Interval Type-2 Fuzzy Sets Research Articles

Two-Stage Fuzzy Interactive Multi-Objective Approach under Interval Type-2 Fuzzy Environment with Application to the Remanufacture of Old Clothes

In this study, a two-stage approach is introduced to obtain a more interactive and flexible solution to deal with the multi-objective programming under interval type-2 fuzzy environment. In the first stage, the fuzzy multi-objective chance-constrained programming with regular symmetric triangular interval type-2 fuzzy set parameters is proposed and transferred into its crisp equivalent form. In the second stage, we use the fuzzy interactive approach to address the crisp multi-objective programming obtained in the first stage by introducing the trade-off rate, which helps the decision maker react via updating their reference member values to obtain a satisfactory solution. Finally, taking a remanufacture of old clothes problem as an example, the comparison of experimental results obtained using a non-interactive method and interactive method shows that the proposed approach is conducive to obtaining satisfactory solutions effectively and efficiently, which broadens the application scope of the multi-objective programming with regular symmetric triangular interval type-2 fuzzy set parameters for sustainable manufacturing.

Altitude control of a quadcopter using interval type-2 fuzzy controller with dynamic footprint of uncertainty

Footprint of uncertainty (FOU) characteristics of interval type-2 membership functions (IT2-MFs) play an important role in the performance and robustness of interval type-2 fuzzy controllers (IT2-FCs). In literature, fixed FOU structures are used in almost all IT2-FC designs. In this study, an IT2-FC with dynamic FOU is proposed to provide high performance and robustness in the altitude control of a quadcopter. A proportional–derivative (PD) type FC with Takagi–Sugeno rule structure is used in the design procedure of the proposed controller. Additionally, input variables (error and derivative of error) are defined by using triangular IT2-MFs. To provide a dynamic FOU structure, the height of the lower MF (LMF) of each interval type-2 fuzzy set is defined as a function of the system error. In this way, FOU levels of IT2-MFs are adjusted dynamically since the height value of the LMF directly determines the FOU level of the IT2-MF. To evaluate the effectiveness of the proposed controller, comparison studies are performed under different conditions, including unmodeled measurement noises, an external disturbance, and a system parameter uncertainty. A classical PD, a type-1 fuzzy PD, and an interval type-2 fuzzy PD with fixed FOU controllers are used in the comparisons. The comparison results demonstrate that the proposed interval type-2 fuzzy PD controller with dynamic FOU exhibits better performance and more robustness than the other controllers.

A linguistic information granulation model based on best-worst method in decision making problems

In the elicitation of decision makers’ fuzzy and uncertain assessments, linguistic terms are natural and efficient as the preference modeling tools. Although the linguistic variables are available, they would not be operational without any detailed quantification. Motivated by the flexibility of information granularity, this paper develops information granules to represent linguistic terms in the form of intervals and interval type-2 fuzzy sets (IT2FSs) in best worst method (BWM). The development is aimed at minimizing inconsistency in the decision making (DM) process to ensure the rationality of the assessments provided by decision makers. Furthermore, the input and output based consistencies of BWM are considered. The granulation of entries of pairwise comparison vectors are the foundation of BWM to formulate an optimization problem where particle swarm optimization (PSO) algorithm serves as the optimization framework. Both individual and group decision making (GDM) scenarios are taken into consideration. For the GDM process, a performance index for measuring the group consensus is also proposed. Several examples and validity analysis are covered to illustrate the major ideas of this study. Finally, as a case study, a recommendation of the sequence of visiting tourist attractions in Wuhan and the corresponding comparative analysis are represented.

Interval Type-2 Fuzzy Application for Diet Journaling

In this article, an improved system is constructed using interval type-2 fuzzy sets (IT2FS) and a fuzzy logic controller (FLC) with non-singleton inputs. The primary purpose is to better model nutritional input uncertainty which is propagated through the Type-2 FLC. To this end, methods are proposed to (1) model nutrient uncertainty in food items, (2) extend the nutritional information of a food item using an IT2FS representation for each nutrient incorporating the uncertainty in the extension process, (3) accumulate uncertainties for IT2FS inputs using fuzzy arithmetic, and (4) build IT2FS antecedents for FLC rules based on dietary reference intakes (DRIs). These methods are then used to implement a web application for diet journaling that includes a client-side Type-2 non-singleton Interval Type-2 FLC. The produced application is then compared with the previous work and shown to be more suitable. This is the first known work on diet journaling that attempts to model uncertainty for all anticipated measurement error.

