Interval type-2 fuzzy membership function generation methods for pattern recognition

Type-2 fuzzy sets (T2 FSs) have been shown to manage uncertainty more effectively than T1 fuzzy sets (T1 FSs) in several areas of engineering [4], [6], [7], [8], [9], [10], [11], [12], [15], [16], [17], [18], [21], [22], [23], [24], [25], [26], [27] and [30]. However, computing with T2 FSs can require undesirably large amount of computations since it involves numerous embedded T2 FSs. To reduce the complexity, interval type-2 fuzzy sets (IT2 FSs) can be used, since the secondary memberships are all equal to one [21]. In this paper, three novel interval type-2 fuzzy membership function (IT2 FMF) generation methods are proposed. The methods are based on heuristics, histograms, and interval type-2 fuzzy C-means. The performance of the methods is evaluated by applying them to back-propagation neural networks (BPNNs). Experimental results for several data sets are given to show the effectiveness of the proposed membership assignments.     

Comparison of fuzzy implication operators by means of fuzzy relational products used for intelligent local path-planning of AUVs

This paper describes the best choice to fuzzy implication operator and α-cut that are proper to the heuristic search technique for real-time collision avoidance of autonomous underwater vehicles (AUVs). A fuzzy implication operator is applied to the computation of fuzzy triangle product that constructs a new fuzzy relation between two fuzzy relations. An α-cut transforms a fuzzy relation into a crisp relation which is represented as a matrix. Those are the theoretical basis of heuristic search technique. In this paper, we review briefly our previous work—a heuristic search technique using fuzzy relational products for the collision avoidance system of AUVs, and propose the selection of a fuzzy implication operator and α-cut which are the most suitable for the search technique. In order to verify the optimality and the efficiency of the selected fuzzy implication operator and α-cut, we simulate every case of α-cut for each fuzzy implication operator in view of the cost of path and the number of α -cut generating acceptable path to the goal. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2007-521-D00433).     

GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

Generalized H2 （GH2） stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.     

An inverse analysis method for design optimization with both statistical and fuzzy uncertainties

If the statistical data for the input uncertainties are sufficient to construct the distribution function, the input uncertainties can be treated as random variables to use the reliability-based design optimization (RBDO) method; otherwise, the input uncertainties can be treated as fuzzy variables to use the possibility-based design optimization (PBDO) method. However, many structural design problems include both input uncertainties with sufficient and insufficient data. This paper proposes a new mixed-variable design optimization (MVDO) method using the performance measure approach (PMA) for such design problems. For the inverse analysis, this paper proposes a new most probable/possible point (MPPP) search method called maximal failure search (MFS), which is an integration of the enhanced hybrid mean value method (HMV+) and maximal possibility search (MPS) method. This paper also improves the HMV+ method using an angle-based interpolation. Mathematical and physical examples are used to demonstrate the proposed inverse analysis method and MVDO method.