In a recent paper, De Baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. In this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. The reasoninglargely ...

With regard to this problem, Di Porto and Filipponi, in [4], conjectured that there are no even-Fibonacci pseudoprimes of the 1 kind, providing some constraints are placed on their existence, and Somer, in [12], extends these constraints by stating some very interesting theorems. Moreover, in [1], a solution has been found for a similar problem, that is, for the sequence {Vn(2,1)}, defined by F...

We consider the periodicity of recursive sequences defined by linear homogeneous recurrence relations of arbitrary order, when they are reduced modulo a positive integer m. We show that the period of such a sequence with characteristic polynomial f can be expressed in terms of the order of ω = x + f as a unit in the quotient ring ‫ޚ‬ m [ω] = ‫ޚ‬ m [x]/ f. When m = p is prime, this order can be ...

in this paper, we define the notions of ultra and involution ideals in $bck$-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative $bck$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $bck$-semilattice, the not...