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Erschienen in:
01.10.2011 | Original Paper
States on finite linearly ordered IMTL-algebras
Erschienen in: Soft Computing | Ausgabe 10/2011
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Abstract
The aim of this paper is to study states on finite linearly ordered IMTL-algebras. We prove that Bosbach states, Riečan states and state-morphisms are equivalent on linearly ordered IMTL-algebras. Furthermore, we investigate the existence of states on finite linearly ordered IMTL-algebra and prove that if \(L\) is locally finite, then \(L\) has a state if and only if \(L\) is an MV-algebra, and that if \(L\) is peculiar and \(H(L)\cup\{0,1\}\) is a subalgebra of \(L\), then \(L\) has a state if and only if \(ord(n)=|H(L)|+1\), where \(H(L)=\{x\in L|ord(x)<\infty, ord(\neg x)<\infty\}, n=\max H(L)\).