Riesz-McNaughton functions and Riesz MV-algebras of nonlinear functions

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• 作者：Antonio Di Nola ^{adinola@unisa.it} ; Giacomo Lenzi ; ^{gilenzi@unisa.it} ; Gaetano Vitale ^{gvitale@unisa.it}
• 关键词：Riesz MV-algebras ; Mathematics ; Non-classical logics
• 刊名：Fuzzy Sets and Systems
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：1-14
• 全文大小：337 K
• 卷排序：311

文摘

We focus on Riesz MV-algebras, which are MV-algebras equipped with a multiplication by numbers in the real interval [0,1][0,1]. We consider for every integer n the Riesz MV-algebra of all continuous functions from the n  -th power of [0,1][0,1] to [0,1][0,1] and the Riesz MV-subalgebras thereof. In particular we study the Riesz MV-subalgebras isomorphic to free Riesz MV-algebras with finitely many generators, possibly different from the usual linear models given by what we call Riesz–McNaughton functions (and which generalize McNaughton functions used in the case of MV-algebras). In doing this we characterize zerosets of Riesz–McNaughton functions by means of polyhedra, and we extend to Riesz MV-algebras a duality for MV-algebras exposed in a paper by Marra and Spada.