In fuzzy set theory, similarity phenomenon is approached using so-called fuzzy equivalence relations. An important role in fuzzy modeling is played by similarity-based closure (called also the extensional hull). Intuitively, the degree to which an element x belongs to a similarity-based closure of a fuzzy set A is the degree to which it is true that there is an element y in A which is similar t...

Let X,Y be normed spaces. The set of bounded linear operators is noted as L(X,Y ). Let now D = D(A) ⊂ X be a linear subspace, and A : D −→ Y a linear (not necessarily bounded!) operator. Notation: (A,D(A)) : X −→ Y Definition: G(A) := {(x,Ax) |x ∈ D} is called the graph of A. Obviously, G(A) is a linear subspace of X × Y . The linear operator A is called closed if G(A) is closed in X × Y . The ...

(Received) We study the Weyl closure Cl(L) = K(x)h@iL \ D for an operator L of the rst Weyl algebra D = Khx;@i. We give an algorithm to compute Cl(L) and we describe its initial ideal under the order ltration. Our main application is an algorithm for constructing a Jordan-HH older series for a holonomic D-module and a formula for its length. Using the closure, we also reproduce a result of Strr...

The aim of this paper is to investigate the fuzzy number intuitionistic fuzzy multiple attribute decision making problems based on the fuzzy number intuitionistic fuzzy sets and Geometric Bonferroni mean operator. Then, we have proposed two aggregation operators: fuzzy number intuitionistic fuzzy geometric Bonferroni mean (FNIFGBM) operator and fuzzy number intuitionistic fuzzy weighted geometr...

We consider different types of aggregation operators such as the heavy ordered weighted averaging (HOWA) operator and the fuzzy ordered weighted averaging (FOWA) operator. We introduce a new extension of the OWA operator called the fuzzy heavy ordered weighted averaging (FHOWA) operator. The main characteristic of this aggregation operator is that it deals with uncertain information represented...

This paper introduces a new class of fuzzy closure operators called implicative closure operators, which generalize some notions of fuzzy closure operators already introduced by different authors. We show that implicative closure operators capture some usual consequence relations used in Approximate Reasoning, like Chakraborty s graded consequence relation, Castro et al. s fuzzy consequence rel...