In this paper a new class of fuzzy sets, namely r-(τi, τj)-θ-generalized fuzzy closed sets is introduced for smooth bitopological spaces. This class falls strictly in between the class of r-(τj, τi)fuzzy θ-closed sets and the class of r-(τi, τj)generalized fuzzy closed sets. Furthermore, by using the class of r-(τi, τj)-θgeneralized fuzzy closed sets we establish a new fuzzy closure operator wh...

Double crises of chaotic oscillators in the presence of fuzzy uncertainty are studied by means of the fuzzy generalized cellmappingmethod.A fuzzy chaotic attractor is characterized by its global topology and membership distribution. A fuzzy crisis implies a simultaneous sudden change both in the topology of the chaotic attractor and in its membership distribution. It happenswhen a fuzzy chaotic...

In an 〈E,M 〉-category X for sinks, we identify necessary conditions for Galois connections from the power collection of the class of (composable pairs) of morphisms in M to factor through the “lattice” of all closure operators on M , and to factor through certain sublattices. This leads to the notion of regular closure operator. As one byproduct of these results we not only arrive (in a novel w...

We study interior operators and interior structures in a fuzzy setting. We investigate systems of “almost open” fuzzy sets and the relationships to fuzzy interior operators and fuzzy interior systems.

In this paper, the local function, weak semi-local function and closure are compared with each other according to inclusion relation. We define a new operator by using investigate its properties. Thanks operator, we obtain two topologies which finer than some previously defined topologies.

The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, since they are not dual. This paper offers them attention, comming to the following conclusions: some kind of hardly describable ”local preduality” still makes pos...

We introduce fuzzy closure systems and fuzzy closure operators as extensions of closure systems and closure operators. We study relationships between fuzzy closure systems and fuzzy closure spaces. In particular, two families F (S) and F (C) of fuzzy closure systems and fuzzy closure operators on X are complete lattice isomorphic.

This paper presents a new genetic operator called adaptive operator to improve local portions of chromosomes. This new operator is implemented into PseudoBacterial Genetic Algorithm (PBGA). The PBGA was proposed by the authors as a new approach combining a genetic algorithm (GA) with a local improvement mechanism inspired by a process in bacterial genetics. The PBGA was applied for the acquisit...

Rough set theory is an excellent mathematical tool for the analysis of a vague description actions in decision problems. Now, this paper by considering notion equality algebra, lower and upper approximations are introduced some properties them given. Moreover, it proved that define interior operator closure operator, respectively. Also, using D-lower D-upper approximation, conditions nonempty s...