Theory Of Interval Type-2 Fuzzy Sets Research Articles

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.

Optimization the reliability of emergency safety barriers based on the subjective safety analysis and evidential reasoning theory. Case study

PurposeThis study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers.Design/methodology/approachThe emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert's imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis.FindingsA real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures.Research limitations/implicationsThis study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account.Originality/valueOur contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.

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.

Modeling vague spatiotemporal objects based on interval type-2 fuzzy sets

Fuzziness is an inherent property of geographical phenomena and the processes of data acquisition, processing, and analysis often introduce uncertainty. Existing methods predominantly use fuzzy set (FS) theory to capture the fuzziness of geographical phenomena as fuzzy spatial objects. However, this approach has a conceptual confusion regarding fuzziness, uncertainty, and vagueness, and the membership degree is expressed using accurate values that ignore uncertainty. Furthermore, FS-based methods lack a vague temporal descriptor. Herein, a vague-spatiotemporal-object model based on the interval type-2 FS theory is proposed to express the vagueness of spatiotemporal objects. To verify the feasibility and superiority of the proposed method, the fuzzy and vague clustering algorithm was used to classify the vegetation cover types on Poyang Lake Plain, China. Furthermore, the classification accuracy was validated via field investigations, and its ability to identify the wet season of the area was verified via the annual vague water area changes of Poyang Lake. The results indicate that, compared with the spatial object model based on FSs, the proposed method increases the ability to measure membership error and express spatiotemporal vagueness.

Fuzzy Frequent Pattern Mining Algorithm Based on Weighted Sliding Window and Type-2 Fuzzy Sets over Medical Data Stream

Real-time data stream mining algorithms are largely based on binary datasets and do not handle continuous quantitative data streams, especially in medical data mining field. Therefore, this paper proposes a new weighted sliding window fuzzy frequent pattern mining algorithm based on interval type-2 fuzzy set theory over data stream (WSWFFP-T2) with a single scan based on the artificial datasets of medical data stream. The weighted fuzzy frequent pattern tree based on type-2 fuzzy set theory (WFFPT2-tree) and fuzzy-list sorted structure (FLSS) is designed to mine the fuzzy frequent patterns (FFPs) over the medical data stream. The experiments show that the proposed WSWFFP-T2 algorithm is optimal for mining the quantitative data stream and not limited to the fragile databases; the performance is reliable and stable under the condition of the weighted sliding window. Moreover, the proposed algorithm has high performance in mining the FFPs compared with the existing algorithms under the condition of recall and precision rates.

Application of Rough and Fuzzy Set Theory for Prediction of Stochastic Wind Speed Data Using Long Short-Term Memory

Despite the great significance of precisely forecasting the wind speed for development of the new and clean energy technology and stable grid operators, the stochasticity of wind speed makes the prediction a complex and challenging task. For improving the security and economic performance of power grids, accurate short-term wind power forecasting is crucial. In this paper, a deep learning model (Long Short-term Memory (LSTM)) has been proposed for wind speed prediction. Knowing that wind speed time series is nonlinear stochastic, the mutual information (MI) approach was used to find the best subset from the data by maximizing the joint MI between subset and target output. To enhance the accuracy and reduce input characteristics and data uncertainties, rough set and interval type-2 fuzzy set theory are combined in the proposed deep learning model. Wind speed data from an international airport station in the southern coast of Iran Bandar-Abbas City was used as the original input dataset for the optimized deep learning model. Based on the statistical results, the rough set LSTM (RST-LSTM) model showed better prediction accuracy than fuzzy and original LSTM, as well as traditional neural networks, with the lowest error for training and testing datasets in different time horizons. The suggested model can support the optimization of the control approach and the smooth procedure of power system. The results confirm the superior capabilities of deep learning techniques for wind speed forecasting, which could also inspire new applications in meteorology assessment.

Interval Type-2 Fuzzy Passive Filtering for Nonlinear Singularly Perturbed PDT-Switched Systems and Its Application

The problem of designing a passive filter for nonlinear switched singularly perturbed systems with parameter uncertainties is explored in this paper. Firstly, the multiple-time-scale phenomenon is settled effectively by introducing a singular perturbation parameter in the plant. Secondly, the interval type-2 fuzzy set theory is employed where parameter uncertainties are expressed in membership functions rather than the system matrices. It is worth noting that interval type-2 fuzzy sets of the devised filter are different from the plant, which makes the design of the filter more flexible. Thirdly, the persistent dwell-time switching rule, as a kind of time-dependent switching rules, is used to manage the switchings among nonlinear singularly perturbed subsystems, and this rule is more general than dwell-time and average dwell-time switching rules. Next, sufficient conditions are provided for guaranteeing that the filtering error system is globally uniformly exponentially stable with a passive performance. Furthermore, on the basis of the linear matrix inequalities, the explicit expression of the designed filter can be obtained. Finally, a tunnel diode electronic circuit is rendered as an example to confirm the correctness and the validity of the developed filter.

