We show here some of our results on intuitionistic fuzzy topological spaces. In 1983, K.T. Atanassov proposed a generalization of the notion of fuzzy set: the concept of intuitionistic fuzzy set [1]. Some basic results on intuitionistic fuzzy sets were publised in [2,3], and the book [4] provides a comprehensive coverage of virtually all results until 1999 in the area of the theory and applicat...

and Applied Analysis 3 Definition 1.3 see 25 . Let X, μ, ν, ∗, be a intuitionistic fuzzy metric space. Let A be any subset of X. Define φ t inf { μ ( x, y, t ) : x, y ∈ A}, ψ t sup{ν(x, y, t) : x, y ∈ A}, 1.2 i A is said to be q-bounded if limt→∞φ t 1 and limt→∞ψ t 0, ii A is said to be semibounded if limt→∞φ t k and limt→∞ψ t 1 − k, 0 < k < 1 iii A is said to be unbounded if limt→∞φ t 0 and li...

We address two open theoretical questions in Policy Gradient Reinforcement Learning. The first concerns the efficacy of using function approximation to represent the state action value function, Q. Theory is presented showing that linear function approximation representations of Q can degrade the rate of convergence of performance gradient estimates by a factor of O(ML) relative to when no func...

Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0, A] are obtained under both the Hellinger distance and the L(p)(Q) distance, where 1 ≤ p < ∞ and Q is a probability measure on [0, A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

We study the convergence properties of an alternating proximal minimization algorithm for nonconvex structured functions of the type: L(x, y) = f(x)+Q(x, y)+g(y), where f : Rn → R∪{+∞} and g : Rm → R∪{+∞} are proper lower semicontinuous functions, and Q : Rn × Rm → R is a smooth C function which couples the variables x and y. The algorithm can be viewed as a proximal regularization of the usual...