Current Issue : October - December Volume : 2015 Issue Number : 4 Articles : 4 Articles
A new approach to fuzzy clustering is proposed in this paper. It aims to relax some constraints imposed by known algorithms using\na generalized geometrical model for clusters that is based on the convex hull computation. A method is also proposed in order\nto determine suitable membership functions and hence to represent fuzzy clusters based on the adopted geometrical model. The\nconvex hull is not only used at the end of clustering analysis for the geometric data interpretation but also used during the fuzzy\ndata partitioning within an online sequential procedure in order to calculate the membership function. Consequently, a pure fuzzy\nclustering algorithm is obtained where clusters are fitted to the data distribution by means of the fuzzy membership of patterns to\neach cluster.The numerical results reported in the paper show the validity and the efficacy of the proposed approach with respect\nto other well-known clustering algorithms....
We further develop the theory of vague soft groups by establishing the concept of normalistic vague soft groups and normalistic\nvague soft group homomorphism as a continuation to the notion of vague soft groups and vague soft homomorphism. The\nproperties and structural characteristics of these concepts as well as the structures that are preserved under the normalistic vague\nsoft group homomorphism are studied and discussed....
We introduce a notion of dimension of maxââ?¬â??min convex sets, following the approach of tropical convexity. We introduce a\nmaxââ?¬â??min analogue of the tropical rank of a matrix and show that it is equal to the dimension of the associated polytope. We\ndescribe the relation between this rank and the notion of strong regularity in maxââ?¬â??min algebra, which is traditionally defined in\nterms of unique solvability of linear systems and the trapezoidal property....
The max-?ukasiewicz semiring is defined as the unit interval [0, 1] equipped with the arithmetics ââ?¬Å?a + bââ?¬Â = max(a, b) and\nââ?¬Å?abââ?¬Â = max(0, a + b ? 1). Linear algebra over this semiring can be developed in the usual way. We observe that any problem of\nthe max-?ukasiewicz linear algebra can be equivalently formulated as a problem of the tropical (max-plus) linear algebra. Based\non this equivalence, we develop a theory of the matrix powers and the eigenproblem over the max-?ukasiewicz semiring....
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