Experiential knowledge representation and reasoning based on linguistic Petri nets with application to aluminum electrolysis cell condition identification

Fuzzy Petri nets (FPNs) play an important role in knowledge representation and reasoning (KRR), and they have been widely used in many fields. Linguistic terms are usually used to express the experiential knowledge of decision-makers in the above fields. However, cognitive nonconformity, fuzziness and uncertainty of experiential knowledge are widespread in industrial production processes, making it difficult for current FPNs to precisely model the experience or cognition of experts. In an effort to overcome the shortcomings of FPNs, linguistic Petri nets (LPNs) are proposed based on interval type-2 fuzzy sets theory and FPNs in this paper. The extended TOPSIS (ETOPSIS) is proposed to fuse together the cognition of multiple decision-makers. An interval type-2 fuzzy ordered weighted averaging operator is proposed to improve the knowledge reasoning capability of LPNs. Two comparisons are presented to demonstrate the validity of the proposed ETOPSIS and LPNs. In addition, the KRR model for aluminum electrolysis cell condition identification (AECCI) is proposed and AECCI results show the proposed methods are efficient to embrace cognitive nonconformity and manage fuzziness and uncertainty of experiential knowledge.

Long-term traffic volume prediction based on K-means Gaussian interval type-2 fuzzy sets

This paper uses Gaussian interval type-2 fuzzy set theory on historical traffic volume data processing to obtain a 24hour prediction of traffic volume with high precision. A K-means clustering method is used in this paper to get 5 minutes traffic volume variation as input data for the Gaussian interval type-2 fuzzy sets which can reflect the distribution of historical traffic volume in one statistical period. Moreover, the cluster with the largest collection of data obtained by K-means clustering method is calculated to get the key parameters of type-2 fuzzy sets, mean and standard deviation of the Gaussian membership function. Using the range of data as the input of Gaussian interval type-2 fuzzy sets leads to the range of traffic volume forecasting output with the ability of describing the possible range of the traffic volume as well as the traffic volume prediction data with high accuracy. The simulation results show that the average relative error is reduced to 8% based on the combined K-means Gaussian interval type-2 fuzzy sets forecasting method. The fluctuation range in terms of an upper and a lower forecasting traffic volume completely envelopes the actual traffic volume and reproduces the fluctuation range of traffic flow.

Long-Term Traffic Volume Prediction Based on Type-2 Fuzzy Sets with Confidence Interval Method

The paper uses Gaussian Interval Type-2 fuzzy sets theory to deal with the 24-h historical traffic volume data with uncertainty and randomness to get the 24-h prediction of traffic volume with higher precision. The central limit theorem is adopted to convert point data of mass traffic flow in sampling time period into interval data (also called confidence interval) which is being used to get the state variables of traffic volume. The historical traffic volume data are divided into a couple of intervals according to the similarity degree of the same sampling period for each day. Each interval represents a traffic state. Take these traffic states as data foundation, Markov chains model is built. Viterbi algorithm is used to find the maximum possible state sequence by decoding from Markov chain model by which the fuzzy inference system is constructed. The confidence interval data retain the uncertainty and randomness of traffic flow, meanwhile reduce the influence of noise from the detection data through the transition from traffic volume data to traffic state data. Fuzzy inference system based on Markov chains and Viterbi algorithm discusses the inherent relevance of traffic volume data. The combined Markov Gaussian Interval Type-2 fuzzy sets leads to interval forecasting traffic volume output with the ability of describing the possible range of the traffic volume as well as the traffic volume prediction data with high accuracy. The simulation results based on actual data show the validity and rationality of the model.

An analysis approach to handle uncertain multi-criteria group decision problems in the framework of interval type-2 fuzzy sets theory

Uncertainty is one of the most important aspects of any decision-making process. One of the tools lately used in uncertain decision making is interval type-2 fuzzy sets (IT2FSs). These sets unlike the traditional fuzzy sets have more flexibility in expressing uncertainty and can be applied in situations in which the level of vagueness is very high. Unfortunately, most of the recently published papers on this issue are concerned with extending the existing fuzzy decision-making methods to type-2 fuzzy environment and the improvements were mainly focused on improving the applied fuzzy tool from classic sets to type-2 fuzzy sets. This paper offers a new analysis approach in an uncertain decision-making process that has enhancements in areas of the soft computing. In other words, this paper introduces an IT2F-based approach that has several novelties. Firstly, the decision-making method presents a new approach in computing the decision makers’ weights. This approach gives ideas of each decision maker a weight based on the gathered judgments. Secondly, the approach employs the concept of relative preference relation to evaluate the importance of each criterion. Thirdly, a novel decision-making index is introduced to rank the alternatives. The application of this novel last aggregation method is illustrated through solving an existing example in the literature on e-waste recycling programs assessment in Sri Lanka.

