Many-valued partial orders in a closed monoidal category

被引：2
|
作者：
Demirci, Mustafa [1 ]
机构：
[1] Akdeniz Univ, Fac Sci, Dept Math, TR-07058 Antalya, Turkiye
来源：
FUZZY SETS AND SYSTEMS | 2023年 / 468卷
关键词：
L-set; Lattice-valued partial order; Fuzzy partial order; Many-valued partial order; Categorical many-valued partial order; Quantale-valued partial order; Monoidal relation system; Partially ordered monoidal relation system; EQUIVALENCE-RELATIONS; VAGUE LATTICES; FUZZY; REPRESENTATION;
D O I：
10.1016/j.fss.2023.108591
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
This paper introduces partially ordered Q-monoidal relation systems on a category C endowed with a closed monoidal structure, and therewith explores a categorical theory of many-valued partial orders in C. For a fixed C-object Q and a partially ordered Q-monoidal relation system ϒ on C, the notion of a many-valued preordered (resp. many-valued partially ordered) C-object is formulated as a ϒ-preordered (resp. ϒ-partially ordered) C-object. Furthermore, the category of ϒ-preordered (resp. ϒ-partially ordered) C-objects is constructed and applied to quantale-valued preorders (resp. partial orders) on ordinary sets as well as on & COPY; 2023 Elsevier B.V. All rights reserved.
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页数：35
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