Fuzzy Variables Research Articles

Dynamic Supplier Selection and Its Optimal Strategy Considering Full Truck Load and Fuzzy Demand using Fuzzy Expected Value-Based Programming

This article proposes a linear integer optimization model incorporating fuzzy parameters to find the optimal solution for a dynamic supplier selection problem with uncertain demand. The uncertain demand value is represented using a fuzzy variable. A fuzzy expected value-based linear optimization solver is used to address the optimization problem, to minimize the total cost under fuzzy demand values. Several computational experiments were conducted to evaluate and analyze the model. The results show that the proposed model effectively identifies the optimal suppliers for each product. Additionally, the model determines the optimal purchase volumes for each product type from the selected suppliers, leading to the minimal total expected cost.

A Hybrid Fuzzy Mathematical Programming Approach for Manufacturing Inventory Models with Partial Trade Credit Policy and Reliability

This study introduces an inventory model for manufacturing that prioritizes product quality and cost efficiency. Utilizing fuzzy logic and mathematical programming, the model integrates fuzzy numbers to describe uncertainties associated with manufacturing costs and quality control parameters. The model extends beyond conventional inventory systems by incorporating a dynamic mechanism to halt production, employing fuzzy decision variables to optimize the economic order quantity and minimize total costs. Key innovations include the application of approaches related to graded mean integration for defuzzification and the use of Kuhn–Tucker conditions to ensure optimal solutions under complex constraints. These approaches facilitate the precise management of production rates, inventory levels, and cost factors, which are essential in achieving a balance between supply and demand. A computational analysis validates the model’s effectiveness, demonstrating cost reductions while maintaining optimal inventory levels. This underscores the potential of integrating fuzzy arithmetic with traditional optimization techniques to enhance decision making in inventory management. The model’s adaptability and accuracy indicate its broad applicability across various sectors facing similar challenges, offering a valuable tool for operational managers and decision makers to improve efficiency and reduce waste in production cycles.

Optimization of Fuzzy Mathematical Model of Regular Octagon-Shaped Parking Space

In the vigorous development of the city population, there is a need to set up clear dimensions for the parking space. Car parking plays a significant part in the residential apartments and commercial buildings. Roadside parking spaces will create a huge traffic problem if the parking lots are not properly designed. Sometimes, it leads to the accident. Hence, keeping all these causes in mind, the flexible parking space is the necessary of the time. In the proposed research work, the parking space considered in the problem is of a regular octagon shape, and the mathematical model is developed under a fuzzy environment. LINGO Optimization Software is used to solve the mathematical model and MATLAB(Matrix Laboratory) is used to define the fuzzy variable. At the outset, the results will reveal the importance of making the length of the parking lot under fuzzy environment.

Modeling and simulation of Fuzzy-rule based WBAN using multi-level fuzzy colored petri-nets and reinforcement learning

By developing IoTs (Internet of Things), a new concept is arising in WBANs (Wireless Body Area Networks), called IoBs (Internet of Bodies). WBANs are the safety-critical devices that use rule-based knowledge with fuzzy variables for monitoring patients. There are two issues with the knowledgebase: (1) appropriate knowledge representation and inference and (2) handling the situations for which there is no rule in the knowledgebase. In this paper, for the first issue we present MFCPN (Multi-level Fuzzy Colored Petri-nets) and for the second one we present a RL (Reinforcement Learning) mechanism for decision making based on the past device’s feedback to the environment. Through a few scenarios and two datasets, the proposed approach has been applied to pacemakers to show the approach's effectiveness. The comparison between decision making by our approach and two real datasets indicates the proposed approach has 79.3 % accuracy.

