Reinforcement learning is one of the most important learning methods for intelligent robots working in unknown/uncertain environments. Multi-dimensional fuzzy Q-learning, an extension of the Q-learning method, has been proposed in this study. The proposed method has been applied for an intelligent robot working in a dynamic environment. The rewards from the evaluation functions and the fuzzy Q-...

In this paper, by using the concept of belongingness (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, we introduce (α, β)-fuzzy positive implicative ideals in BCK-algebras where α, β are any of {∈, q, ∈ ˅ q, ∈ ˄ q} with α ≠ ∈ ˄ q.

Using fuzzy filters in the sense of P. Eklund and W. Gähler [2], it turns out that fuzzy preuniform convergence spaces introduced in [11] form a strong topological universe in which fuzzy topological spaces as well as fuzzy (quasi) uniform spaces can be studied. Thus, better tools such as the existence of natural function spaces, the existence of one-point extensions (and consequently, the here...

Fuzzy set theory has entered into a large variety of disciplines of sciences,technology and humanities having established itself as an extremely versatileinterdisciplinary research area. Accordingly different notions of fuzzystructure have been developed such as fuzzy normed linear space, fuzzytopological vector space, fuzzy sequence space etc. While reviewing theliterature in fuzzy sequence sp...

For any two points P = (p (1) ,p (2) ,...,p (n)) and Q = (q (1) ,q (2) ,...,q (n)) of R n , we define the crisp vector → PQ = (q (1) −p (1) ,q (2) −p (2) ,...,q (n) −p (n)) = Q(−)P. Then we obtain an n-dimensional vector space E n = { → PQ | for all P,Q ∈ R n }. Further, we extend the crisp vector into the fuzzy vector on fuzzy sets of R n. Let D, E be any two fuzzy sets on R n and define the f...

Using the belongs to relation (∈) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (α, β)-fuzzy subalgebras where α, β are any two of {∈, q, ∈∨ q, ∈ ∧ q} with α 6=∈ ∧ q is introduced, and related properties are

On the basis of the concept of grades of a fuzzy point to belongingness (∈) or quasi-coincident (q) or belongingness and quasi-coincident (∈ ∧q) or belongingness or quasi-coincident (∈ ∨q) in an intuitionistic fuzzy set of a ring, the notion of a (α,β )intuitionistic fuzzy subring and ideal is introduced by applying the Lukasiewicz 3-valued implication operator. Using the notion of fuzzy cut se...

Abstract Extending the belongs to (∈) relation and quasi-coincidence with(q) relation between fuzzy points and a fuzzy subsets, the concept of (α, β)-fuzzy filters and (α, β)-fuzzy filters of lattice implication algebras are introduced, where α, β ∈ {∈h , qδ, ∈h ∨qδ, ∈h ∧qδ}, α, β ∈ {∈h, qδ, ∈h ∨ qδ, ∈h ∧ qδ} but α ∈h ∧qδ, α ∈h ∧ qδ, respectively, and some related properties are investigated. S...

in this paper, new definitions of $l$-fuzzy closure operator, $l$-fuzzy interior operator, $l$-fuzzy remote neighborhood system, $l$-fuzzy neighborhood system and $l$-fuzzy quasi-coincident neighborhood system are proposed. it is proved that the category of $l$-fuzzy closure spaces, the category of $l$-fuzzy interior spaces, the category of $l$-fuzzy remote neighborhood spaces, the category of ...

is the Hecke L-series attached to the eigenform f . Hecke’s theory shows that L(f, s) has an Euler product expansion identical to (2), and also that it admits an integral representation as a Mellin transform of f . This extends L(f, s) analytically to the whole complex plane and shows that it satisfies a functional equation relating its values at s and 2− s. The modularity of E thus implies tha...