The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...

In this paper, we study fuzzy congruence relations and kernel ideals of an Ockham algebra A , f , whose truth values are in a complete lattice satisfying the infinite meet distributive law. Some equivalent conditions derived for ideal...

In this paper, we shall introduce generalized fuzzy compactness in L-spaces where L is a complete de Morgan algebra. This definition does not rely on the structure of basis lattice L and no distributivity is required. The intersection of a generalized fuzzy compact L-set and a generalized closed Lset is a generalized fuzzy compact L-set. The generalized irresolute image of a generalized fuzzy c...

A fuzzy logic-based color histogram analysis technique is presented for discriminating benign skin lesions from malignant melanomas in dermoscopy images. The approach extends previous research for utilizing a fuzzy set for skin lesion color for a specified class of skin lesions, using alpha-cut and support set cardinality for quantifying a fuzzy ratio skin lesion color feature. Skin lesion disc...

Image thresholding has played an important role in image segmentation. In this paper, we present a novel spatially weighted fuzzy c-means (SWFCM) clustering algorithm for image thresholding. The algorithm is formulated by incorporating the spatial neighborhood information into the standard FCM clustering algorithm. Two improved implementations of the k-nearest neighbor (k-NN) algorithm are intr...

What is granular computing? As we have said in [6]: There are no mathematically valid formal definitions yet. Informally, any computing theory/technology that involves elements and granules (generalized subsets) may be called granular computing (GrC). Intuitively, elements are the data, and granules are the basic knowledge. So granular computing includes data and knowledge computing/engineering...

In this paper, an adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time delays and unmeasured states. By using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive state observer is designed for estimating the unmeasured states. By combining the adaptive backstepping technique with adaptive fuzzy control desi...

Experts in machine learning and fuzzy system frequently identify understanding the data with the use of logical rules. Reasons for inadequacy of crisp and fuzzy rule-based explanations are presented. An approach based on analysis of probabilities of classification p(Ci|X;ρ) as a function of the size of the neighborhood ρ of the given case X is presented. Probabilities are evaluated using Monte ...