On equivalent forms of fuzzy logic systems NM and IMTL
Fuzzy Sets and Systems
Bosbach states on fuzzy structures
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Every Linear Pseudo BL-Algebra Admits a State
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Boolean filters and positive implicative filters of residuated lattices
Information Sciences: an International Journal
States on semi-divisible residuated lattices
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue (pp 315-357) "Ordered structures in many-valued logic"
Is there a need for fuzzy logic?
Information Sciences: an International Journal
Soft Computing - A Fusion of Foundations, Methodologies and Applications
States on semi-divisible generalized residuated lattices reduce to states on MV-algebras
Fuzzy Sets and Systems
The radical of a perfect residuated structure
Information Sciences: an International Journal
On interval fuzzy S-implications
Information Sciences: an International Journal
Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics
Information Sciences: an International Journal
On varieties of MV-algebras with internal states
International Journal of Approximate Reasoning
Generalized Bosbach and Riečan states based on relative negations in residuated lattices
Fuzzy Sets and Systems
Information Sciences: an International Journal
On the existence of states on MTL-algebras
Information Sciences: an International Journal
Generalized Bosbach and Riečan states on nucleus-based-Glivenko residuated lattices
Archive for Mathematical Logic
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The aim of this paper is to study the existences of Bosbach states and Riecan states on finite monoidal t-norm based algebras (MTL-algebras for short). We give some examples to show that there exist MTL-algebras having no Bosbach states and Riecan states. The conditions under which MTL-algebras have Bosbach states and Riecan states are investigated, respectively. We prove that Riecan states on MTL-algebras are reduced to states on IMTL-algebras. Furthermore, the necessary and sufficient conditions for finite linearly ordered locally finite MTL-algebras and peculiar MTL-algebras having Bosbach states and Riecan states are obtained, respectively. In addition, the notions of pseudo-quasi-equivalent and a subalgebra under pseudo-quasi-equivalent are proposed and some of their properties are investigated.