Related papers: Polar fuzzy topologies on fuzzy topological vector…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After…
This essay builds on the idea of grouping the polar curves of 2-variable function germs into polar clusters. In the topological category, one obtains a bijective correspondence between certain partitions of the polar quotients of two…
In this paper, we introduce the concepts of m-quasiconvex, originally m-quasiconvex,and generalized m-quasiconvex functionals on topological vector spaces. Then we extend the concept of point separable topological vector spaces (by the…
We enlarge the category of bornological coarse spaces by adding transfer morphisms and introduce the notion of an equivariant coarse homology theory with transfers. We then show that equivariant coarse algebraic $K$-homology and equivariant…
In this paper, a new concept, the fuzzy rate of an operator in linear spaces is proposed for the very first time. Some properties and basic principles of it are studied. Fuzzy rate of an operator $B$ which is specific in a plane is…
Let $Covering$ be the category of the category of fuzzy coverings, and $Partition$, the category of fuzzy partitions. We geometrically construct an isomorphism of categories between $Partition$ and a full subcategory of $Covering$, which…
A few of the algebraic and topological properties of int. fuzzy continuity and int. fuzzy uniform continuity are investigated. Also, the concept of int. fuzzy uniform convergence is introduced thereafter a few result on int. fuzzy uniform…
In this paper, we consider the system of linear equations $Ax=b$, where $A\in \Bbb{R}^{n \times n}$ is a crisp H-matrix and $b$ is a fuzzy $n$-vector. We then investigate the existence and uniqueness of a fuzzy solution to this system. The…
Freezing sets and cold sets have been introduced as part of the theory of fixed points in digital topology. In this paper, we introduce a generalization of these notions, the limiting set, and examine properties of limiting sets.
This paper introduces the concept of kernels on fuzzy sets as a similarity measure for $[0,1]$-valued functions, a.k.a. \emph{membership functions of fuzzy sets}. We defined the following classes of kernels: the cross product, the…
This book has five chapters. Chapter one is introductory in nature. Fuzzy linguistic spaces are introduced in chapter two. Fuzzy linguistic vector spaces are introduced in chapter three. Chapter four introduces fuzzy linguistic models. The…
In this paper, we introduce the notion of a total polar for an arbitrary subspace of a Cayley-Klein space in an analytical framework. We show that the set of all total polars of a subspace is a Schubert variety. The notion of total polar…
By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize those pairs of fuzzy sets which form fuzzy rough sets w.r.t. a t-similarity relation…
In this book, the authors define the new notion of set vector spaces which is the most generalized form of vector spaces. Set vector spaces make use of the least number of algebraic operations, therefore, even a non-mathematician is…
We discuss the holonomic dual of tautological systems, with a view towards applications to linear free divisors and to homogeneous spaces. As a technical tool, we consider a Chevalley--Eilenberg type complex, generalizing Euler--Koszul…
Closure operators are very useful tools in several areas of classical mathematics and in general category theory. In fuzzy set theory, fuzzy closure operators have been studied by G. Gerla (1966). These works generally define a fuzzy subset…
Fuzzy ordered linear spaces, Riesz spaces, fuzzy Archimedean spaces and $\sigma$-complete fuzzy Riesz spaces were defined and studied in several works. Following the efforts along this line, we define fuzzy Riesz subspaces, fuzzy ideals,…
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…
Graph theory has successfully used to solve a wide range of problems encountered in diverse fields such as medical sciences, neural networks, control theory, transportation, clustering analysis, expert systems, image capturing, and network…
We review the interplay of fuzzy field theories and matrix models, with an emphasis on the phase structure of fuzzy scalar field theories. We give a self-contained introduction to these topics and give the details concerning the saddle…