In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

Complex arrays with good aperiodic properties are characterised and it is shown how the joining of dimensions can generate sequences which retain the aperiodic properties of the parent array. For the case of 2× 2× . . .× 2 arrays we define two new notions of aperiodicity by exploiting a unitary matrix represention. In particular, we apply unitary rotations by members of a size-3 cyclic subgroup...

the importance as well as the diculty of the problem of ranking fuzzy numbers is pointed out. here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its signal/noise ratios, where the signal and the noise are dened as the middle-point and the spread of each a-cut of a fuzzy number, respectively. we use the value of a ...