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.

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.

Comparison of categorical and dimensional approaches to the diagnosis of personality disorders

2020 ◽  
pp. 15-25
Author(s):  
T. G. Gadisov ◽  
A. A. Tkachenko
Keyword(s):  
Comparative Study ◽  
Personality Disorders ◽  
Big Five ◽  
Factor Model ◽  
Five Factor Model ◽  
Personality Structure ◽  
Categorical Approach ◽  
Personal Traits ◽  
Clinical Method ◽  
Neo Five Factor Inventory

Summary. Objective: A comparative study of the personality structure from the perspective the Five-factor personality model (“Big Five”) in mentally healthy and in people with personality disorders depending on the leading radical determined by the clinical method.Materials and methods: a comparative study of personality structures in the mentally healthy (13 people) and in individuals with personality disorders (47 people) was carried out. To assess the personality structure, the NEO-Five Factor Inventory questionnaire was used. Persons with personality disorders were divided into groups in accordance with the leading radical: 24 — with emotionally unstable; 13 — with a histrionic; 6 — with schizoid; 4 — with paranoid radicals.Results: There were no differences in the values of the domains of the Five-Factor personality model between a group of individuals with personality disorders and the norm. The features of domain indicators of the Five-factor personality model were revealed in individuals with personality disorder depending on theradical.Conclusion: The NEO-Five Factor Inventory questionnaire, like most other tools from the perspective of the Five-Factor Model, is not suitable for assessing a person in terms of assigning it to variants of a mental disorder. When comparing the categorical and dimensional approaches to assessing the structure of personality disorders, it was found that the obligate personality traits identified using the categorical approach are fully reflected in the «Big Five» in individuals with a leading schizoid radical. The relations of obligate personal traits with the domains of the Five-factor model of personality in individuals with other (paranoid, histrionic,and emotionally unstable) radicals are less clear.

An Ode to the Categorical Approach

2019 ◽  
Author(s):  
Amit Jain ◽  
Phillip Warren
Keyword(s):  
Categorical Approach

(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.

From K-Nets to PK-Nets: A Categorical Approach

2016 ◽  
Vol 54 (2) ◽  
pp. 5-63
Author(s):  
Alexandre Popoff ◽  
Carlos Agon ◽  
Moreno Andreatta ◽  
Andrée Ehresmann
Keyword(s):  
Categorical Approach

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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