find the initial basic feasible solution (IBFS) and optimal solution of the TP. Finally, the feasibility and richness of the obtained optimal solution is discussed.

Investment Decision Making in Digital Business Using Tsukamoto Fuzzy Logic

This research investigates the application of Tsukamoto's Fuzzy Logic in investment decision making in a digital business context. By integrating human knowledge and numerical data, this method seeks to overcome the challenges of complexity and uncertainty that often arise in the fast-changing digital business environment. Through analysis of case studies and interviews with industry practitioners, this study identifies the steps for implementing effective Tsukamoto Fuzzy Logic, including the formation of fuzzy variables, determination of membership functions, application of fuzzy rules, and defuzzification processes. The results of Tsukamoto's Fuzzy Logic calculations are applied to digital investment cases, providing an overview of investment quality based on various input variables. This research shows that this method can produce a holistic and informative approach in making investment decisions. In addition, the diverse participation of practitioners in various regions provides valuable insights in dealing with the uncertainties of digital business. In this challenging digital era, this research provides guidance for decision makers in dealing with the complexities of a dynamic business environment.

A Proposed DEA Window Analysis for Assessing Efficiency from Asymmetry Dynamic Data

Nowadays, one of the main challenges facing production management is how to enhance the performance of manufacturing processes by utilizing asymmetry input and output data. This research, therefore, developed a framework for window analysis in data envelopment analysis (DEA) for evaluating the overall technical efficiencies from asymmetry dynamic input and output data. The framework was applied to assess the technical (TE), managerial (PTE), and scale (SE) efficiencies of a blowing machine under three fuzzy input variables (planned production quantity, number of defectives, and idle time) and a fuzzy output variable (actual or target production quantity). The efficiency measures were then evaluated for all DMUs at low (L), middle (M), and high (H) data levels. The obtained optimal fuzzy efficiencies were then transformed into a single crisp optimal efficiency. The results showed that all seven DMUs of the blowing machine were technically inefficient. The input and output slacks were estimated and utilized to determine the necessary improvement actions. Improvement results revealed that the optimal TE, PTE, and SE were significantly improved, which may result in significant savings in production and quality costs. In conclusion, the proposed framework is effective in improving the efficiency of the blowing process and can be utilized for efficiency assessment in a wide range of applications.

Augmented first-order reliability method for estimating fuzzy failure probabilities

This paper presents an approach for estimating the fuzzy failure probability associated with reliability problems where uncertainty is characterized through random variables whose distribution parameters are described as fuzzy variables. The main contribution of this work is addressing such problem with the First-Order Reliability Method, with some minor modifications. The epistemic uncertainty is addressed by resorting to an augmented reliability problem. In this way, a single reliability analysis suffices for estimating the membership function associated with the fuzzy failure probability. Numerical results suggest that the proposed approach is most useful for providing an estimate of the membership function associated with the failure probability with reduced numerical costs.

Fuzzy Structural Analysis Using Improved Jaya-based Optimization Approach

A new approach to performing the α-level optimization in the fuzzy analysis of structural systems is developed in this study. The method uses a simple global optimizer, the Jaya algorithm, together with an innovative dimension reduction technique. The dimension reduction technique aims to transform the original large α-level optimization problem into a low-dimension one by making use of the monotonic behavior of the system output with respect to the input variables. Then, the Jaya algorithm is applied to solve the reduced max/min α-level optimization problems to determine the bounds of the fuzzy output. Two numerical examples, including a 2D truss and a 3D truss, with a relatively large number of fuzzy input variables are analyzed and the fuzzy displacements under static loads are predicted. It is demonstrated that the proposed approach can save a significant computational amount and also estimate the fuzzy displacement with high accuracy.