New Fermatean Fuzzy Distance Metric and Its Utilization in the Assessment of Security Crises Using the MCDM Technique

The problem of insecurity is a global phenomenon that has several forms like terrorism, banditry, kidnappings, etc. Insecurity has taken hold in the Sub-Saharan Region of West Africa, especially in Nigeria, for over two decades. Nigeria’s security crisis is more pronounced in the Northern Region, with a new wave in the North-Central Region of Nigeria. It is herculean to assess insecurity in the North-Central Region of Nigeria because of the region’s fuzzy or imprecise nature of insecurity. This constitutes the rationale for deploying the Fermatean fuzzy technique to assess insecurity due to the capacity of the Fermatean fuzzy scheme to handle imprecision. To this end, a new Fermatean fuzzy distance metric is presented to evaluate insecurity in the North-Central Region of Nigeria using a multi-criteria decision-making technique. To express the logic for creating the new Fermatean fuzzy distance metric, some existing Fermatean fuzzy distance metrics are discussed, along with their drawbacks. The mathematical properties of the new technique are discussed, and the new method is applied computationally to assess insecurity in the North-Central Region of Nigeria. The data for the security assessment are collected via Fermatean fuzzy linguistic variables using the opinions of security experts and analyzed using the technique for order of preference by similarity to ideal solution, which is a commonly used multi-criteria decision-making method. Finally, the numerical validity of the new technique is expressed with comparative results, and the finding shows the benefit of the new distance approach over the existing methodologies. The outcome of the work will provide reliable traveling advisories for safe voyages within the region.

Cryptocurrency Portfolio Allocation under Credibilistic CVaR Criterion and Practical Constraints

The cryptocurrency market offers attractive but risky investment opportunities, characterized by rapid growth, extreme volatility, and uncertainty. Traditional risk management models, which rely on probabilistic assumptions and historical data, often fail to capture the market’s unique dynamics and unpredictability. In response to these challenges, this paper introduces a novel portfolio optimization model tailored for the cryptocurrency market, leveraging a credibilistic CVaR framework. CVaR was chosen as the primary risk measure because it is a downside risk measure that focuses on extreme losses, making it particularly effective in managing the heightened risk of significant downturns in volatile markets like cryptocurrencies. The model employs credibility theory and trapezoidal fuzzy variables to more accurately capture the high levels of uncertainty and volatility that characterize digital assets. Unlike traditional probabilistic approaches, this model provides a more adaptive and precise risk management strategy. The proposed approach also incorporates practical constraints, including cardinality and floor and ceiling constraints, ensuring that the portfolio remains diversified, balanced, and aligned with real-world considerations such as transaction costs and regulatory requirements. Empirical analysis demonstrates the model’s effectiveness in constructing well-diversified portfolios that balance risk and return, offering significant advantages for investors in the rapidly evolving cryptocurrency market. This research contributes to the field of investment management by advancing the application of sophisticated portfolio optimization techniques to digital assets, providing a robust framework for managing risk in an increasingly complex financial landscape.

Enhancing group decision-making: Maximum consensus aggregation for fuzzy cross-efficiency under hesitant fuzzy linguistic information

Group decision-making (GDM) is essential as it recognizes the inherent complexity of many decision scenarios, which frequently require the collective wisdom and knowledge of multiple decision-makers (DMs) to be effectively resolved. The proposed method aims to develop fuzzy data envelopment analysis (DEA) cross-efficiency models tailored to address GDM challenges, wherein attribute values are provided by DMs using hesitant fuzzy linguistic term sets (HFLTSs). For this purpose, we initially transform HFLTSs into their corresponding fuzzy envelopes, defined as trapezoidal fuzzy numbers (TrFNs). This conversion strategy effectively minimizes the loss in assessments based on HFLTSs while retaining the inherent ambiguity of the original information. Building upon this foundation, we develop fuzzy cross-efficiency models by leveraging the α-level sets of fuzzy envelopes. These models are designed to handle fuzzy input and output variables under various α-level sets, which are capable of considering all possible attribute values for each alternative. Following this, we implement a maximum consensus model using fuzzy cross-efficiency to assign weights to DMs. These weights facilitate the aggregation of individual fuzzy cross-efficiency intervals obtained from DMs’ assessments into collective ones, which serve to rank alternatives. Finally, we showcase the effectiveness and superiority of our proposal through numerical validation and comparative analysis.

