In this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form Ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where A~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisting o...

Fuzzy Gaussian mixture modeling method is proposed in this paper for network anomaly detection. A mixture of Gaussian distributions was used to represent the network data in multi-dimensional feature space. Gaussian parameters were estimated using fuzzy c-means estimation. The method was tested with the KDD Cup data set. Experimental results have shown that the proposed method is more effective...

It is shown that multi-dimensional generalization of the vector product is only possible in seven dimensional space. The three-dimensional vector product proved to be useful in various physical problems. A natural question is whether multi-dimensional generalization of the vector product is possible. This apparently simple question has somewhat unexpected answer, not widely known in physics com...

In this paper, we consider the model that the information on the rewards in vector-valued Markov decision processes includes imprecision or ambiguity. The fuzzy reward model is analyzed as follows: The fuzzy reward is represented by the fuzzy set on the multi-dimensional Euclidian space R and the infinite horizon fuzzy expected discounted reward(FEDR) from any stationary policy is characterized...

Sufficient conditions are established for the solvability of the boundary value problem x(t) = f(x)(t), hi(x) = 0 (i = 1, . . . , n), where f is an operator (hi (i = 1, . . . , n) are operators) acting from some subspace of the space of (n − 1)-times differentiable on the interval ]a, b[ m-dimensional vector functions into the space of locally integrable on ]a, b[ m-dimensional vector functions...

The concept of comonotonicity is a useful tool for solving various problems in insurance and financial economics. The credibilistic comonotonicity of fuzzy vector is defined via its comonotonic support. In general case, the properties of comonotonic fuzzy vector are discussed based on the relation between the joint monotone distribution of a fuzzy vector and its marginal monotone distributions....

ly, regression is orthogonal projection in n-dimensional space. The data y are a vector of dimension n, which we consider an element of the vector space Rn. Let x1, . . ., xp denote the columns of X. Then