Abstract
For L a complete chain with order-reversing involution α→ α′, Rodabaugh [7] defined a fuzzy addition ⊛ in the Hutton fuzzy real line R( L) and studied some of its properties. Subsequently, Lowen [3] made a considerably simpler description of ⊛ and gave a direct proof of the continuity of ⊛. In this paper, we introduce the fuzzy addition ⊛ in the Lowen fuzzy real line μ <( R) [6]. We give several equivalent descriptions of ⊛ which may be used for investigating some properties of ⊛. Moreover, we prove the closedness of ⊛ in the four important subspaces A <( R), F <( R), μ < Z ( R), μ < Q ( R) [4] of μ <( R). This implies, in particular, that the sum of two fuzzy rational numbers is fuzzy rational.
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