we have the crisp vector → PQ= (y(1)−x(1),y(2)−x(2), . . . ,y(n)−x(n)) in a pseudo-fuzzy vector space Fn p (1)= {(a(1),a(2), . . . ,a(n))1∀(a(1),a(2), . . . ,a(n))∈Rn}. There is a one-to-one onto mapping P = (x(1),x(2), . . . ,x(n)) ↔ P̃ = (x(1),x(2), . . . , x)1. Therefore, for the crisp vector → PQ, we can define the fuzzy vector → P̃ Q̃= (y(1)− x(1),y(2)−x(2), . . . ,y(n)−x(n))1 = Q̃ P̃ . Let the...

we have the crisp vector → PQ= (y(1)−x(1),y(2)−x(2), . . . ,y(n)−x(n)) in a pseudo-fuzzy vector space Fn p (1)= {(a(1),a(2), . . . ,a(n))1∀(a(1),a(2), . . . ,a(n))∈Rn}. There is a one-to-one onto mapping P = (x(1),x(2), . . . ,x(n)) ↔ P̃ = (x(1),x(2), . . . , x)1. Therefore, for the crisp vector → PQ, we can define the fuzzy vector → P̃ Q̃= (y(1)− x(1),y(2)−x(2), . . . ,y(n)−x(n))1 = Q̃ P̃ . Let the...

The vector space model of information retrieval is one of the classical and widely applied retrieval models. Paradoxically, it has been characterised by a discrepancy between its formal framework and implementable form. The underlying concepts of the vector space model are mathematical terms: linear space, vector, and inner product. However, in the vector space model, the mathematical meaning o...

the aim of this paper is to introduce $(l,m)$-fuzzy closurestructure where $l$ and $m$ are strictly two-sided, commutativequantales. firstly, we define $(l,m)$-fuzzy closure spaces and getsome relations between $(l,m)$-double fuzzy topological spaces and$(l,m)$-fuzzy closure spaces. then, we introduce initial$(l,m)$-fuzzy closure structures and we prove that the category$(l,m)$-{bf fc} of $(l,m...

A non-trivial example of an L-topological space, the L-fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.

this paper is concerned with the development of a novel classifier for automatic mass detection of mammograms, based on contourlet feature extraction in conjunction with statistical and fuzzy classifiers. in this method, mammograms are segmented into regions of interest (roi) in order to extract features including geometrical and contourlet coefficients. the extracted features benefit from...

To design a fuzzy rule-based classification system (fuzzy classifier) with good generalization ability in a high dimensional feature space has been an active research topic for a long time. As a powerful machine learning approach for pattern recognition problems, support vector machine (SVM) is known to have good generalization ability. More importantly, an SVM can work very well on a high(or e...

To design a fuzzy rule-based classification system (fuzzy classifier) with good generalization ability in a high dimensional feature space has been an active research topic for a long time. As a powerful machine learning approach for pattern recognition problems, support vector machine (SVM) is known to have good generalization ability. More importantly, an SVM can work very well on a high (or ...

an idea of fuzzy reexivity of felbin's type fuzzy normed linear spaces is introduced and its properties are studied. concept of fuzzy uniform normal structure is given and using the geometric properties of this concept xed point theorems are proved in fuzzy normed linear spaces.