Interval Type-2 Fuzzy Sets Research Articles

An IT2FS-ANP- and IT2FS-CM-Based Approach for Conducting Safety Risk Assessments of Nuclear Power Plant Building Projects

This study proposes an approach for simultaneously treating fuzziness and randomness when conducting safety risk assessments of nuclear power plant building projects (NPPBPs). First, the interval type-2 fuzzy set (IT2FS) and analytic network process (ANP) were employed to establish an IT2FS-ANP method for modifying the solution for the weight vector and determining the mutual relationships between the assessment indexes and their weights. Second, the IT2FS and cloud model (CM) were used to establish the IT2FS-CM method to modify the solution for the expectation value. Third, the IT2FS-ANP and IT2FS-CM methods were combined to establish a model for ranking the safety risks and determining the overall safety risk level. Finally, the approach was applied to an NPPBP in northeast China to validate its applicability.

Interval type-2 possibilistic picture C-means clustering incorporating local information for noisy image segmentation

Picture fuzzy C-means clustering is a novel computational intelligence method that has some advantages over fuzzy clustering in pattern analysis and machine intelligence. However, picture fuzzy clustering is easily affected by noise and weighting exponent, which seriously limits its widespread application. To address this issue, this paper proposes a new robust possibilistic clustering method called “interval type-2 possibilistic picture C-means clustering with local information”. This method combines interval type-2 fuzzy sets with possibilistic C-means clustering based on picture fuzzy sets, strengthening the noise resistance of picture fuzzy clustering. Firstly, this paper creatively extends an improved possibilistic clustering with double weighing exponents to picture fuzzy sets, solving the problem of consistency clustering in existing possibilistic picture clustering. Second, this paper originally introduces a new picture local information factor in possibilistic picture clustering and further enhances the anti-noise robustness of the method by using spatial possibilistic picture partition information. Finally, this paper skillfully extends this clustering method to interval type-2 fuzzy sets, which can handle more flexibly high-order uncertainties than type-1 clustering method. Experimental results indicate that this proposed method has better segmentation performance and stronger noise suppression ability compared with existing picture fuzzy clustering and interval type-2 fuzzy clustering. In summary, this work has made significant contributions to the development of picture fuzzy clustering theory and its applications.

Analyzing the Shelter Site Selection Criteria for Disaster Preparedness Using Best–Worst Method under Interval Type-2 Fuzzy Sets

Shelters are vital for affected people after a disaster because of the accommodation, safety, and security. In this paper, we analyze the shelter site selection criteria for disaster preparedness applying the best–worst method under interval type-2 fuzzy sets. The proposed approach utilizes the advantages of fewer pairwise comparisons with the best–worst method and better reflection of uncertainty with interval type-2 fuzzy sets. For this reason, the criteria are determined based on a literature review and the opinion of nine disaster experts. The experts have worked as disaster officers in a variety of locations, including Sivrice (Elazığ), Pazarcık, and Elbistan (Kahramanmaras) and Syrian refugee camps such as Nizip container city. In this step, 6 main criteria and 25 sub-criteria are evaluated using the proposed approach. According to the nine experts’ opinions, the most important main criterion is determined as proximity. Distribution center capacity, adequate distribution logistics personnel, available electricity, distance to settlement, and landslides and flooding are also determined as the five most important sub-criteria. For disaster preparedness, responsible organizations and managers should consider these important criteria for temporary shelter site selection.

Data Driven Type-2 Fuzzy Modeling and Control of Personalized Thermal Comfort

Since the room thermal comfort has high uncertainties, it is difficult but necessary to study the modeling and control of thermal comfort. This paper tries to solve the modeling and control problem for the room thermal comfort by utilizing the temperature and humidity data collected from the working or living room. Firstly, in order to discard the noisy data and to obtain the reasonable intervals for modeling the temperature and humidity, a statistic method based preprocessing strategy is presented. Secondly, the Gaussian interval type-2 fuzzy set models are constructed to depict the personalized temperature and humidity comfort by measuring the uncertainty degrees of the obtained intervals. Thirdly, a interval type-2 fuzzy method based control scheme is proposed to realize the personalized thermal comfort regulation. Finally, some experimental results are given. And, the results show that the proposed thermal comfort models and control scheme can not only recommend a reasonable temperature and humidity range, but also can realize the optimal thermal comfort control.

