Characterizations of M-fuzzifying convex spaces via Galois connections

2021 ◽  
pp. 1-11
Author(s):  
Shao-Yu Zhang
Keyword(s):  
Galois Connection ◽  
Galois Connections ◽  
Reflective Subcategory ◽  
Convex Spaces

This paper introduces a special Galois connection combined with the wedge-below relation. Furthermore, by using this tool, it is shown that the category of M-fuzzifying betweenness spaces and the category of M-fuzzifying convex spaces are isomorphic and the category of arity-2 M-fuzzifying convex spaces can be embedded in the category of M-fuzzifying interval spaces as a reflective subcategory.

scholarly journals Galois connections between sets of paths and closure operators in simple graphs

2018 ◽  
Vol 16 (1) ◽  
pp. 1573-1581 ◽  
Author(s):  
Josef Šlapal
Keyword(s):  
Positive Integer ◽  
Digital Images ◽  
Galois Connection ◽  
Simple Graph ◽  
Closure Operators ◽  
Simple Graphs ◽  
Galois Connections ◽  
Digital Plane ◽  
Vertex Set

AbstractFor every positive integer n,we introduce and discuss an isotone Galois connection between the sets of paths of lengths n in a simple graph and the closure operators on the (vertex set of the) graph. We consider certain sets of paths in a particular graph on the digital line Z and study the closure operators associated, in the Galois connection discussed, with these sets of paths. We also focus on the closure operators on the digital plane Z2 associated with a special product of the sets of paths considered and show that these closure operators may be used as background structures on the plane for the study of digital images.

scholarly journals Invariance groups of functions and related Galois connections

2020 ◽  
Author(s):  
Eszter K. Horváth ◽  
Reinhard Pöschel ◽  
Sven Reichard
Keyword(s):  
Boolean Functions ◽  
Group Actions ◽  
Galois Connection ◽  
General Context ◽  
Abstract Group ◽  
Galois Connections ◽  
Invariance Groups ◽  
Galois Closures

Abstract Invariance groups of sets of Boolean functions can be characterized as Galois closures of a suitable Galois connection. We consider such groups in a much more general context using group actions of an abstract group and arbitrary functions instead of Boolean ones. We characterize the Galois closures for both sides of the corresponding Galois connection and apply the results to known group actions.

scholarly journals A categorical approach to abstract convex spaces and interval spaces

2019 ◽  
Vol 17 (1) ◽  
pp. 374-384 ◽  
Author(s):  
Bing Wang ◽  
Qing-Hua Li ◽  
Zhen-Yu Xiu
Keyword(s):  
Categorical Approach ◽  
Reflective Subcategory ◽  
Convex Spaces

Abstract In this paper, we establish the axiomatic conditions of hull operators and introduce the category of interval spaces. We also investigate their relations with convex spaces from a categorical sense. It is shown that the category CS of convex spaces is isomorphic to the category HS of hull spaces, and they are all topological over Set. Also, it is proved that there is an adjunction between the category IS of interval spaces and the category CS of convex spaces. In particular, the category CS(2) of arity 2 convex spaces can be embedded in IS as a reflective subcategory.

scholarly journals Representation of $L$-fuzzy binary relations via a Galois connection

2009 ◽  
Vol 40 (3) ◽  
pp. 287-305
Author(s):  
Nistala V. E. S. Murthy ◽  
Peruru G. Prasad
Keyword(s):  
Complete Lattice ◽  
Galois Connection ◽  
Binary Relations ◽  
Truth Values ◽  
Galois Connections ◽  
Fuzzy Point ◽  
Point Set

Our aim in this Paper is to establish Galois connections between various types of fuzzy binary relations and fuzzy I-ary relations on a crisp set, that take their truth values in a complete lattice, and same type of crisp binary and I-ary relations on the associated fuzzy-point-set.

(L, M)- fuzzy (restricted) convex derived hull spaces

2021 ◽  
pp. 1-13
Author(s):  
Xiu-Yun Wu ◽  
Chun-Yan Liao ◽  
Yan-Hui Zhao
Keyword(s):  
Convex Hull ◽  
Convex Spaces

In this paper, the notion of (L, M)- fuzzy convex derived hull spaces is introduced. It is proved that the category of (L, M)- fuzzy convex derived hull spaces is isomorphic to the category of (L, M)- fuzzy convex spaces and the category of (L, M)- fuzzy convex enclosed relation spaces. Based on this, the notion of (L, M)- fuzzy restricted convex derived hull spaces is introduced. It is further proved that the category of (L, M)- fuzzy restricted convex derived hull spaces is isomorphic to the category of (L, M)- fuzzy restricted convex hull spaces.

scholarly journals M-Hazy Vector Spaces over M-Hazy Field

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1118
Author(s):  
Faisal Mehmood ◽  
Fu-Gui Shi
Keyword(s):  
Vector Space ◽  
Linear Transformation ◽  
Binary Operation ◽  
Vector Spaces ◽  
Fundamental Properties ◽  
Classical Algebra ◽  
Important Development ◽  
Fuzzy Algebra ◽  
Convex Spaces

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space.

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