New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

Fuzzy-Rough Sets Assisted Attribute Selection

R. Jensen and Q. Shen. Fuzzy-Rough Sets Assisted Attribute Selection. IEEE Transactions on Fuzzy Systems, vol. 15, no. 1, pp. 73-89, 2007.

Tolerance-based and Fuzzy-Rough Feature Selection.

R. Jensen and Q. Shen, 'Tolerance-based and Fuzzy-Rough Feature Selection,' Proceedings of the 16th International Conference on Fuzzy Systems (FUZZ-IEEE'07), pp. 877-882, 2007.

Fuzzy ARTMAP, Slow Learning and Probability Estimation

A nonparametric probability estimation procedure using the fuzzy ARTMAP neural network is here described. Because the procedure does not make a priori assumptions about underlying probability distributions, it yields accurate estimates on a wide variety of prediction tasks. Fuzzy ARTMAP is used to perform probability estimation in two different modes. In a 'slow-learning' mode, input-output associations change slowly, with the strength of each association computing a conditional probability estimate. In 'max-nodes' mode, a fixed number of categories are coded during an initial fast learning interval, and weights are then tuned by slow learning. Simulations illustrate system performance on tasks in which various numbers of clusters in the set of input vectors mapped to a given class.

Towards Possibilistic Fuzzy Answer Set Programming

Fuzzy answer set programming (FASP) is a generalization of answer set programming to continuous domains. As it can not readily take uncertainty into account, however, FASP is not suitable as a basis for approximate reasoning and cannot easily be used to derive conclusions from imprecise information. To cope with this, we propose an extension of FASP based on possibility theory. The resulting framework allows us to reason about uncertain information in continuous domains, and thus also about information that is imprecise or vague. We propose a syntactic procedure, based on an immediate consequence operator, and provide a characterization in terms of minimal models, which allows us to straightforwardly implement our framework using existing FASP solvers.

Hidden Markov Models With Set-Valued Parameters

Hidden Markov models (HMMs) are widely used probabilistic models of sequential data. As with other probabilistic models, they require the specification of local conditional probability distributions, whose assessment can be too difficult and error-prone, especially when data are scarce or costly to acquire. The imprecise HMM (iHMM) generalizes HMMs by allowing the quantification to be done by sets of, instead of single, probability distributions. iHMMs have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. In this paper, we consider iHMMs under the strong independence interpretation, for which we develop efficient inference algorithms to address standard HMM usage such as the computation of likelihoods and most probable explanations, as well as performing filtering and predictive inference. Experiments with real data show that iHMMs produce more reliable inferences without compromising the computational efficiency.

A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

Vision-based target tracking and surveillance with robust set-valued state estimation

Tracking a target from a video stream (or a sequence of image frames) involves nonlinear measurements in Cartesian coordinates. However, the target dynamics, modeled in Cartesian coordinates, result in a linear system. We present a robust linear filter based on an analytical nonlinear to linear measurement conversion algorithm. Using ideas from robust control theory, a rigorous theoretical analysis is given which guarantees that the state estimation error for the filter is bounded, i.e., a measure against filter divergence is obtained. In fact, an ellipsoidal set-valued estimate is obtained which is guaranteed to contain the true target location with an arbitrarily high probability. The algorithm is particularly suited to visual surveillance and tracking applications involving targets moving on a plane.

A robust set-valued state estimation approach to the problem of vision based SLAM for mobile robots

The problem of visual simultaneous localization and mapping (SLAM) is examined in this paper using ideas and algorithms from robust control and estimation theory. Using a stereo-vision based sensor, a nonlinear measurement model is derived which leads to nonlinear measurements of the landmark coordinates along with optical flow based measurements of the relative robot-landmark velocity. Using a novel analytical measurement transformation, the nonlinear SLAM problem is converted into the linear filter is guaranteed stable and the ALAM state estimation error is bounded within an ellipsoidal set. No similar results are available for the commonly employed extended Kalman filter which is known to exhibit divergent and inconsistency characteristics in practice.

Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model

When using linguistic approaches to solve decision problems, we need the techniques for computing with words (CW). Together with the 2-tuple fuzzy linguistic representation models (i.e., the Herrera and Mart´ınez model and the Wang and Hao model), some computational techniques for CW are also developed. In this paper, we define the concept of numerical scale and extend the 2-tuple fuzzy linguistic representation models under the numerical scale.We find that the key of computational techniques
based on linguistic 2-tuples is to set suitable numerical scale with
the purpose of making transformations between linguistic 2-tuples
and numerical values. By defining the concept of the transitive
calibration matrix and its consistent index, this paper develops an optimization model to compute the numerical scale of the linguistic term set. The desired properties of the optimization model are also presented. Furthermore, we discuss how to construct the transitive calibration matrix for decision problems using linguistic preference relations and analyze the linkage between the consistent index of the transitive calibration matrix and one of the linguistic preference relations. The results in this paper are pretty helpful to complete the fuzzy 2-tuple representation models for CW.

Fusion based 3D tracking of mobile transmitters via robust set-valued state estimation with RSS measurements

This paper investigates the problem of location and velocity detection of a mobile agent using Received Signal Strength (RSS) measurements captured by geographically distributed seed nodes. With inherently nonlinear power measurements, we derive a powerful linear measurement scheme using an analytical measurement conversion technique which can readily be used with RSS measuring sensors. We also employ the concept of sensor fusion in conjunction for the case of redundant measurements to further enhance the estimation accuracy.

Short term load forecasting using interval type-2 fuzzy logic systems

Accurate Short Term Load Forecasting (STLF) is essential for a variety of decision making processes. However, forecasting accuracy may drop due to presence of uncertainty in the operation of energy systems or unexpected behavior of exogenous variables. This paper proposes the application of Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) for the problem of STLF. IT2 FLSs, with extra degrees of freedom, are an excellent tool for handling prevailing uncertainties and improving the prediction accuracy. Experiments conducted with real datasets show that IT2 FLS models appropriately approximate future load demands with an acceptable accuracy. Furthermore, they demonstrate an encouraging degree of accuracy superior to feedforward neural networks used in this study.

Interval type-2 fuzzy logic systems for load forecasting : a comparative study

Accurate short term load forecasting (STLF) is essential for a variety of decision-making processes. However, forecasting accuracy can drop due to the presence of uncertainty in the operation of energy systems or unexpected behavior of exogenous variables. This paper proposes the application of Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) for the problem of STLF. IT2 FLSs, with additional degrees of freedom, are an excellent tool for handling uncertainties and improving the prediction accuracy. Experiments conducted with real datasets show that IT2 FLS models precisely approximate future load demands with an acceptable accuracy. Furthermore, they demonstrate an encouraging degree of accuracy superior to feedforward neural networks and traditional type-1 Takagi-Sugeno-Kang (TSK) FLSs.