• 대한수학회논문집
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• 제9권3호
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• pp.687-700
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• 1994

Throughout this paper we will let H denote the complete Heyting algebra ($H, \vee, \wedge, *$) with order reversing involution *. 0 and 1 denote the supermum and the infimum of $\emptyset$, respectively. Given any set X, any element of $H^X$ is called H-fuzzy set (or, simply f.set) in X and will be denoted by small Greek letters, such as $\mu, \nu, \rho, \sigma$. $H^X$ inherits a structure of H with order reversing involution in natural way, by definding $\vee, \wedge, *$ pointwise (sam notations of H are usual). If $f$ is a map from a set X to a set Y and $\mu \in H^Y$, then $f^{-1}(\mu)$ is the f.set in X defined by f^{-1}(\mu)(x) = \mu(f(x))$. Also for $\sigma \in H^X, f(\sigma)$ is the f.set in Y defined by $f(\sigma)(y) = sup{\sigma(x) : f(x) = y}$ ([4]). A preorder R on a set X is reflexive and transitive relation on X, the pair (X,R) is called preordered set. A map $f$ from a preordered set (X, R) to another one (Y,T) is said to be preorder preserving (inverting) if for $x,y \in X, xRy$ implies $f(x)T f(y) (resp. f(y)Tf(x))$. For the terminology and notation, we refer to [10, 11, 13] for category theory and [7] for H-fuzzy semitopogenous spaces.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2006년도 한국컴퓨터종합학술대회 논문집 Vol.33 No.1 (A)
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• pp.400-402
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• 2006

Matrix multiplication is an important problem in linear algebra. its main significance for combinatorial algorithms is its equivalence to a variety of other problems, such as transitive closure and reduction, solving linear systems, and matrix inversion. Thus the development of high-performance matrix multiplication implies faster algorithms for all of these problems. In this paper. we present a quantitative comparison of the theoretical and empirical performance of key matrix multiplication algorithms and use our analysis to develop a faster algorithm. We propose a Hybrid approach on Winograd's and Strassen's algorithms that improves the performance and discuss the performance of the hybrid Winograd-Strassen algorithm. Since Strassen's algorithm is based on a $2{\times}2$ matrix multiplication it makes the implementation very slow for larger matrix because of its recursive nature. Though we cannot get the theoretical threshold value of Strassen's algorithm, so we determine the threshold to optimize the use of Strassen's algorithm in nodes through various experiments and provided a summary shown in a table and graphs.