Confined seepage analysis of saturated soils using fuzzy fields

Seepage refers to the flow of water through porous materials. This phenomenon has a crucial role in dam, slope, excavation, tunnel, and well design. Performing seepage analysis usually is a challenging task, as one must cope with the uncertainty associated with the parameters such as the hydraulic conductivity in the horizontal and vertical directions that drive this phenomenon. However, at the same time, the data on horizontal and vertical hydraulic conductivities are typically scarce in spatial resolution. In this context, so-called non-traditional approaches for uncertainty quantification (such as intervals and fuzzy variables) offer an interesting alternative to classical probabilistic methods, since they have been shown to be quite effective when limited information on the governing parameters of a phenomenon is available. Therefore, the main contribution of this study is the development of a framework for conducting seepage analysis in saturated soils, where uncertainty associated with hydraulic conductivity is characterized using fuzzy fields. This method to characterize uncertainty extends interval fields towards the domain of fuzzy numbers. In fact, it is illustrated that fuzzy fields are an effective tool for capturing uncertainties with a spatial component, since they allow one to account for available physical measurements. A case study in confined saturated soil shows that with the proposed framework, it is possible to quantify the uncertainty associated with seepage flow, exit gradient, and uplift force effectively.

Research and Application of Emergency Logistics Resource Allocation Algorithm based on Supply Chain Network

The ”Fuzzy-Enhanced for Emergency Logistics Resource Allocation in Supply Chain Networks (FEM-ELRAS)” presents a novel approach to optimizing emergency logistics and resource allocation in supply chain networks, especially during critical disaster response scenarios. This research integrates fuzzy logic with the improve Multi Agent Genetic Algorithm (MAGA), creating a more adaptive and efficient framework capable of handling the uncertainties and complexities inherent in emergency situations. FEM-ELRAS employs fuzzy decision variables to represent ambiguous and fluctuating parameters like demand at disaster sites, supply availability, and variable transportation conditions. It incorporates a fuzzy inference system, utilizing expert-derived rules to guide the allocation process amidst uncertain and rapidly changing conditions. The algorithm’s evaluation mechanism is enhanced with fuzzy logic, offering a refined assessment of solution effectiveness, balancing multiple logistical objectives such as minimizing response time, optimizing costs, and maximizing resource utilization and delivery precision. Moreover, fuzzy logic principles are integrated into the genetic algorithm’s operators, enabling more context-sensitive and flexible solution adaptations. FEM-ELRAS is particularly designed to navigate the trade-offs between different logistical goals in emergency scenarios, making it a robust tool for decision-makers in disaster management. Its application promises significant improvements in emergency response efficiency, showcasing a step forward in the field of emergency logistics and supply chain management.

Constrained large-scale multiobjective optimization based on a competitive and cooperative swarm optimizer

Many engineering application problems can be modeled as constrained multiobjective optimization problems (CMOPs), which have attracted much attention. In solving CMOPs, existing algorithms encounter difficulties in balancing conflicting objectives and constraints. Worse still, the performance of the algorithms deteriorates drastically when the size of the decision variables scales up. To address these issues, this study proposes a competitive and cooperative swarm optimizer for large-scale CMOPs. To balance conflict objectives and constraints, a bidirectional search mechanism based on competitive and cooperative swarms is designed. It involves two swarms, approximating the true Pareto front from two directions. To enhance the search efficiency in large-scale space, we propose a fast-converging competitive swarm optimizer. Unlike existing competitive swarm optimizers, the proposed optimizer updates the velocity and position of all particles at each iteration. Additionally, to reduce the search range of the decision space, a fuzzy decision variables operator is used. Comparison experiments have been performed on test instances with 100–1000 decision variables. Experiments demonstrate the superior performance of the proposed algorithm over five peer algorithms.

Robust Optimization Research of Cyber-Physical Power System Considering Wind Power Uncertainty and Coupled Relationship.