Incorporating artificial intelligence in detecting crop diseases: Agricultural decision-making based on group consensus model with MULTIMOORA and evidence theory

The continuous advancements in artificial intelligence (AI) technology are facilitating its widespread integration across various sectors, prominently within agriculture. This evolving synergy is reshaping farming practices, specifically by innovating intelligent mechanisms to monitor and combat crop diseases through intelligent decision-making. Wheat assuming particular significance on the global agricultural stage. Addressing the concerning spread of the wheat soil-borne mosaic (WSBM), this paper employs modern methodologies to gauge the severity of virus infection in wheat through quantitative evaluation. Our contribution lies in the exploration of a group consensus model method within the context of interval type-2 fuzzy sets (IT2FSs). Navigating the intricacies of decision makers (DMs) reaching consensus, we address the challenge of selecting a consensus degree threshold by introducing random variables. Experimentally determining an objective consensus degree threshold. Then, we combine the Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form (MULTIMOORA) method with Dempster-Shafer (D-S) evidence fusion theory. This result in an evidence fusion decision-making model rooted in IT2F information, offering enhanced stability. Leveraging the MULTIMOORA method for decision-making, we then fuse the outcomes through D-S evidence fusion theory, yielding stable decision results. Subsequently, we validate the feasibility of our established decision model within the context of WSBM. In conclusion, we subject it to sensitivity and comparative analyses, comparing it with other methods. This thorough evaluation aims to validate the effectiveness and feasibility of our proposed approach, providing insights into its potential applications and contributions in the realm of agricultural decision-making.

Modeling, design and control of a 4-arm delta parallel manipulator employing type-1 and interval type-2 fuzzy logic-based techniques for precision applications

This paper presents the virtual design of a four-arm Delta parallel robot for potential applications in the food industry, specifically for the automated preparation of fast foods. Kinematic and dynamic models were developed based on the morphology of this type of robot. Cutting-edge and previously unexplored control strategies for these types of manipulators are then designed and implemented based on Fuzzy PD and Fuzzy PID configurations. Several performance indicators, such as the Integral Square Error (ISE), Integral Time Absolute Error (ITAE) and Integral Time Square Error (ITSE), were used to conduct a performance comparison of the control techniques, considering type-1 and interval type-2 fuzzy sets. In all the analyzed scenarios, the fuzzy controllers correspond to the Takagi–Sugeno–Kang model using linear functions of the inputs in the outputs. Among the main contributions of this work is the development of a detailed dynamic model of the robot in Simscape, incorporating realistic aspects that are often overlooked during analytical modeling. To ensure more accurate results, the rejection of external disturbances is thoroughly analyzed in simulations, considering elements such as time delays and control signal saturations. The results demonstrate the veracity of the proposed design for a four-arm Delta robot, both in models and in the Simscape/Simulink implementation. In the trajectory tracking task and external disturbance rejection, the superiority of the Fuzzy PID controller with interval type-2 fuzzy sets over fuzzy controllers with PD structure and over type-1 fuzzy sets is evidenced.

