Abstract As an important class of aggregation operators, the notion overlap functions was first presented in 2009 order to be considered for applications image processing context. Later, many other researches arised bringing some variations those different purposes. Here, our main goal is defining on lattices and discuss how a weakned version it, named quasi-overlaps, works when continuity elim...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

The circle map in one and two dimensions is studied. Both its stability and synchronization , using a bounded control and persistence, are discussed. This work is expected to be applicable in ecology where spatial effects are known to be important. Also, it will be relevant to systems where delay effects are not negligible.

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...

Linguistic terms are often used to represent the truth degree or credibility degree to manage the uncertainty or imprecision as one of popular ways of knowledge representation in the perception-based decision making problem. This present work represents the credibility of uncertain knowledge using linguistic values. The linguistic-valued credibility is then modeled based on a lattice ordered lo...