In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC)L or (TC)R axioms and the L-relations induced by two L-fuzzy topologi...

Abstract The variety of (pointed) residuated lattices includes a vast proportion the classes algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among outliers, one counts orthomodular and other varieties quantum algebras. We suggest ...

We discuss a formal many-valued logic called EQlogic which is based on a recently introduced special class of algebras called EQ-algebras. The latter have three basic binary operations (meet, multiplication, fuzzy equality) and a top element and, in a certain sense, generalize residuated lattices. The goal of EQ-logics is to present a possible direction in the development of mathematical logics...

It is shown that the Boolean center of complemented elements in a bounded integral residuated lattice characterizes direct decompositions. Generalizing both Boolean products and poset sums of residuated lattices, the concepts of poset product, Priestley product and Esakia product of algebras are defined and used to prove decomposition theorems for various ordered algebras. In particular, we sho...

As an extension of interval-valued pseudo t-norms, pseudo-overlap functions (IPOFs) play a vital role in solving multi-attribute decision making problems. However, their corresponding algebraic structure has not been studied yet. On the other hand, with development non-commutative (non-associative) fuzzy logic, study residuated lattice theory is gradually deepening. Due to conditions operators ...

In this paper, we enlarge the language of triangle algebra by addinga unary operation that describes properties of a state. Thesestructure algebras are called state triangle algebra. The vitalproperties of these algebras are given. The notion of state interval-valued residuated lattice (IVRL)-filters are introduced and givesome examples and properties of them are given. ...

Lattice-valued semiuniform convergence structures are important mathematical in the theory of lattice-valued topology. Choosing a complete residuated lattice $L$ as background, we introduce new type filters using tensor and implication operations on $L$, which is called $\top$-filters. By means $\top$-filters, propose concept $\top$-semiuniform counterpart structures. Different from usual discu...

Recently, three-way concept lattice is studied to handle the uncertainty and incompleteness in the given attribute set based on acceptation, rejection, and uncertain regions. This paper aimed at analyzing the uncertainty and incompleteness in the given fuzzy attribute set characterized by truth-membership, indeterminacy-membership, and falsity membership functions of a defined single-valued neu...

The firing rule of Petri nets relies on a residuation operation for the commutative monoid of natural numbers. We identify a class of residuated commutative monoids, called Petri algebras, for which one can mimic the token game of Petri nets to define the behaviour of generalized Petri net whose flow relation and place contents are valued in such algebraic structures. We show that Petri algebra...