The existence of vague objects. (English) Zbl 1373.03034
Summary: We consider a category whose objects are defined as triplets \((S, e, \underline{c})\) where \(S\) is a set, \(e\) is a similarity and \(\underline{c} \in S\). An object is called crisp if the similarity is crisp, vague otherwise. We indicate different ways of obtaining a similarity and therefore different ways to obtain an object. The paper is mathematical in nature, nevertheless I hope that the proposed formalisms are in some ways connected with the very interesting ontological question about the existence of vague objects in real world.
MSC:
| 03B52 | Fuzzy logic; logic of vagueness |
| 03A05 | Philosophical and critical aspects of logic and foundations |
| 18A15 | Foundations, relations to logic and deductive systems |
| 20N25 | Fuzzy groups |
Keywords:
vague objects; category theory; ontology; similarity; fuzzy subgroups; fuzzy logic; ontic vaguenessReferences:
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