Three-way decision theory based on interval type-2 fuzzy linguistic term sets

This study examines decision theory based on interval type-2 fuzzy sets with linguistic information for the three-way decision approach by addressing the challenge of uncertainty for information analysis and fusion in subjective decision-making processes. First, the interval type-2 fuzzy linguistic term sets (IT2 FLTSs) are defined to represent and normalize the uncertain preference information in linguistic decision-making. Subsequently, perception computing based on computing with words paradigm is introduced to implement information fusion among different decision-makers in the linguistic information-based fuzzy logic reasoning process. Then, a three-way decision (3WD) theory based on IT2 FLTSs with fuzzy neighborhood covering is proposed, and the corresponded tri-partitioning strategies that satisfy Jaccard similarity of membership distributions are given. Finally, 3WD theory is applied to multi-criteria group decision-making with linguistic terms, and the algorithm steps are illustrated by a promising application under the background of coronavirus disease 2019 to reveal the feasibility and practicability of the proposed approach.

Knowledge-based prognostics and health management of a pumping system under the linguistic decision-making context

The process industry implements important maintenance strategies on the basis of the health status of system operation to reduce engineering maintenance cost and concurrently ensure reliability and safety. This study presents an architecture for knowledge-based prognostics and health management (K-PHM) by applying the trapezoidal interval type-2 fuzzy linguistic term sets. The proposed K-PHM methodology successfully provides operational information for diagnostics, prognostics, and subsequent actionable knowledge for health management in subjective decision making. It emphasizes knowledge-driven maintenance strategies to increase system reliability and safety within linguistic decision making. The main objective of this study is to focus on the uncertainty within the knowledge formation derived from data and subsequent information expressed with linguistic terms generated from domain experts in the K-PHM methodology. Fuzzy sets and fuzzy logic reasoning techniques are used in conjunction to enhance the capability of handling uncertainty throughout the PHM process. The effectiveness of the proposed K-PHM is verified with the authentic case study for the predictive maintenance of a chemical pumping system against abnormal vibration.

Barrier identification, analysis and solutions of hydrogen energy storage application in multiple power scenarios based on improved DEMATAL-ISM approach

China is ambitiously moving towards “carbon emission peak” and “carbon neutral” targets, and the power sector is in the vanguard. The coordination of power and hydrogen energy storage (HES) can improve energy utilization rate, promoting the deep decarbonization of power industry and realizing energy cascade utilization. However, limited by technology, cost, environment, society and other factors there are few application projects. Identifying major barriers and eliminating unimportant factors can make problem solving more efficient. Decision-making trial and evaluation laboratory (DEMATEL) combined with interpretative structural modeling (ISM) method is innovatively used to establish a barrier analysis framework for HES applied in multiple power scenarios. This method can show the direction and degree of the impact relationship between barriers and determine key ones, which is conducive to presenting targeted and effective solutions. Additionally, the interval type-2 fuzzy set (IT2FS) is introduced to reduce the distortion of evaluation information and ensure the rationality of analysis. Specifically, a comprehensive barrier system taking into account both commonalities and characteristics is established firstly. For different decision considerations, four typical power scenarios are screened to better illustrate how critical barriers play different roles in different scenarios. Then, the proposed analytical framework is applied to identify the key barriers in each scenario and find out the interlinking relationship among the barriers. The results suggest that technical barriers tend to dominate the fundamental barriers. Among that, immature hydrogen storage and transportation technology is a prevalent and fundamental barrier. Besides, high initial investment cost and high P2X conversion costs are crucial reasons that prevent relevant investors from entering the market. And inadequate policy has led to a poor environment for HES development. It's worth noting that, other key barriers focused on each scenario are not the same, and also are discussed in detail in this study. Finally, comprehensive solutions and policy suggestions to eliminate or reduce the barriers are presented.

Spacecraft tracking control and synchronization: An assessment of conventional, unconventional, and combined methods

Artificial intelligence (AI) promises breakthroughs in space operations, from mission design planning to satellite data processing and navigation systems. Advances in AI and space transportation have enabled AI technologies in spacecraft tracking control and synchronization. This study assesses and evaluates three alternative spacecraft tracking control and synchronization (TCS) approaches, including non-AI TCS methods, AI TCS methods, and combined TCS methods. The study proposes a hybrid model, including a new model for defining weight coefficients and interval type-2 fuzzy sets based combined compromised solution (IT2FSs-CoCoSo) to solve the spacecraft TCS problem. A new methodology is used to calculate the weight coefficients of criteria, while IT2FSs-CoCoSo is applied to rank the prioritization of TCS methods. A comparative analysis is conducted to demonstrate the performance of the proposed hybrid model. We present a case study to illustrate the applicability and exhibit the efficacy of the proposed method for prioritizing the alternative TCS approaches based on ten different sub-criteria, grouped under three main aspects, including complexity aspects, operational aspects, and efficiency aspects. AI and non-AI methods combined are the most advantageous alternative, whereas non-AI methods are the least advantageous, according to the findings of this study.