To mitigate the impact of wind power uncertainty and power-communication coupling on the robustness of a new power system, a bi-level mixed-integer robust optimization strategy is proposed. Firstly, a coupled network model is constructed based on complex network theory, taking into account the coupled relationship of energy supply and control dependencies between the power and communication networks. Next, a bi-level mixed-integer robust optimization model is developed to improve power system resilience, incorporating constraints related to the coupling strength, electrical characteristics, and traffic characteristics of the information network. The upper-level model seeks to minimize load shedding by optimizing DC power flow using fuzzy chance constraints, thereby reducing the risk of power imbalances caused by random fluctuations in wind power generation. Furthermore, the deterministic power balance constraints are relaxed into inequality constraints that account for wind power forecasting errors through fuzzy variables. The lower-level model focuses on minimizing traffic load shedding by establishing a topology-function-constrained information network traffic model based on the maximum flow principle in graph theory, thereby improving the efficiency of network flow transmission. Finally, a modified IEEE 39-bus test system with intermittent wind power is used as a case study. Random attack simulations demonstrate that, under the highest link failure rate and wind power penetration, Model 2 outperforms Model 1 by reducing the load loss ratio by 23.6% and improving the node survival ratio by 5.3%.

Chance-constrained programming for drinking water quality management under fuzziness and randomness

ABSTRACT In this paper, an inexact fuzzy random chance-constrained programming (IFRCCP) model was proposed to deal with the randomness and fuzziness in the optimization of booster cost for the water distribution system (WDS). The IFRCCP model was applied to a WDS to analyze the effects of randomness and fuzziness on the booster costs. The booster cost intervals were obtained under various violation levels and confidence levels. The results indicated that the lower and upper booster costs increased with the confidence levels of the lower limits and decreased with the violation levels of the lower limits for both normal and log-normal distribution fuzzy random variables (FRVs). Moreover, the increased magnitude of lower and upper booster costs under normal distribution FRV is a little less than that under log-normal distribution FRV, while the decreased magnitude of lower and upper booster costs under normal distribution FRV is larger than that under log-normal distribution FRV. The same regulation can be found for the FVR with both triangular and trapezoidal distribution FRVs. With the increase of booster number, the increased magnitude of the lower and upper booster costs decreased for both normal and log-normal distribution FRVs.

Fuzzy system reliability analysis based on new aging indexes

The concept of aging plays an important role in reliability analysis. The aim of this paper is providing the novel method to definition aging indexes based on fuzzy random variables and using the concept of α-pessimistic in both parametric and non-parametric approaches. In parametric approach, the concepts of survival function, hazard rate function and mean residual function were extended for fuzzy random variables. After that, we obtain and analyse these indexes for fuzzy exponential and fuzzy two-parameter Weibull distributions as two frequently used lifetime distribution in reliability theory. Moreover, with the assumption that the distribution of fuzzy observations is unknown (non-parametric approach), first an estimate for the fuzzy distribution function is presented, and then an estimate for the aging indices of the system is investigated. To do this, the concept of fuzzy empirical distribution function is investigated as an estimator of cumulative distribution function. Moreover, some properties of investigated estimator have been established.

A NOVEL METHOD FOR SOLVING FULLY FUZZY SOLID TRANSPORTATIONS PROBLEMS

In this paper, we proposes a new method for solving solid transportation problem under uncertainty environments. The fully fuzzy solid transportation problem has been formulated. To reduce the model into crisp equivalent, we have used existing method for approximation of fuzzy numbers by interval numbers and its arithmatics. A simplex method and existing method for solving Interval Linear Programming problems are used for solving solid transportation problem with fuzzy parameters and decision variables. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy and reasonable.

Group decision making method for third-party logistics management: An interval rough cloud optimization model

Group decision making in third-party logistics service selection plays an essential role for improving service quality, increasing efficiency and reducing the net cost. Fuzzy and uncertain linguistic variables are commonly used to represent experts‘rankings in optimization problems. To recognize the limits of human cognition and subjectivity of human evaluations, several optimization approaches have been studied to select remanufacturing alternatives in decision making processes, however these methods have certain deficiencies such as lacking manipulation tools of diverse information, randomness, use of predefined parameters increasing uncertainty, interpersonal relations among evaluation criteria. The integration of interval numbers, rough approximations, and cloud model theory plays a significant role to model incomplete and inadequate information occurring in decision making problems. This research paper focuses on the integration of dual interval rough integrated cloud model with best-worst optimization technique, Multi-Attributive Border Approximation area Comparison (MABAC) and Weighted Aggregated Sum Product Assessment (WASPAS) approaches. A novel min–max optimization model based dual interval rough integrated cloud values is designed to compute the weight coefficients and consistency ratio for each criteria. The consistency of proposed optimization model is checked using a consistency ratio test. Secondly, the alternatives are ranked using the proposed DIRI cloud based MABAC and WASPAS approaches using interval clouds based weighted sum and weighted product coefficients, approximation area values and distance formulae. The significance of the proposed model is highlighted with a case study of third-party logistics service management of an electronic firm. The rationality and out-performance of the proposed methodology is studied by a comparative analysis with existing approaches and detailed sensitivity analysis on different variations of criteria weights and parameter.

