Geodesic
Characterization of fuzzy order relation by fuzzy cone
Kybernetika, Tome 58 (2022) no. 5, pp. 779-789
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In the present paper, fuzzy order relations on a real vector space are characterized by fuzzy cones. It is well-known that there is one-to-one correspondence between order relations, that a real vector space with the order relation is an ordered vector space, and pointed convex cones. We show that there is one-to-one correspondence between fuzzy order relations with some properties, which are fuzzification of the order relations, and fuzzy pointed convex cones, which are fuzzification of the pointed convex cones.
In the present paper, fuzzy order relations on a real vector space are characterized by fuzzy cones. It is well-known that there is one-to-one correspondence between order relations, that a real vector space with the order relation is an ordered vector space, and pointed convex cones. We show that there is one-to-one correspondence between fuzzy order relations with some properties, which are fuzzification of the order relations, and fuzzy pointed convex cones, which are fuzzification of the pointed convex cones.
DOI : 10.14736/kyb-2022-5-0779
Classification : 03E72, 18B35
Keywords: fuzzy order relation; fuzzy cone 
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Kon, Masamichi. Characterization of fuzzy order relation by fuzzy cone. Kybernetika, Tome 58 (2022) no. 5, pp. 779-789. doi: 10.14736/kyb-2022-5-0779

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