L-fuzzy version of Stone's representation theorem for distributive lattices
Fuzzy Sets and Systems - Special issue on mathematical aspects of fuzzy set theory
Fuzzy set representations of some quantum structures
Fuzzy Sets and Systems
On the logic foundation of fuzzy reasoning
Information Sciences: an International Journal
Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras
Fuzzy Sets and Systems
The Paradoxical Success of Fuzzy Logic
IEEE Expert: Intelligent Systems and Their Applications
R0 implication: characteristics and applications
Fuzzy Sets and Systems - Mathematics
A triangular-norm-based propositional fuzzy logic
Fuzzy Sets and Systems - Logic and algebra
On equivalent forms of fuzzy logic systems NM and IMTL
Fuzzy Sets and Systems
Formalized theory of general fuzzy reasoning
Information Sciences—Informatics and Computer Science: An International Journal
Fuzzy implicative and Boolean filters of R0 algebras
Information Sciences—Informatics and Computer Science: An International Journal
Involutive monoidal t-norm based logic and R0 logic
International Journal of Intelligent Systems
Information Sciences: an International Journal
Unified forms of fully implicational restriction methods for fuzzy reasoning
Information Sciences: an International Journal
Boolean filters and positive implicative filters of residuated lattices
Information Sciences: an International Journal
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Topology on the set of R 0 semantics for R 0 algebras
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Normal forms and free algebras for some extensions of MTL
Fuzzy Sets and Systems
Boolean representation of bounded BCK-algebras
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic)
Fuzzy Sets and Systems
Unified forms of Triple I method
Computers & Mathematics with Applications
Undefinability of min-conjunction in MTL
Fuzzy Sets and Systems
Simplification and independence of axioms of fuzzy logic systems IMTL and NM
Fuzzy Sets and Systems
Fuzzy Boolean and positive implicative filters of BL-algebras
Fuzzy Sets and Systems
Information Sciences: an International Journal
Nuclei and conuclei on residuated lattices
Fuzzy Sets and Systems
Generalized Bosbach and Riečan states based on relative negations in residuated lattices
Fuzzy Sets and Systems
Generalized Bosbach and Riečan states on nucleus-based-Glivenko residuated lattices
Archive for Mathematical Logic
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Nilpotent minimum algebras (NM-algebras) are algebraic counterpart of a formal deductive system where conjunction is modeled by the nilpotent minimum t-norm, a logic also independently introduced by Guo-Jun Wang in the mid 1990s. Such algebras are to this logic just what Boolean algebras are to the classical propositional logic. In this paper, by introducing respectively the Stone topology and a three-valued fuzzy Stone topology on the set of all maximal filters in an NM-algebra, we first establish two analogues for an NM-algebra of the well-known Stone representation theorem for a Boolean algebra, which state that the Boolean skeleton of an NM-algebra is isomorphic to the algebra of all clopen subsets of its Stone space and the three-valued skeleton is isomorphic to the algebra of all clopen fuzzy subsets of its three-valued fuzzy Stone space, respectively. Then we introduce the notions of Boolean filter and of three-valued filter in an NM-algebra, and finally we prove that three-valued filters and closed subsets of the Stone space of an NM-algebra are in one-to-one correspondence and Boolean filters uniquely correspond to closed subsets of the subspace consisting of all ultrafilters.