Abstract
Abstract In this paper we discuss the algebraic structure of fuzzy numbers assuming that they are generated by a subset of mappings from R to a lattice ordered monoid, particularly to a positive or a negative cone, and for every fuzzy number there is a center defined. Using a special ordering on the set of fuzzy numbers and introducing special binary fuzzy-algebraic operations we obtain different structural properties of these fuzzy numbers. We study these algebraic structures using different class of generator mappings and establish the isomorphism between the real line and the set of the centered fuzzy numbers.
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