A novel threat assessment method for maritime defense integrating improved IT2FBWM, prospect theory and VIKOR under hybrid fuzzy environment

The weaponized unmanned aerial vehicle (UAV) swarms have posed a significant threat to maritime civilian and military installations. For effective defense deployment, threat assessment has become a critical part of maritime defense decision-making. However, due to the uncertainty of threat information and the ignorance of decision-makers’ psychological behaviors, there are great challenges in obtaining a reliable and accurate threat assessment result to assist in maritime defense decision-making. To this end, this paper proposes an integrated threat assessment method for maritime defense against UAV swarms based on improved interval type-2 fuzzy best-worst method (IT2FBWM), prospect theory and VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje, in Serbian). Firstly, the improved IT2FBWM is designed by introducing interval type-2 fuzzy set (IT2FS) and entropy-based information to obtain attribute weights with high reliability. Then, the hybrid fuzzy scheme covering IT2FS and interval number is constructed to express the uncertainty of different types of threat information. Next, VIKOR is extended to hybrid fuzzy environment and combined with prospect theory to consider the influence of psychological behaviors of decision-makers. Finally, the improved IT2FBWM and extended VIKOR are integrated to determine the threat ranking of targets and the priority defense targets. A case study of maritime threat assessment is provided to illustrate the performance of the proposed method. Moreover, sensitivity and comparative experiments were conducted, and the results indicate that the proposed method not only obtain the reliable threat assessment result but also outperforms the other methods in terms of attribute weight determination, decision preference consideration and decision mechanism.

Assessment of suppliers through the resiliency and sustainability paradigms using a new MCDM model under interval type-2 fuzzy sets

Assessment of suppliers through the resiliency and sustainability paradigms using a new MCDM model under interval type-2 fuzzy sets

Noninvasive system for weight estimation in cactus crops: A YOLOv5-decision tree approach based on interval type-2 fuzzy sets

This study proposes a noninvasive system to estimate the weight of a prickly pear cactus (Opuntia ficus-indica), which combines a model based on deep learning to detect and estimate its area and a model based on supervised learning and developed under a type-2 interval fuzzy sets approach to estimate its weight. YOLOv5 was used for detection, which achieved results with an accuracy of 0.999, recall of 0.999, mAP_0.5 of 0.995, and mAP_0.5:0.95 of 0.990. Area estimation is performed based on the object's coordinates in the image. To perform the weight estimation task, a comparative analysis of models based on supervised learning was performed to identify the model that best described the response variable, selecting a decision tree model. The training and adjustment process included the uncertainty in a weight evaluation system using a granatary scale to enhance the weight estimation capability. Using a trapezoidal membership function, the type-2 interval fuzzy set approach was used to convert the collected data into fuzzy numbers. The model findings for the weight estimation task were also favorable, with a model-explained variance R2 of 0.98, a root mean square error (RMSE) of 10.02, and a mean absolute error (MEA) of 6.33 g. Finally, both models were incorporated into a graphical user interface to facilitate their use in the real weight estimation process. A real case application with the proposed system demonstrated its effectiveness in detecting and estimating weight dynamically with an error of 9 g. Therefore, its viability as an alternative system for weight estimation in cactus crops was demonstrated. Furthermore, a comparative analysis demonstrated the superiority of the proposed hybrid approach over similar approaches in the literature.

Let us take a walk to the sustainable tourism practices: a qualitative study through the lens of tourism experts.

The rising opportunities of sustainable tourism have brought many policies to control the exploitation of the environment and increase the reach of luxurious, safe, and authentic experiences to the different segments of tourists. This study seeks to prioritize the variables influencing the development of sustainable tourism and pinpoint key success factors that align with the Sustainable Development Goals (SDGs). It adopts a tri-dimensional framework encompassing economic, social, and environmental aspects, further delineated into eleven sub-dimensions, to provide a quantitative evaluation of sustainable tourism. We conducted interviews with 26 tourism industry experts hailing from eight countries, analyzing their responses using interval type-2 fuzzy sets. The results underscore the critical role of specific components in advancing sustainable tourism. In the economic dimension, "financial resources and tourism costs" emerge as vital factors. In the social dimension, "health and safety" takes center stage, while "green infrastructure" plays a pivotal role in the environmental dimension. These findings underscore the significance of these aspects in promoting sustainable tourism. Furthermore, this study explores the strategic importance of sustainable tourism equity in shaping tourism planning and development for emerging markets.