Switched Fuzzy Output Feedback Control and Its Application to a Mass–Spring–Damping System

This paper investigates the dynamic output feedback control problem for interval type-2 (IT2) fuzzy systems. A switched output feedback controller, which depends on the values of membership functions, is constructed. The membership functions of IT2 fuzzy systems contain parameter uncertainties and are different from the type-1 Takagi–Sugeno fuzzy systems. Based on the IT2 fuzzy set theory, the parameter uncertainties can be effectively obtained by upper and lower membership functions. A novel IT2 switched output feedback controller is designed to ensure that the closed-loop system is asymptotically stable with an $H_{\infty }$ performance. Finally, a mass–spring–damping system is proposed to show the feasibility and the merit of the proposed scheme over the other existing ones.

Traffic flow data forecasting based on interval type-2 fuzzy sets theory

This paper proposes a long-term forecasting scheme and implementation method based on the interval type-2 fuzzy sets theory for traffic flow data. The type-2 fuzzy sets have advantages in modeling uncertainties because their membership functions are fuzzy. The scheme includes traffic flow data preprocessing module, type-2 fuzzification operation module and long-term traffic flow data forecasting output module, in which the Interval Approach acts as the core algorithm. The central limit theorem is adopted to convert point data of mass traffic flow in some time range into interval data of the same time range (also called confidence interval data) which is being used as the input of interval approach. The confidence interval data retain the uncertainty and randomness of traffic flow, meanwhile reduce the influence of noise from the detection data. The proposed scheme gets not only the traffic flow forecasting result but also can show the possible range of traffic flow variation with high precision using upper and lower limit forecasting result. The effectiveness of the proposed scheme is verified using the actual sample application.

An interval type-2 fuzzy model of computing with words

As a methodology, computing with words allows the use of words, instead of numbers or symbols, in the process of computing and reasoning and thus conforms more to humans’ inference when it is used to describe real-world problems. Motivated by Zadeh’s paradigm of computing with words, the literature has proposed a kind of type-1 fuzzy automata as a formal model of computing with words, which takes type-1 fuzzy subsets of symbols as input. However, type-1 fuzzy representation provides a limited platform for approximating the meaning of words since it is not able to capture linguistic uncertainty. In this paper, we develop a formal interval type-2 fuzzy model of computing with words by generalizing the existing type-1 fuzzy sets-based model to an interval type-2 fuzzy environment. Concretely, we take interval type-2 fuzzy automata (i.e., interval type-2 fuzzy finite automata and interval type-2 fuzzy pushdown automata), which combine interval type-2 fuzzy set theory and automaton theory, as a computational model of computing with words. Furthermore, we develop the extension principles to extend from computing with values to computing with words and show that computing with words can be implemented with computing with values in the interval type-2 fuzzy setting at an extra computational cost.

On characterization of generalized interval type-2 fuzzy rough sets

This paper presents a systematic study of interval type-2 fuzzy rough sets integrating rough set theory with interval type-2 fuzzy set theory using constructive and axiomatic approaches. From the perspective of a constructive approach, a pair of lower and upper interval type-2 fuzzy rough approximation operators with respect to an interval type-2 fuzzy relation is defined. The basic properties of the interval type-2 fuzzy rough approximation operators are studied. Using cut sets of interval type-2 fuzzy sets, classical representations of interval type-2 fuzzy rough approximation operators are then presented, and the connections between special interval type-2 fuzzy relations and interval type-2 fuzzy rough approximation operators are investigated. Adopting an axiomatic approach, an operator-oriented characterization of interval type-2 fuzzy rough sets is proposed; in other words, interval type-2 fuzzy rough approximation operators are characterized by axioms. Different axiom sets of interval type-2 fuzzy set-theoretic operators guarantee the existence of different types of interval type-2 fuzzy relations that produce the same operators. Finally, the relationship between interval type-2 fuzzy rough sets and interval type-2 fuzzy topological spaces is examined. We obtain sufficient and necessary conditions for the conjecture that an interval type-2 fuzzy interior (closure) operator derived from an interval type-2 fuzzy topological space can associate with an interval type-2 fuzzy reflexive and transitive relation such that the corresponding lower (upper) interval type-2 fuzzy rough approximation operator is the interval type-2 fuzzy interior (closure) operator.

A two-stage servo feed controller of micro-EDM based on interval type-2 fuzzy logic

In order to improve the performance of micro-electrical discharge machining (micro-EDM), the most important issue is to develop a highly stable servo control system. In order to account for the characteristics of high frequency, serious signal distortion, and high noise in micro-EDM process, type-2 fuzzy logic sets are introduced which is able to handle these uncertainties effectively. Based on interval type-2 fuzzy sets theory, a two-stage servo feed controller is designed. The first stage of the controller is for detecting the discharge state for a single sample point, and the second stage is used to obtain the servo feed speed. In addition, the discrimination and statistical methods for discharge states of sample points are proposed to obtain the proportion of each discharge state in an analytical period. Experiments demonstrate that the new controller can obviously improve the processing efficiency of micro-EDM compared with traditional controllers. Therefore, the proposed interval type-2 fuzzy logic-based two-stage servo feed controller is an effective way to enhance the efficiency and stability of micro-EDM and meanwhile to achieve good processing quality.