Breast Cancer Prediction Using Oversampling Technique, Particle Swarm Optimization, and Fuzzy Logic

Background: Breast cancer is one of the most devastating and prominent reasons for women's life loss on the planet today. Therefore, the development of tools for the early detection of breast cancer based on the use of a large amount of available clinical data in combination with machine learning/artificial intelligence models can be a cost-effective and game-changer solution for saving women's lives. Researchers have been working hard to put such a tool into practice in recent years. Introduction: Breast cancer is a serious health issue, and detecting it early is crucial to improving patient outcomes. Breast cancer is the second most prevalent chronic illness in women behind lung cancer and can also affect males, though it does so significantly on a smaller scale Objective: For early detection of breast cancer, a wide range of methods, including oversampling, feature selection, fuzzy logic, and machine learning algorithms, have been explored. This research article aims to predict the type and risk factors of breast cancer. Methods: In this study, the support vector machine-synthetic minority oversampling technique (SVM-SMOTE) was used to balance the Wisconsin Breast Cancer Original (WBCO) dataset from the UCI repository. To enhance the models’ performance and decrease the number of features, features were extracted using particle swarm optimization (PSO). Furthermore, thirteen types of models are proposed: Decision Tree (DT), Logistic Regression (LR), Random Forest (RF), Naïve Bayes (NB), K-Nearest Neighbors (KNN), Support Vector Machine (SVM), Gradient Boosting (GB), Extreme Gradient Boosting (XGB), Adaptive Boosting (AB), Categorical Boosting (CB), Light Gradient Boosting Machine (LGBM), Multi-Layer Perceptron (MLP), and Extra Trees (ET). The PSO-suggested features are utilized as input fuzzy variables, and fuzzy logic is trained. Results: As a result of these proposed techniques, the highest accuracy was obtained at 92.64%, 98.31%, and 97.19% using SVM-SMOTE, SVM-SMOTE+PSO, and PSO+fuzzy logic, respec-tively. Conclusion: In our investigation, we used fewer attributes (three), such as clump thickness, mar-ginal adhesion, and Bland chromatin, in the fuzzy logic systems and obtained satisfactory results.

Fuzzy random sensitivity analysis for the overall structure reliability of reinforced concrete freezing wellbores in deep alluvium based on hidden Markov model

To address the shortcomings of traditional reliability theory in characterizing the stability of deep underground structures, the advanced first order second moment of reliability was improved to obtain fuzzy random reliability, which is more consistent with the working conditions. The traditional sensitivity analysis model was optimized using fuzzy random optimization, and an analytical calculation model of the mean and standard deviation of the fuzzy random reliability sensitivity was established. A big data hidden Markov model and expectation-maximization algorithm were used to improve the digital characteristics of fuzzy random variables. The fuzzy random sensitivity optimization model was used to confirm the effect of concrete compressive strength, thick-diameter ratio, reinforcement ratio, uncertainty coefficient of calculation model, and soil depth on the overall structural reliability of a reinforced concrete double-layer wellbore in deep alluvial soil. Through numerical calculations, these characteristics were observed to be the main influencing factors. Furthermore, while the soil depth was negatively correlated, the other influencing factors were all positively correlated with the overall reliability. This study provides an effective reference for the safe construction of deep underground structures in the future.

