By using the notion of fuzzy functions introduced by Dib and Youssef, we obtain fuzzy analogues of some results concerning ordinary functions. In particular, we give the definition different from one of invertible fuzzy function introduced by Dib and Youssef. And we show that the two definitions are equivalent. Furthermore, we introduce the concepts of fuzzy increasing functions and fuzzy isomo...

Let A be a commutative semi-local ring containing 1/2. We construct natural isomorphisms

We give a complete description of ring isomorphisms between algebras measurable operators affiliated with von Neumann type II$_1.$

An algorithm has been developed that �nds isomorphisms between both graphs and subgraphs. The development is introduced in the object recognition problem domain. The method isolates matching subgraphs, �nds a node-to-node mapping and reorders nodes thus permitting a direct comparison to be made between the resultant graphs. The algorithm is of polynomial order. It yields approximate results, ma...

Datatypes which differ inessentially in their names and structure are said to be isomorphic; for example, a ternary product is isomorphic to a nested pair of binary products. In some canonical cases, the conversion function is uniquely determined solely by the two types involved. In this article we describe and implement a program in Generic Haskell which automatically infers this function by n...

c W W L Chen, 1991, 1993, 2013. This chapter is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, this document may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible t...

Definition: If (G, *) and (H, •) are groups, then a function f : G −→ H is a homomorphism if f (x * y) = f (x) • f (y) for all x, y ∈ G. Example: Let (G, *) be an arbitrary group and H = {e}, then the function f : G −→ H such that f (x) = e for any x ∈ G is a homomorphism. In fact, f (x * y) = e = e • e = f (x) • f (y).

We study the poset 〈Iκ ,⊆〉 as a measure of how similar the structures A and B are to each other. A subset X of Iκ has the κ back-and-forth property if for all λ < κ ∀p ∈ X[∀a ∈ λA∃b ∈ B (p ∪ {〈a(i), b(i)〉 : i < λ} ∈ X) ∧ ∀b ∈ λB∃a ∈ A(p ∪ {〈a(i), b(i)〉 : i < λ} ∈ X)]. It is obvious that there is a largest κ-back-and-forth set which we denote by I∗ κ . The structures A and B are said to be parti...

Given a graph X, define the presentation PX to have generators the vertices of X, and a relation xy = yx for each pair x, y of adjacent vertices. Let GX be the group with presentation PX, and given a field K, let KX denote the K"-algebra with presentation PX. Given graphs X and Y and a field K, it is known that the algebras KX and KY are isomorphic if and only if the graphs X and Y are isomorph...

There has been a considerable amount of work on retrieving functions in function libraries using their type as search key. The availability of rich component specifications, in the form of behavioral types, enables similar queries where one can search a component library using the behavioral type of a component as the search key. Just like for function libraries, however, component libraries wi...