Related papers: Smarandache Fuzzy Algebra
This book introduces the concept of neutrosophic bilinear algebras and their generalizations to n-linear algebras, n>2. This book has five chapters. The first chapter is introductory in nature and gives a few essential definitions and…
The concept of Smarandache isotopy is introduced and its study is explored for Smarandache: groupoids, quasigroups and loops just like the study of isotopy theory was carried out for groupoids, quasigroups and loops. The exploration…
This article computes the number of fuzzy subgroups of symmetric group $S_5$. First, an equivalence relation on the set of all fuzzy subgroups of a group G is defined.Without any equivalence relation on fuzzy subgroups of group G, the…
It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We show that other symmetries which have been studied for…
Red and blue galaxies are traditionally classified using some specific cuts in colour or other galaxy properties, which are supported by empirical arguments. The vagueness associated with such cuts are likely to introduce a significant…
Bigraphs and their algebra is a model of concurrency. Fuzzy bigraphs are a generalization of birgraphs intended to be a model of concurrency that incorporates vagueness. More specifically, this model assumes that agents are similar,…
This paper presents three new families of fractional Sobolev spaces and their accompanying theory in one-dimension. The new construction and theory are based on a newly developed notion of weak fractional derivatives, which are natural…
The purpose of this paper is to introduce different types of operations on fuzzy ideals of $\Gamma$-semirings and to prove subsequently that these oprations give rise to different structures such as complete lattice, modular lattice on some…
The fuzzification of classical set theory came into existence when Zadeh [1] laid down the concept of a fuzzy set as a generalization of a crisp set. The objective of this paper is to extend the concept of fuzzy endomorphism to fuzzy…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy…
The operator semirings of a $\Gamma$-semiring have been brought into use to study $\Gamma$-semiring in terms of fuzzy subsets. This is accomplished by obtaining various relationships between the set of all fuzzy ideals of a…
Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…
In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory and lattice theory point of view. Ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic and first, we…
Fuzzy relation equations (FRE)are associated with the composition of binary fuzzy relations. In the present work FRE are used as a tool for studying the process of learning a new subject matter by a student class. A classroom application…
For the first time we represent every finite group in the form of a graph in this book. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group.…
B. Tanay et. al. introduced and studied fuzzy soft topological spaces. Here we introduce fuzzy soft point and study the concept of neighborhood of a fuzzy soft point in a fuzzy soft topological space. We also study fuzzy soft closure and…
In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…