Interval type-2 fuzzy set based time series forecasting using a data-driven partitioning approach

Interval type-2 fuzzy set based time series forecasting using a data-driven partitioning approach

A Spatial Fuzzy Co-Location Pattern Mining Method Based on Interval Type-2 Fuzzy Sets

The goal of spatial co-location pattern mining is to find subsets of spatial features whose instances are often neighbors in a geographical space. In many practical cases, instances of spatial features contain not only spatial location information but also attribute information. Although there have been several studies that use type-1 fuzzy membership functions to mine spatial fuzzy co-location patterns, there is great uncertainty associated with such membership functions. To address this problem, we propose a spatial fuzzy co-location pattern mining method based on interval type-2 fuzzy sets. First, we collect the interval evaluation values of the interval data of attribute information from experts to form granular data. Next, the original type-1 fuzzy membership function is extended to a granular type-2 fuzzy membership function based on elliptic curves. We use a gradual method to adjust the parameters of the fuzzy membership function so that its footprint of uncertainty satisfies both the connectivity and the given confidence. Based on this granular type-2 fuzzy membership function, we fuzzify the attribute information of instances and define the concepts of fuzzy features and fuzzy co-location patterns. A fuzzy co-location pattern mining algorithm based on spatial cliques is then proposed, termed the FCPM-Clique algorithm. In order to improve the efficiency of the algorithm, we propose two pruning strategies. In addition, we extend two classical spatial pattern mining algorithms, the Join-based algorithm and the Joinless algorithm, to mine fuzzy co-location patterns based on interval type-2 fuzzy sets. Many experiments on synthetic and real-world datasets are conducted, the performance of the three algorithms is compared, and the effectiveness and efficiency of our proposed FCPM-Clique algorithm is demonstrated.

Dynamic collaborative optimization for disaster relief supply chains under information ambiguity.

Large-scale disasters occur worldwide, with a continuing surge in the frequency and severity of disruptive events. Researchers have developed several optimization models to address the critical challenges of disaster relief supply chains (e.g., emergency material reserving and scheduling inefficiencies). However, most developed algorithms are proven to have low fault tolerance, which makes it difficult for disaster relief supply chain managers to obtain optimal solutions and meet the emergency distribution requirements within a limited time frame. Considering the uncertainty and ambiguity of disaster relief information and using Interval Type-2 Fuzzy Set (IT2TFS), this paper presents a collaborative optimization model based on an integrative emergency material supplier evaluation framework. The optimal emergency material suppliers are first selected using a multi-attribute group decision-making ranking method. Multi-objective fuzzy optimization is then run in three emergency phases: early -, mid-, and late-disaster relief stages. Focusing on a massive flash flood disaster event in Yunnan Province as a case study, a comprehensive numerical analysis tests and validates the developed model. The results revealed that the proposed optimization method can optimize emergency material planning while ensuring that reserve material safety inventory is always maintained at a reasonable level. The presented method suggests a fuzzy interval to prevent emergency materials’ safety inventory shortage and minimize continuous life/property losses in disaster-affected areas.

A new regret theory-based risk decision-making method for renewable energy investment under uncertain environment

Renewable energy is considered as a promising solution to alleviate the exploitation of fossil fuel energy and to keep sustainable development. Hence, renewable energy investments are attracting more and more attention. To solve the renewable energy investment problems under uncertain environment, this paper proposes a new multi-criteria risk decision-making method based on interval type-2 fuzzy sets (IT2FSs) and regret theory. First, to describe the uncertainty of real-world situation, the evaluation information is expressed by linguistic terms and encoded into IT2FSs. Second, a new interval type-2 fuzzy projection model is proposed to measure the relationships between alternatives under interval type-2 fuzzy environment. Then, to determine the criteria weights, a new interval type-2 fuzzy entropy weight determination model is developed. Moreover, some new rules are provided to explore the difference between alternatives under different spaces (i.e., positive space and negative space). Finally, the regret theory is extended to describe the psychological behavior of decision makers and select the optimal alternative under risk and uncertainty environment. A case study including comparative analysis is provided to manifest the feasibility and advantages of the proposed method.

