This study presents a fuzzy varying coefficient regression model after deleting the outliers to improve the feasibility and effectiveness of the fuzzy regression model. The objective of our methodology is to allow the fuzzy regression coefficients to vary with a covariate, and simultaneously avoid the impact of data contaminated by outliers. In this paper, fuzzy regression coefficients are repr...

We propose to use Chu categories as a general framework for uncertainty analysis, with a special attention to fuzzy theory. We emphasize the fact that by viewing fuzzy concepts as Chu spaces, we can discover new aggregation operators, and model interactions and relationship between fuzzy data; these possibilities are due, in essence, to the category structure of Chu spaces, and especially to th...

In this study, we first define the concept of inverse and direct system in category of fuzzy modules. We investigate whether or not limit of inverse (direct) system of exact sequences of fuzzy modules is exact. Later, we show that direct system limit of exact sequences of fuzzy modules is exact. Generally, limit of inverse system of exact sequences is not exact. Then we define the notion ← (1) ...

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L−ordered fuzzifying convergence spaces, in which the category of L−fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called th...

this paper extends the notion of ditopology to the case where openness and closedness are given in terms of {em a priori} unrelated drading functions. the resulting notion of graded ditopology is considered both in the setting of lattices and in that textures, the relation between the two approaches being discussed in detail. interrelations between graded ditopologies and ditopologies on textur...

$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...

Adaptive Resonance Theory (ART) neural network architectures, such as Fuzzy ARTMAP (FAM), have solved successfully a variety of classification problems. However, FAM suffers from an inherent problem that of creating larger architectures than it is necessary to solve the problem at hand (referred to as the ART category proliferation problem). This problem is especially amplified for classificati...

This survey paper, specifically targeted at a readership of fuzzy logicians and fuzzy set theorists, aims to provide a gentle introduction to the basic notions of quantaloidenriched category theory. We discuss at length the definitions of quantaloid, quantaloidenriched category, distributor and functor, always giving several examples that – hopefully – appeal to the intended readership. To indi...

Morphisms of some categories of sets with similarity relations (Ω-sets) are investigated, where Ω is a complete residuated lattice. Namely a category SetF(Ω) with morphisms (A, δ) → (B, γ) defined as special maps A → B and a category SetR(Ω) with morphisms defined as a special relations A × B → Ω. It is proved that arbitrary maps A → Ω and A × B → Ω can be extended onto morphisms (A, δ) → (Ω,↔)...

Fuzzy ARTMAP (FAM) is currently considered to be one of the premier neural network architectures in solving classification problems. One of the limitations of Fuzzy ARTMAP that has been extensively reported in the literature is the category proliferation problem. That is, Fuzzy ARTMAP has the tendency of increasing its network size, as it is confronted with more and more data, especially if the...