Results 141 to 150 of about 74,358 (176)

On filter theory of residuated lattices

Information Sciences, 2010
The authors study filters, Boolean filters (implicative filters), G-filters (positive implicative filters), MV-filters (fantastic filters) and also the corresponding fuzzy filters, fuzzy Boolean filters (fuzzy implicative filters), fuzzy G-filters (fuzzy positive implicative filters), fuzzy MV-filters (fuzzy fantastic filters) of a residuated lattice ...
Yiquan Zhu, Yang Xu 0001
exaly   +4 more sources

On ideals of residuated lattices

Journal of Intelligent & Fuzzy Systems, 2021
In this paper, we first point out some mistakes in [12]. Especially the Theorem 3.9 [12] showed that: Let A be residuated lattice and ∅ ≠ X ⊆ A, then the least ideal containing X can be expressed as: 〈X〉 = {a ∈ A|a ≤ (·· · ((x1 ⊕ x2) ⊕ x3) ⊕ ·· ·) ⊕ xn, xi ∈ X, i = 1, 2 ·· · , n}. But we present an example to illustrate the ideal generation formula may
Yan Yan Dong, Jun Tao Wang 0001
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Topological residuated lattices

Soft Computing, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Saeed Rasouli, Amin Dehghani
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Skew residuated lattices

Fuzzy Sets and Systems, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ivan Chajda, Jan Krnávek
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Rickart residuated lattices

Soft Computing, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On state residuated lattices

Soft Computing, 2015
The authors have adapted the notion of state operator to residuated lattices, and describe elementeray properties of these operators, state residuated lattices, and state filters on them. State filters are studied more thoroughly. It is shown that state filters of a state residuated lattice \((L,\tau)\) with a state operator \(\tau\) form a coherent ...
Pengfei He 0001, Xiaolong Xin 0001, Yongwei Yang 0001   +2 more
openaire   +3 more sources

Residuated lattices and lattice effect algebras

Fuzzy Sets and Systems, 2007
The authors study two partial operations in effect algebras, namely \(a \odot b = (a' \oplus b')'\) if \(a' \oplus b'\) is defined and \(a \to_p b = a' \oplus b\) if \(a' \oplus b\) is defined. They show, e.g., that for an effect algebra \((E, \oplus, 0, 1)\) we obtain a (dual) effect algebra \((E, \odot,0,1)\). Using these operations they construct an
Xiang-Nan Zhou, Qingguo Li, Guo-Jun Wang
openaire   +3 more sources

Roughness in Residuated Lattices

2012
Commutative bounded integral residuated lattices (= residuated lattices) form a large class of algebras containing among others several classes of algebras of fuzzy logics which are related to reasoning under uncertainty. The paper investigates approximation spaces in residuated lattices based on their filters.
Jirí Rachunek, Dana Salounová
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THE STRUCTURE OF COMMUTATIVE RESIDUATED LATTICES

International Journal of Algebra and Computation, 2002
A commutative residuated lattice, is an ordered algebraic structure [Formula: see text], where (L, ·, e) is a commutative monoid, (L, ∧, ∨) is a lattice, and the operation → satisfies the equivalences [Formula: see text] for a, b, c ∊ L. The class of all commutative residuated lattices, denoted by [Formula: see text], is a finitely based variety of ...
James B. Hart, Lori Rafter, Constantine Tsinakis   +2 more
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Prime Filters on Residuated Lattices

2012 IEEE 42nd International Symposium on Multiple-Valued Logic, 2012
In this short paper we give an affirmative answer to the problem left open in \cite{IEEE how to: GDCK}, that is, for any residuated lattice $L$, if prime filters and prime filters of the second kind coincide, then $L$ must be an MTL-algebra.
Michiro Kondo, Esko Turunen
openaire   +1 more source