In this paper, we have generalized the definition of vector space by considering the group as a canonical $m$-ary hypergroup, the field as a krasner $(m,n)$-hyperfield and considering the multiplication structure of a vector by a scalar as hyperstructure. Also we will be consider a normed $m$-ary hypervector space and introduce the concept of convergence of sequence on $m$-ary hypernormed space...

n-Dimensional fuzzy sets are a set extension where the membership values n-tuples of real numbers in unit interval [0,1] increasingly ordered, called n-dimensional intervals. The intervals is denoted by Ln([0,1]). This paper aims to investigate semi-vector spaces over weak semifield and aggregation functions concerning an admissible order on construction Ln([0,1]) based operations spaces. In pa...

We consider a reduced model of four-dimensional Yang-Mills theory with a mass term. This matrix model has two classical solutions, two-dimensional fuzzy sphere and two-dimensional fuzzy torus. These classical solutions are constructed by embedding them into three or four dimensional flat space. They exist for finite size matrices, that is, the number of the quantum on these manifolds is finite....

In this work, we propose an approach for computing the compromised solution of an LR fuzzy linear system by using of a ranking function when the coefficient matrix is a crisp mn matrix. To do this, we use expected interval to find an LR fuzzy vector, X , such that the vector (AX ) has the least distance from (b) in 1 norm and the 1 cut of X satisfies the crisp linear system AX = b ...

Algorithms of fuzzy -means clustering with kernels employed in nonlinear transformations into high dimensional spaces in the support vector machines are studied. The objective functions in the standard method and the entropy based method are considered and iterative solutions in the alternate optimization algorithm are derived. Explicit cluster centers in the data space are not obtained by this...

“Fuzzy Functions” are proposed to be determined separately by two regression estimation models: the least squares estimation (LSE), and Support Vector Machines for Regression (SVR), techniques for the development of fuzzy system models. LSE model tries to estimate the fuzzy function parameters linearly in the original space, whereas SVR algorithm maps the data samples into higher dimensional fe...

We generalize the ElGamal signature scheme for cyclic groups to a signature scheme for n-dimensional vector spaces. The higher dimensional version is based on the untractability of the vector decomposition problem (VDP). Yoshida has shown that under certain conditions, the VDP on a two-dimensional vector space is at least as hard as the computational Diffie-Hellman problem (CDHP) on a one-dimen...

the linear system of equations ax = b where a = [aij ] in cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. in this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as drazin inverse andpseudo-inverse are investigated.

In this paper, we give a generalization of the osculating curves to $n$-dimensional Euclidean space. Based on definition an curve in 3 and 4 dimensional spaces, new type has been defined such that is independent ( n − ) (n−3) th binormal vector n-dimensional space, which called ”a generalized ”. We find relationship between curvatures for any unit speed be congruent E En . particular, character...