Interval Type-2 Fuzzy Disturbance Observer-Based T–S Fuzzy Control for a Pneumatic Flexible Joint

In this article, an interval type-2 fuzzy disturbance observer (IT2FDO) is proposed for the trajectory tracking control of a flexible joint actuated by a pneumatic artificial muscle and a torsion spring. Interval type-2 fuzzy sets are introduced into the fuzzy disturbance observer (FDO) to enhance the fuzzy approximation capability. A novel adaptive law that updates all the parameters of the FDO, including the control representative values, the center vectors, and the width vectors, is developed. A new control strategy incorporating the proposed IT2FDO and Takagi–Sugeno (T–S) fuzzy model-based control is designed for the trajectory tracking task. With the newly designed adaptive law, the stability of the IT2FDO and that of the closed-loop system are guaranteed. Simulation studies verify the effectiveness of the proposed IT2FDO, and real-world experiments demonstrate the robustness of the proposed control strategy to the external disturbance.

Multiobjective Evolutionary Interpretable Type-2 Fuzzy Systems With Structure and Parameter Learning for Hexapod Robot Control

This article proposes a data-driven multiobjective evolutionary interval type-2 fuzzy-logic system (IT2FLS) learning approach that considers both system performance and rule interpretability. One characteristic of the evolutionary learning framework is that the IT2FLS structure is incrementally generated instead of searching from an initially huge grid-type rule base, which significantly reduces the parameter search space. Another one is that a new constrained objective function is proposed to improve the distinguishability of the generated interval type-2 fuzzy sets (FSs) without restricting them to be evenly distributed. Because of the tradeoff between system performance and interpretability, a new multiobjective ant colony optimization (ACO) algorithm is proposed to optimize the IT2FLS parameters and improve optimization performance. The evolutionary IT2FLS learning approach is applied to control a real wall-following hexapod robot. The approach shows the advantages of model-free design and interpretability and robustness to noise in the evolved type-2 fuzzy rules. Simulations with performance comparisons and experiments in controlling a real robot show the advantages of the learning approach.

Multi-attribute decision making application using hybridly modelled Gaussian Interval Type-2 Fuzzy sets with uncertain mean

Multi-attribute decision making application using hybridly modelled Gaussian Interval Type-2 Fuzzy sets with uncertain mean

Interval type-2 outlier-robust picture fuzzy clustering and its application in medical image segmentation

Based on picture fuzzy set theory, picture fuzzy clustering has achieved good results on some data as more information is involved in the clustering process. However, current picture fuzzy clustering methods still suffer from two common weaknesses, i.e., the sensitivity to outliers and the neglect of the uncertainty caused by different fuzzy degrees, which influence their performance in practical applications like medical image segmentation. To solve these issues, we present two new picture fuzzy clustering methods in this paper. First, to improve immunity to outliers, we propose an outlier-robust picture fuzzy clustering method named ORPFC by using a robust distance measurement, which treats the data objects far away from cluster prototypes as outliers and limits their effects on the prototype update. Second, to handle the uncertainty caused by fuzzy degrees, we further present an interval type-2 enhanced method called IT2ORPFC by incorporating the interval type-2 fuzzy set theory into ORPFC. In each iteration, IT2ORPFC estimates positive memberships, neutral memberships, and refusal memberships according to different fuzzification coefficients and then conducts type reduction for reliable type-1 clustering results. In the experiments, the proposed methods obtain robust and reliable results on eleven datasets. Specifically, ORPFC and IT2ORPFC achieve rewarding performance on segmenting medical images with noise.

Soft clustering and interval type-2 fuzzy set based inference strategy for I.T. personnel selection

Impreciseness and uncertainty are the fabrics that make life interesting. For decades, human beings have developed strategies to cope with uncertainties and automate them. In personnel selection for the I.T. field, selectors often find it very difficult to select candidates by going through a set of resumes containing similar kinds of skills. Hence the selection task becomes a fuzzy decision making with the uncertainty involved. A combination of fuzzy clustering and Interval Type-2 fuzzy sets (IT2FS) is proposed in such scenarios. An experiment is conducted over a resume dataset containing fifteen hundred resumes for a particular job description. Firstly, Fuzzy C-means clustering (FCM) is applied for selective clustering, while decision-making under uncertainty is carried through IT2FS. The candidates in the selected cluster are given a score for ranking as per the skillset criteria. The final decision for shortlisting the resumes is carried through IT2FS. The model shows an average accuracy of 88.2% with an F1-score of 0.76 compared to (K-means + IT2FS) model with an F1-score of 0.72. Thus, the proposed model performs better while decision-making under uncertainty.