Process accident prediction using Bayesian network based on IT2Fs and Z-number: A case study of spherical tanks.

This study aimed to propose a novel method for dynamic risk assessment using a Bayesian network (BN) based on fuzzy data to decrease uncertainty compared to traditional methods by integrating Interval Type-2 Fuzzy Sets (IT2FS) and Z-numbers. A bow-tie diagram was constructed by employing the System Hazard Identification, Prediction, and Prevention (SHIPP) approach, the Top Event Fault Tree, and the Barriers Failure Fault Tree. The experts then provided their opinions and confidence levels on the prior probabilities of the basic events, which were then quantified utilizing the IT2FS and combined using the Z-number to reduce the uncertainty of the prior probability. The posterior probability of the critical basic events (CBEs) was obtained using the beta distribution based on recorded data on their requirements and failure rates over five years. This information was then fed into the BN. Updating the BN allowed calculating the posterior probability of barrier failure and consequences. Spherical tanks were used as a case study to demonstrate and confirm the significant benefits of the methodology. The results indicated that the overall posterior probability of Consequences after the failure probability of barriers displayed an upward trend over the 5-year period. This rise in IT2FS-Z calculation outcomes exhibited a shallower slope compared to the IT2FS mode, attributed to the impact of experts' confidence levels in the IT2FS-Z mode. These differences became more evident by considering the 10-4 variance compared to the 10-5. This study offers industry managers a more comprehensive and reliable understanding of achieving the most effective accident prevention performance.

A time feature modeling and expression method for vague geographic processes

ABSTRACT Geographic processes are dynamic, wherein geographical entities and phenomena change over time and are characterized by vagueness. However, most studies on geographic processes employ precise expression methods to describe and express the changing trajectories of geographical entities and phenomena, ignoring vagueness. This strategy fails to facilitate the objective description and expression of the entire process and may affect analysis results. Herein, a time feature expression model of vague geographic processes is established based on the interval type-2 fuzzy set theory to describe and express the vague time characteristics comprising three model stages that reflect the geographic process evolution sequence: production (beginning), development, and extinction (end). Finally, the practicability of the proposed model is verified using two case studies, i.e. the landing process of typhoon ‘Lekima’ and the desert greening process in Xinjiang, China.

Elliptic interval Type-2 intuitionistic fuzzy logic system for non-linear system identification

An elliptic membership function has been proposed in the literature for interval type-2 fuzzy logic system. In this paper, elliptic non- membership function is incorporated into the conventional elliptic membership function model to obtain elliptic interval type-2 intuitionistic fuzzy sets for the first time. The elliptic interval type-2 intuitionistic fuzzy logic system so formed is applied for the prediction of two benchmark non-linear systems and results compared with Gaussian interval type-2 intuitionistic fuzzy logic system. Experimental results show that the elliptic interval type-2 intuitionistic fuzzy logic system outperforms the traditional Gaussian interval type-2 intuitionistic fuzzy logic system in the problem instances investigated.

Assessing sustainability of food supply chains by using a novel method integrating group multi-criteria decision-making and interval Type-2 fuzzy set

Assessing sustainability of food supply chains by using a novel method integrating group multi-criteria decision-making and interval Type-2 fuzzy set

A novel type-2 hexagonal fuzzy logic approach for predictive safety stock management for a distribution business

