Control Systems

A Characterization of the Orthogonal Grid Constructions of Copulas
A framework for constructing copulas that can be regarded as a patchwork-like assembly of arbitrary copulas, with nonoverlapping rectangles as patches, is studied in [B. De Baets and H. De Meyer, “Orthogonal grid constructions of copulas,” IEEE Trans. Fuzzy Syst., vol. 15, no. 6, pp. 1053–1062, Dec. 2007], where the authors provide sufficient conditions to derive a family o...


Orness Measure of OWA Operators: A New Approach
The ordered weighted averaging (OWA) operators are an extensively used class of aggregation operators. The weight vector that is associated with an OWA can determine the attitudinal characters of the aggregation. One of these characterizing measures is called the orness measure. The aim of this paper is to introduce orness measures in an axiomatic framework and to propose an alternate definitio...
Stability Analysis of Positive Interval Type-2 TSK Systems With Application to Energy Markets
Positive systems play an important role in many fields including biology, chemistry, and economics, among others. This paper discusses the stability of interval type-2 discrete-time positive Takagi–Sugeno–Kang (TSK) fuzzy systems. It discusses positive TSK systems and their nonzero equilibrium point. It then provides sufficient conditions for their exponential stability and instab...


Fuzzy-Model-Based ${{cal D}}$-Stability and Nonfragile Control for Discrete-Time Descriptor Systems With Multiple Delays
This paper is concerned with the problems of ${{cal D}}$ -stability and nonfragile control for a class of discrete-time descriptor Takagi–Sugeno (T–S) fuzzy systems with multiple state delays. ${{cal D}}$-stability criteria are proposed to ensure that all the poles of the descriptor T–S fuzzy system are located within a disk contained in the unit circle. Furthermore, a suff...
GT2FC: An Online Growing Interval Type-2 Self-Learning Fuzzy Classifier
In this paper, we propose a Growing Type-2 Fuzzy Classifier (GT2FC) for online rule learning from real-time data streams. While in batch rule learning, the training data are assumed to be drawn from a stationary distribution, in online rule learning, data can dynamically change over time becoming potentially nonstationary. To accommodate dynamic change, GT2FC relies on a new semi-supervised onl...


Generalized Markov Models for Real-Time Modeling of Continuous Systems
This paper presents a modeling framework based on finite-state space Markov chains (MCs) and fuzzy subsets to represent signals that vary in a continuous range. Our special attention to this extension of finite-state space MC modeling is motivated by numerous opportunities in applying MC models to represent physical variables in automotive and aerospace systems and, subsequently, using these mo...
Dual Bipolar Measures of Atanassov's Intuitionistic Fuzzy Sets
Measures of Atanassov's intuitionistic fuzzy sets (AIFSs), such as subsethood, cardinality, distance, similarity, correlation, and evaluation functions, are often used in application problems. This paper investigates such measures from various perspectives. First, based on the relative relations of an AIFS to other AIFSs, four functions, namely superiority, noninferiority, determinacy, a...

Hypermatching: Similarity Matching With Extreme Values
An approach is developed for object similarity to support a focus on the role of extreme values in object matching, which is termed hypermatching. Importance weights are first introduced to the matching and variations formulated for objects that do not share all the same attributes. Extreme attribute values are considered by introducing amplification of attribute importance and several signific...
The Generalized TP Model Transformation for T–S Fuzzy Model Manipulation and Generalized Stability Verification
This paper integrates various ideas about the tensor product (TP) model transformation into one conceptual framework and formulates it in terms of the Takagi–Sugeno (T–S) fuzzy model manipulation and control design framework. Several new extensions of the TP model transformation are proposed, such as the quasi and “full,” compact and rank-reduced higher order singula...

OptiFel: A Convergent Heterogeneous Particle Swarm Optimization Algorithm for Takagi–Sugeno Fuzzy Modeling
Data-driven design of accurate and reliable Takagi–Sugeno (T–S) fuzzy systems has attracted a lot of attention, where the model structures and parameters are important and often solved in an optimization framework. The particle swarm optimization (PSO) algorithm is widely applied in the field. However, the classical PSO suffers from premature convergence, and it is trapped easily ...
Simulation of Fuzzy Queueing Systems With a Variable Number of Servers, Arrival Rate, and Service Rate
Fuzzy queueing theory (FQT) is a powerful tool used to model queueing systems taking into account their natural imprecision. The traditional FQT model assumes a fixed number of servers with constant fuzzy arrival and service rates. It is quite common, however, to encounter situations where the number of servers, the arrival rate, and the service rate change with time. In those cases, the variab...

Multicriteria Decision-Making With Imprecise Importance Weights
Our interest here is in multicriteria decision-making when we use a fuzzy measure to capture information about the importances and relationships between the criteria. We describe the use of an integral, such as the Choquet or Sugeno integral, to evaluate the overall satisfaction of each of the available alternatives. We discuss three measures particularly useful for these multicriteria decision...
Robust $mathscr{H}_{infty }$ Control for Stochastic T–S Fuzzy Systems via Integral Sliding-Mode Approach
In this paper, a novel dynamic integral sliding-mode control (ISMC) scheme is proposed for a class of uncertain stochastic nonlinear time-delay systems represented by Takagi–Sugeno fuzzy models. The key advantage of the proposed scheme is that two very restrictive assumptions in most existing ISMC approaches for stochastic fuzzy systems have been removed. It is shown that the closed-loop...
From Fuzzy Cognitive Maps to Granular Cognitive Maps
Fuzzy cognitive maps (FCMs) form a class of graph-oriented fuzzy models describing causal relationships among concepts. In this study, we augment these models by introducing their generalization coming in the form of granular FCMs. In contrast with FCMs, in the granular FCMs, the connections between the nodes (states) are described in the form of information granules, especially intervals and f...
The Reduction of Interval Type-2 LR Fuzzy Sets
Type reduction of interval type-2 (IT2) fuzzy sets is essential in conducting the type-2 fuzzy sets expressed with the resolution forms of IT2 fuzzy sets. Several type reduction methods, such as KM, EKM, and centroid flow, have been proposed. These methods are relatively easy to implement but still computation-intensive because they need to invoke an iterative switching point finding procedure....