scholarly journals Cartesian product and Topology On Fuzzy BI-Algebras

2021 ◽  
Vol 8 ◽  
pp. 29-33
Author(s):  
Gerima Tefera ◽  
Abdi Oli
Keyword(s):  
Cartesian Product ◽  
Fuzzy Topology ◽  
Basic Properties ◽  
And Topology

In this paper,the concepts of homomorphism in fuzzy BI-algebra is intro- duced, and also basic properties of homo- morphisms are investigated. The cartesian product in fuzzy ideals of BI-algebra is investigated with related prop- erties; The concepts of fuzzy topology on BI- algebra elaborated.

Topological systems and Artin glueing

2012 ◽  
Vol 62 (4) ◽  
Author(s):  
Sergey Solovyov
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Fuzzy Topology ◽  
Adjoint Functor ◽  
And Topology ◽  
Necessary And Sufficient

AbstractUsing methods of categorical fuzzy topology, the paper shows a relation between topological systems of S. Vickers and Artin glueing of M. Artin. Inspired by the problem of interrelations between algebra and topology, we show the necessary and sufficient conditions for the category, obtained by Artin glueing along an adjoint functor, to be (co)algebraic and (co)monadic, incorporating the respective result of G. Wraith. As a result, we confirm the algebraic nature of the category of topological systems, showing that it is monadic.

scholarly journals Fuzzy functions: a fuzzy extension of the category SET and some related categories

2000 ◽  
Vol 1 (1) ◽  
pp. 115 ◽  
Author(s):  
Ulrich Höhle ◽  
Hans-E. Porst ◽  
Alexander P. Sostak
Keyword(s):  
Fuzzy Sets ◽  
The Other ◽  
Basic Properties ◽  
And Topology ◽  
Other Hand

<p>In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -&gt; L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.</p>

scholarly journals Fuzzy Bigroup from another Viewpoint

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
L S Akinola
Keyword(s):  
Group Theory ◽  
Group Algebra ◽  
Cartesian Product ◽  
Basic Properties ◽  
Fuzzy Function ◽  
Fuzzy Group ◽  
Definition Of ◽  
Product Of Groups

In group theory, given two groups G and H, it is possible to construct a new group from the Cartesian product of G and H, G × H. With this as a motivation, we replicate this concept in fuzzy group algebra. In this paper, we take a slight deviation from the familiar definition of fuzzy bigroup by looking at fuzzy bigroup from the idea of Cartesian product of groups. We define Cartesian fuzzy function on groups and give examples. We also define Cartesian fuzzy bigroup and study some of its basic properties.

GENERALIZED RELATIVE CARDINALITIES OF FUZZY SETS

2005 ◽  
Vol 13 (01) ◽  
pp. 1-10 ◽  
Author(s):  
DANIEL PILARSKI
Keyword(s):  
Fuzzy Sets ◽  
Main Part ◽  
Cartesian Product ◽  
Product Rule ◽  
Triangular Norm ◽  
Basic Properties ◽  
The Subject

The subject of this paper is a generalized approach to relative scalar cardinalities of fuzzy sets. In the main part of the paper, we discuss basic properties of triangular norm-based relative cardinality such as valuation property, the cartesian product rule and complementary rule. Examples of cardinalities satisfying those properties are also given.

scholarly journals An Investigation on Algebraic Structure of Soft Sets and Soft Filters over Residuated Lattices

ISRN Algebra ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. Rasouli ◽  
B. Davvaz
Keyword(s):  
Algebraic Structure ◽  
Cartesian Product ◽  
Residuated Lattices ◽  
Soft Sets ◽  
Basic Properties ◽  
The Family

We introduce the notion of soft filters in residuated lattices and investigate their basic properties. We investigate relations between soft residuated lattices and soft filter residuated lattices. The restricted and extended intersection (union), ∨ and ∧-intersection, cartesian product, and restricted and extended difference of the family of soft filters residuated lattices are established. Also, we consider the set of all soft sets over a universe set U and the set of parameters P with respect to U, SoftP(U), and we study its structure.

scholarly journals Soft ditopological spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 209-222 ◽  
Author(s):  
Tugbahan Dizman ◽  
Alexander Sostak ◽  
Saziye Yuksel
Keyword(s):  
Fuzzy Sets ◽  
Soft Set ◽  
Fuzzy Topology ◽  
Basic Properties ◽  
Soft Topology ◽  
Continuous Mappings ◽  
Basic Concepts

We introduce the concept of a soft ditopological space as the "soft Generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Ert?rk, ?. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147 (2) (2004), 171-199. Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology. The first one is used to describe openness-type properties of a space while the second one deals with its closedness-type properties. We study basic properties of such spaces and accordingly defined continuous mappings between such spaces.

scholarly journals Neutrosophic Semiopen Hypersoft Sets with an Application to MAGDM under the COVID-19 Scenario

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
D. Ajay ◽  
J. Joseline Charisma ◽  
N. Boonsatit ◽  
P. Hammachukiattikul ◽  
G. Rajchakit
Keyword(s):  
Soft Sets ◽  
Basic Properties ◽  
Optimal Decisions ◽  
And Topology

Hypersoft set is a generalization of soft sets, which takes into account a multiargument function. The main objective of this work is to introduce fuzzy semiopen and closed hypersoft sets and study some of their characterizations and also to present neutrosophic semiopen and closed hypersoft sets, an extension of fuzzy hypersoft sets, along with few basic properties. We propose two algorithms based on neutrosophic hypersoft open sets and topology to obtain optimal decisions in MAGDM. The efficiency of the algorithms proposed is demonstrated by applying them to the current COVID-19 scenario.

scholarly journals Fuzzyr-continuous and fuzzyr-semicontinuous maps

2001 ◽  
Vol 27 (1) ◽  
pp. 53-63 ◽  
Author(s):  
Seok Jong Lee ◽  
Eun Pyo Lee
Keyword(s):  
Fuzzy Topology ◽  
Basic Properties

We introduce a new notion of fuzzyr-interior which is an extension of Chang's fuzzy interior. Using fuzzyr-interior, we define fuzzyr-semiopen sets and fuzzyr-semicontinuous maps which are generalizations of fuzzy semiopen sets and fuzzy semicontinuous maps in Chang's fuzzy topology, respectively. Some basic properties of fuzzyr-semiopen sets and fuzzyr-semicontinuous maps are investigated.

scholarly journals The first general Zagreb coindex of graph operations

2020 ◽  
Vol 5 (2) ◽  
pp. 109-120
Author(s):  
Melaku Berhe Belay ◽  
Chunxiang Wang
Keyword(s):  
Tensor Product ◽  
Cartesian Product ◽  
Molecular Graphs ◽  
Basic Properties ◽  
Graph Operations ◽  
Nano Structures ◽  
Product Composition ◽  
Product Of Graphs

AbstractMany chemically important graphs can be obtained from simpler graphs by applying different graph operations. Graph operations such as union, sum, Cartesian product, composition and tensor product of graphs are among the important ones. In this paper, we introduce a new invariant which is named as the first general Zagreb coindex and defined as \overline{M}^\alpha_1(G)=\Sigma_{uv\in E(\overline{G})}[d_G(u)^\alpha+d_G(v)^\alpha] , where α ∈ ℝ, α ≠ 0. Here, we study the basic properties of the newly introduced invariant and its behavior under some graph operations such as union, sum, Cartesian product, composition and tensor product of graphs and hence apply the results to find the first general Zagreb coindex of different important nano-structures and molecular graphs.

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