An extended multi-criteria group decision-making method with psychological factors and bidirectional influence relation for emergency medical supplier selection

The COVID-19 pandemic outbreak spread rapidly worldwide, posing a severe threat to human life. Due to its unpredictability and destructiveness, the emergency has aroused great common in society. At the same time, the selection of emergency medical supplier is one of the critical links in emergency decision-making, so undertaking appropriate decision-making using scientific tools becomes the primary challenge when an emergency outbreak occurs. The multi criteria group decision-making (MCGDM) method is an applicable and common method for choosing supplier. Nevertheless, because emergency medical supplier selection should consider regarding many aspects, it is difficult for decision makers (DMs) to develop a comprehensive assessment method for emergency medical supplier. Therefore, few academics have focused on emergency situation research by the MCGDM method, and the existing MCGDM method has some areas for improvement. In view of this situation, in this study, we propose a new MCGDM method, which considers the bidirectional influence relation of the criteria, consensus and the psychological factors of DMs. It providers a good aid in emergency decision-making and it could apply to other types of MCGDM research. Firstly, DMs give their assessment in interval type-2 fuzzy sets (IT2FSs). Secondly, an extended IT2FSs assessment method and a novel ISM-BWM-Cosine Similarity-Max Deviation Method (IBCSMDM) are used for weighing all alternatives. The TODIM (an acronym for interactive and multi-criteria decision-making in Portuguese) can obtain the ranking results under different risk attenuation factors. Eventually, this extended IT2FSs-IBCSMDM-TODIM method is applied in a real case in Wuhan in the context of COVID-19 to illustrate the practicability and usefulness.

Design of single and double acceptance sampling plans based on interval type-2 fuzzy sets

Defectiveness of items is generally considered as a certain value in acceptance sampling plans (ASPs). It is clear that, it may not be certainly known in some real-case problems. Uncertainties of the inspection process such as measurement errors, inspectors’ hesitancies or vagueness of the process etc. should be taken into account to obtain more reliable results. The fuzzy set theory (FST) is one of the best methods to overcome these problems. There are some studies in the literature formulating the ASPs with the help of FST. Deciding the right membership functions of the fuzzy sets (FSs) has a vital importance on the quality of the uncertainty modeling. Additionally, the fuzzy set extensions have been offered to model more complicated uncertainties to achieve better modeling. As one of these extensions, type-2 fuzzy sets (T2FSs) gives an ability to model uncertainty in situations where it is not possible to determine exact membership function parameters. In this study, single and double ASPs based on interval T2FSs (IT2FSs) have been designed for binomial and Poisson distributions. Thus, it becomes possible to make more flexible, sensitive and descriptive sensitivity analyzes. The main characteristic functions of ASPs have been derived and the suggested formulations have been illustrated on a comparative application from manufacturing process. Results allowing for more comprehensive analysis as against to the traditional and T1FSs based plans have been obtained.

A metaheuristic approach for interval type-2 fuzzy fractional order fault-tolerant controller for a class of uncertain nonlinear system*

A new optimum interval type-2 fuzzy fractional-order controller for a class of nonlinear systems with incipient actuator and system component faults is introduced in this study. The faults of the actuator and system component (leak) are taken into account using an additive model. The Interval Type-2 Fuzzy Sets (IT2FS) is used to design an optimal fuzzy fractional order controller, and two different nature inspired metaheuristic algorithms, Follower Pollination Algorithm (FPA) and Genetic Algorithm (GA), are used to optimize the parameters of the fuzzy PID controller and Interval Type-2 Fuzzy Tilt-Integral-Derivative Controller (IT2FTID) for nonlinear system. The suggested control approach consists of two parts: an Interval Type-2 Fuzzy Logic Controller (IT2FLC) controller and a fractional order TID controller. Additionally, the two inputs of the IT2FLC are also calibrated using two fine tuning parameters and , respectively. The stability of the proposed controller is presented with some conditions. In addition to unknown dynamics, some unknown process disturbances, such as rapid changes in the control variable, are taken into account to check the efficacy of the proposed control scheme. Two nonlinear conical two-tank level systems are used in the simulation as a case study. The performance of the suggested approach is also compared to that of a widely recognized Interval Type-2 Fuzzy Proportional-Integral-Derivative (IT2FPID) Controller. Finally, the proposed control scheme's fault-tolerant behaviour is demonstrated using fault-recovery time results and statistical Z-tests for both controllers, and the proposed IT2FTID controller's effectiveness is demonstrated when compared to IT2FPID and existing passive fault tolerant controllers in recent literature.