Fuzzy Riesz homomorphism on fuzzy Riesz space
N.Cheng, G.G. Chen
TL;DR
This paper explores properties of fuzzy Riesz homomorphisms on fuzzy Riesz spaces, including quotient spaces, order continuity, and factorization, advancing the theoretical framework of fuzzy lattice structures.
Contribution
It introduces new definitions and characterizations of fuzzy quotient spaces and extends the theory of fuzzy Riesz homomorphisms and their extensions.
Findings
Fuzzy Riesz homomorphisms are fuzzy order continuous.
Characterizations of fuzzy Archimedean quotient spaces are provided.
Factorization of fuzzy Riesz homomorphisms is studied.
Abstract
In this paper, we give some properties of fuzzy Riesz homomorphism on fuzzy Riesz space. We give definitions of fuzzy quotient spaces, and some characterizations of fuzzy Archimedean quotient spaces. We prove the properties which fuzzy Riesz homomorphism is fuzzy order continuous, and study the extension of fuzzy lattice homomorphism and the extension of fuzzy order continuous lattice homomorphism. Finally, we investigate the factorization by fuzzy Riesz homomorphisms.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Fixed Point Theorems Analysis · Approximation Theory and Sequence Spaces