Safety stock is an important method to overcome variability in inventory management. The classical approach to safety stock decisions relies on historical demand and lead time statistical data, which may not capture the uncertainty and complexity of the real world. Human knowledge and experience are valuable assets for making better decisions, especially when facing unpredictable situations. The fuzzy method is widely used for employing human intuition for decisions. When fuzzy opinions are input, decisions can be made proactively rather than reactively while benefiting from future predictions. The paper aims to integrate human intuition using Hexagonal Type-2 Fuzzy Sets (HT2FS) for safety stock management. HT2FS is a generalization of Interval Type-2 Fuzzy Sets that can represent more uncertainty in the membership functions. Predictions may be integrated into the safety stock models using human intuition. The proposed model uses novel fuzzy approaches to integrate human intuition into the traditional safety stock model. Applying fuzzy sets to safety stock management allowed experts' opinions under fuzzy logic to be integrated into decision-making. The proposed novel approach uses the centre of gravity method of Polygonal Interval Type-2 Fuzzy sets for defuzzification, which is a computationally efficient method that can handle any shape of the footprint of uncertainty. A mathematical model is developed to validate fuzzy opinions that may replace historical data. The data is received from a real-life case, and human intuition is integrated using an expert’s input. After the validation, a real-life numerical example has been considered to illustrate the model and its validity compared to the classical model. The outcomes show that the proposed model may contribute to the classical models, mainly when experts' inputs offer good predictions. When expert opinion on HT2FS is used for a real-life case, the results show that the expert's better representation of future variances lowers total cost by 2.8%. The results, coupled with the sensitivity analysis, underline that the proposed approach may contribute to the literature on safety stock management.

Assessment of human error contribution to container loss risk under fault tree analysis and interval type-2 fuzzy logic-based SLIM approach

Human is a key element of the safety of life on board ships and a significant contributing factor to most of the accidents and incidents in the maritime industry. At this point, risk analysis plays a critical role in ensuring operational safety and maritime transportation sustainability. This paper aims to systematically evaluate how human errors (HEs) contribute to operational risks. Based on this, Fault Tree Analysis (FTA) is combined under an Interval Type-2 Fuzzy Logic environment with Success Likelihood Index Method (SLIM). Whilst the FTA evaluates the criticality of the operational activities, the Interval Type-2 Fuzzy Sets (IT2FS) deals with vagueness and subjectivity in using experts’ judgements, and the SLIM estimates the probabilities for the human error-related basic events. Since container losses can lead to severe damage and catastrophic events in a container terminal, loading operation was investigated as a case study. Safety culture, experience, and fatigue were observed as highly effective factors in crew performance. The obtained results also indicate that this hybrid approach can effectively be applied to determine the operational vulnerabilities in high-risk industries. The paper intends to improve safety control levels and lower losses in the future of maritime container transport besides emphasising the potential consequences of failures and crucial human errors in the operational process.

Evaluating sustainability of urban mobility of Asian cities: An integrated approach of interval type-2 fuzzy best-worst method and MULTIMOORA

The motivation for sustainable urban mobility is driven by the need to create environmentally friendly, socially inclusive, economically viable, and healthier cities for current and future generations. It requires a comprehensive approach that combines infrastructure development, policy changes, behavioral shifts, and technological advancements to transform urban transportation systems. The importance of creating increasingly sustainable urban transportation is now greater than it has ever been. One of the attempts in this field is the sustainable urban transport index (SUTI) developed by the United Nations (UN). Although the SUTI has a comprehensive pool of criteria for the evaluation of mobility sustainability of cities, considering the criteria weights as equal and disregarding the uncertainties present in expert opinions is viewed as a significant drawback. To satisfy the aforementioned deficiency, a novel integrated approach including the best-worst method (BWM), multi-objective optimization by ratio analysis (MOORA) and MOORA plus full multiplicative form (MULTIMOORA) method is develloped and applied for the SUTI evaluation. In order to manage ambiguous linguistic approximations, the utilization of BWM is applied within the framework of interval type-2 fuzzy (IT2F) sets. While IT2F-BWM is used to prioritize the main and sub-indicators of SUTI, MULTIMOORA approach is applied to rank the Asian cities. The findings imply that the proposed approach not only provides a more scientific perspective but also provides the opportunity to perform sensitivity analysis on criteria weights. Therefore, the results obtained in this study are expected to help cities to create a road map for planning sustainable urban mobility (e.g. Sustainable Urban Mobility Plan).

