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...

We introduce the notion of (L, e)-filters with fuzzy partially order e on complete residuated lattice L. We investigate (L, e)-filters induced by the family of (L, e)-filters and functions. In fact, we study the initial and final structures for the family of (L, e)-filters and functions. From this result, we define the product and co-product for the family of (L, e)-filters and functions.

In this note first by considering the notion of general fuzzy automata (for simplicity GFA), we define the notions of direct product, restricted direct product and join of two GFA. Also, we introduce some operations on (Fuzzy) sets and then prove some related theorems. Finally we construct the general fuzzy recognizers and recognizable sets and give the notion of (trim) reversal of a given GFA....

A t-tautology (triangular tautology) is a propositional formula which is a tautology in all fuzzy logics deened by continuous triangular norms. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable.

We provide a methodology to introduce proof search oriented calculi for a large class of many-valued logics, and a sufficient condition for their Co-NP completeness. Our results apply to many well known logics including Gödel, Lukasiewicz and Product Logic, as well as Hájek’s Basic Fuzzy Logic.

In this paper, we introduce the notion of fuzzy C-matroids, a new class of fuzzy matroids. We study properties of this class and define several new types of fuzzy maps between fuzzy matroids. In addition, we define fuzzy C-inner and fuzzy C-closure operators in this class and characterize fuzzy C-matroids and fuzzy maps between matroids in terms of these notions.

We develop methods that construct an optimal set of vectors with a specified inner product structure, from a given set of vectors in a complex Hilbert space. The optimal vectors are chosen to minimize the sum of the squared norms of the errors between the constructed vectors and the given vectors. Four special cases are considered. In the first, the constructed vectors are orthonormal. In the s...