Abstract—This paper is concerned with knowledge representation and extraction of fuzzy if-then rules using Interval Type-2 Context-based Fuzzy C-Means clustering (IT2-CFCM) with the aid of fuzzy granulation. This proposed clustering algorithm is based on information granulation in the form of IT2 based Fuzzy C-Means (IT2-FCM) clustering and estimates the cluster centers by preserving the homoge...

In system modeling with Fuzzy Rule-Based Systems (FRBSs), we may usually find two contradictory requirements, the interpretability and the accuracy of the model obtained. As known, Linguistic Modeling (LM)—where the main requirement is the interpretability—is developed by linguistic FRBSs, while Fuzzy Modeling (FM)—where the main requirement is the accuracy—is developed, among others, by approx...

The concept of fuzzy super irresolute function was considered and studied by Šostak's (1985). A comparison between this type and other existing ones is established. Several characterizations, properties, and their effect on some fuzzy topo-logical spaces are studied. Also, a new class of fuzzy topological spaces under the terminology fuzzy S *-closed spaces is introduced and investigated. 1. In...

A generalized fuzzy topological space called countable fuzzy topological space has already been introduced by the authors. The generalization has been performed by relaxing the criterion of preservation of arbitrary supremum of fuzzy topology to countable supremum. In this paper the notion of fuzzy compactness called c-compactness has been initiated and various properties are studied. Other rel...

In [3], we started the investigation of compactness in fuzzy function spaces in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. This paper goes somewhat deeper in the investigation of fuzzy function spaces using the notion of splitting and conjoining structures on fuzzy subsets. We discuss the connection to the exponential law and give several examples of such...

The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...

The concept of a fuzzy topology on a fuzzy set was introduced in [Fuzzy Set Syst. 45 (1992) 103]. The aim of this paper is to introduce fuzzy semicontinuity and fuzzy semiseparation axioms in this new situation and validity of some characterization of these concepts have been examined. Also, we define a fuzzy generalized semiopen set and introduce fuzzy separation axioms by using this concept. ...

Let D be the open unit disc and, as usual, let H(D) be the algebra of bounded analytic functions on D with ‖f‖ = supz∈D |f(z)|. With pointwise addition and multiplication, H(D) is a well known uniform algebra. In this note we characterize the compact endomorphisms of H(D) and determine their spectra. We show that although not every endomorphism T of H(D) has the form T (f)(z) = f(φ(z)) for some...

Using fuzzy filters in the sense of P. Eklund and W. Gähler [2], it turns out that fuzzy preuniform convergence spaces introduced in [11] form a strong topological universe in which fuzzy topological spaces as well as fuzzy (quasi) uniform spaces can be studied. Thus, better tools such as the existence of natural function spaces, the existence of one-point extensions (and consequently, the here...