A novel deep belief network architecture with interval type-2 fuzzy set based uncertain parameters towards enhanced learning

This paper proposes a novel Deep Belief Network (DBN) architecture, the ‘Interval Type-2 Fuzzy DBN (IT2FDBN)’, which models the weights and biases with IT2 FSs. Thus, it introduces a novel algorithm for augmented deep leaning, which has the capability to address all the limitations of the classical DBN (CDBN) and T1 fuzzy DBN (T1FDBN). We comparatively evaluate the performance of the IT2FDBN by conducting experiments using the popular MNIST handwritten digit recognition datasets. Additionally, to demonstrate its robustness and generalization capabilities, we also conduct experiments taking two noisy variants of MNIST dataset, viz. the MNIST with AWGN (additive white Gaussian noise) and the MNIST with motion blur. We conduct extensive simulations by considering different combinations of nodes in the hidden layers of the DBN for better model selection. We thoroughly compare the results using well-known performance measures such as root mean square error (RMSE) and Error rate. We show that, in terms of RMSE values and error rates, the proposed IT2FDBN outperforms both T1FDBN and CDBN across all the three datasets. Further, we also provide the results of convergence, runtime-based comparison, and statistical analysis in support of our proposal.

A multi-criteria decision-making model for analyzing a project-driven supply chain under interval type-2 fuzzy sets

Reviewing and integrating decisions in the supply chain and project management is crucial. This problem is known as a project-driven supply chain problem. By the growing dependency of project-driven companies on suppliers since they prefer to concentrate on their core and subcontracting processes, the project-based organization's dependence on suppliers has increased. A project-driven supply chain (PDSC) focuses on integrating project management activities into the supply chain. In this paper, a new model is presented for the integration of supply chain and project management decisions. Firstly, a new method is proposed to determine the resilience score of suppliers. This new model consists of three parts: the weighting of criteria, the weighting of experts, and the ranking of suppliers. To give weight to the experts, a new version of the combinative distance-based assessment (CODAS) method is presented based on the average and positive ideal concepts. Also, the importance of the criteria is specified by an expanded best-worst method (BWM). Computing the resilience score of suppliers is done through a developed CODAS method that is extended by the average and positive concepts. Furthermore, in order to consider the uncertainty of project-driven supply chain problems, interval type-2 fuzzy sets (IT2FSs) are used. Secondly, a new subtraction operation is defined to avoid producing negative in recursive critical path method (CPM) calculations in the IT2F environment. Also, the criticality score of the project's activities is defined. According to the criticality and resilience indexes of activities, suggestions are made to project management to prevent delays. Finally, a case study of hospital construction is solved to illustrate the strengths of the proposed model.

An Integrated Interval Type-2 Fuzzy Set Model for Evaluating Circular Low Carbon Suppliers in a Developing Country

Increasing carbon emissions and environmental degradation have led to rapid depletion of resources. This requires circular low carbon (CLC) supply chains which extend the lifecycle of resources as much as possible. The aim of this study is to propose an integrated model for CLC supplier selection. First, economic, environmental and social responsibilities related to carbon management are identified. Then, DANP (Dematel-Analytic Network Process) and COPRAS (Complex Proportional Assessment) model with interval type-2 (IT-2) fuzzy sets are applied to evaluate the suppliers of a case energy company in Turkey. In this study, the ranking of dimensions from the most important to the least yielded the following order: environmental, social, and economic. In turn, carbon policy, carbon emission risks and low carbon supplier collaboration are found to be the most important environmental criteria. The current study has been used for the first time for a CLC supplier selection problem. Further, the study innovatively employs IT-2 fuzzy sets to better address differences and uncertainties that may come into play with a group of experts’ linguistic judgments. The validity of the proposed method is determined through sensitivity and comparative analysis.