In this research a genetic fuzzy system (GFS) is proposed that performs discretization parameter learning in the context of the Fuzzy Inductive Reasoning (FIR) methodology and the Linguistic Rule FIR (LR-FIR) algorithm. The main goal of the GFS is to take advantage of the potentialities of GAs to learn the fuzzification parameters of the FIR and LR-FIR approaches in order to obtain reliable and...

This is the fourth in a series of papers extending Martin-Löf’s meaning explanation of dependent type theory to higher-dimensional types. In this installment, we show how to define cubical type systems supporting a general schema of cubical inductive types, inductive types whose constructors may take dimension parameters and may have specified boundaries. Using this schema, we are able to speci...

Land covers mix and high input dimension are two important issues that affect the classification accuracy of remote sensing images. Fuzzy classification has been developed to represent the mixture of land covers. Two fuzzy classifiers of fuzzy rules-based (FRB) and fuzzy neural network (FNN) were studied to illustrate the interpretability of fuzzy classification. Based on the FNN classifier, a ...

The ability to analyze large amounts of data for the extraction of valuable information presents a competitive advantage for any organization. The technologies of data warehousing, OLAP, and data classification support that ability. The data warehouse is a central data pool which integrates heterogeneous data sources and provides strategic information for analysis and decision support. OnLine A...

A text mining system using domain-dependent dictionaries efficiently analyzes text data. The dictionaries store not only important words for the domains, but also rules composed of some important words. This paper proposes a method that automatically acquires the rules from the text data and their classes by using an inductive learning method. The paper shows that a fuzzy inductive learning alg...

Alexandroff T0-spaces have been studied as topological models of the supports of digital images and as discrete models of continuous spaces in theoretical physics. Recently, research has been focused on the dimension of such spaces. Here we study the small inductive dimension of the digital space X (W) constructed in [15] as a minimal open quotient of a fenestrationW ofRn . There are fenestrati...

In this paper, the local fuzzy fractal dimension (LFFD) is proposed to represent the feature of local image complexity. The definition of LFFD is an extension of the box-counting dimension of discrete sets by incorporating the fuzzy set. The relationship between LFFD and local intensity changing is investigated by experiments, which proves that LFFD is an important feature of edges and is insen...

Although fuzzy operators have deserved a large attention in the Euclidean case, almost nothing exists concerning the geodesic case. In this paper, we address this question, by de"ning fuzzy geodesic distances between points in a fuzzy set, and geodesic balls in a fuzzy set (based on the comparison of fuzzy numbers), from which we derive fuzzy geodesic mathematical morphology operators. The prop...

We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension. 0. Asymptotic dimension asdim of a metric space was defined by Gromov for studying asymptotic invariants of discrete groups [1]. This dimension can be considered as ...

In this paper n denotes a natural number, X denotes a set, and F1, G1 denote families of subsets of X. Let us consider X, F1. We say that F1 is finite-order if and only if: (Def. 1) There exists n such that for every G1 such that G1 ⊆ F1 and n ∈ CardG1 holds ⋂ G1 is empty. Let us consider X. Observe that there exists a family of subsets of X which is finite-order and every family of subsets of ...