Optimizing Production Planning and Inventory Management in Post-Pandemic Recovery Using A Multi-Period Hybrid Uncertain Optimization Model

During the post-COVID-19 pandemic recovery phase, decision-makers in the manufacturing and retail sectors are confronted with numerous uncertainties. These issues comprise various aspects of operations, including the acquisition of raw materials or components and planning production activities. Therefore, this research aimed to introduce an innovative dynamic hybrid optimization model that combined probabilistic and fuzzy techniques. The model would offer a solution for addressing the challenges posed by uncertain parameters, particularly in the context of post-pandemic scenarios for production planning and inventory management with multiple periods of observation. The model was designed to handle exceptional circumstances such as parameter uncertainties, augmented demand fluctuations, fuzzy variables, and probabilistic factors. The primary objective of the model was to maximize the expected total profit of the operational process. To achieve this aim, an uncertain programming algorithm based on the interior point method was used to compute the optimal decision for the problem at hand. Through the execution of simulations using randomly generated data, the proposed model was thoroughly evaluated and analyzed with six suppliers, three raw part types, three product types, and six periods. All six suppliers were selected to supply raw parts, however, not all suppliers were selected to supply particular raw part types. Furthermore, it was derived that the expectation of the maximum profit is 897261.40; this is the best expected profit generated by the optimization model, meaning that other decisions may result in a smaller expectation of the profit. The results of these simulations unequivocally showed the effectiveness of the decision-making model in providing optimal solutions, specifically in terms of raw material procurement and production planning strategies. Subsequently, this model could serve as a valuable tool for decision-makers operating within the manufacturing and retail industries.

Group decision making based on dice similarity measure and 2-dimension linguistic fuzzy weighted arithmetic aggregation operator for 2-dimension linguistic fuzzy variables

In the process of decision-making, it usually applies 2-dimension linguistic fuzzy variable (2DLFV) to describe the uncertainty caused by the decision objects and the decision makers. This proposal aims to design group decision making method based on dice similarity measure (DSM) and 2-dimension linguistic fuzzy weighted arithmetic aggregation (2DLFWAA) operator for 2-dimension linguistic fuzzy framework. Based on the psychological theory and prospect theory, 2-dimension linguistic scale function (2DLSF) about 2DLFV is firstly proposed, and new operational rules of 2DLFV are introduced. Two forms of DSM are proposed to measure the closeness between two 2-dimension linguistic fuzzy sets (2DLFSs). A definition is given for 2DLFWAA operator and some of its properties are studied. Based on the DSM and the 2DLFWAA operator for 2DLFSs, the technique for order of preference by similarity to ideal solution (TOPSIS) method is extended to handle the multiple attribute group decision making (MAGDM) problems under 2-dimension linguistic fuzzy environments. Finally, an illustrative example is provided to show the concrete process of the proposed method. Comparative analysis and sensitivity analysis are conducted to test the rationality and robust of the proposed method. The results suggest that the proposed method offers a flexible and reliable approach in 2-dimension linguistic fuzzy scenarios.

Enhancing Transportation Efficiency with Interval-Valued Fermatean Neutrosophic Numbers: A Multi-Item Optimization Approach

In this study, we derive a simple transportation scheme by post-optimizing the costs of a modified problem. The strategy attempts to make the original (mainly feasible) option more practicable by adjusting the building components’ costs. Next, we employ the previously mentioned cell or area cost operators to gradually restore the modified costs to their initial levels, while simultaneously implementing the necessary adjustments to the “optimal” solution. This work presents a multi-goal, multi-item substantial transportation problem with interval-valued fuzzy variables, such as transportation costs, supplies, and demands, as parameters to maintain the transportation cost. This research addresses two circumstances where task ambiguity may occur: the interval solids transportation problem and the fuzzy substantial transportation issue. In the first scenario, we express data problems as intervals instead of exact values using an interval-valued fermatean neutrosophic number; in the second case, the information is not entirely obvious. We address both models when uncertainty solely affects the constraint set. For the interval scenario, we define an additional problem to solve. Our existing efficient systems have dependable transportation, so they are also capable of handling this new problem. In the fuzzy case, a parametric technique generates a fuzzy solution to the preceding problem. Since transportation costs have a direct impact on market prices, lowering them is the primary goal. Using parametric analysis, we provide optimal parameterization solutions for complementary situations. We provide a recommended algorithm for determining the stability set. In conclusion, we offer a sensitivity analysis and a numerical example of the transportation problem involving both balanced and imbalanced loads.