Chernoff face is a technique of multidimensional data visualization in multivariate statistics. This paper proposes a new method to quantify the overall features of Chernoff faces, and presents a new programmed method for clustering Chernoff faces. Using this method misjudgment caused by human eyes can be avoided. Moreover, people can further evaluate the samples if the evaluation standard is g...

Developing computer software system is a crucial part of the intelligent design. In order to solve problems presented in software system quality analysis, this paper proposes a quality analysis model for computer software system based on fuzzy information content. In this model, fuzzy information content of quality analysis indicators is defined according to information axiom, and a software sy...

Imprecise choices can be described using either a probabilistic or a fuzzy formalism. No relation between them has been studied so far. In this contribution we present a connection between the two formalisms that strongly makes use of fuzzy implication operators and t-norms. In this framework, Luce’s Choice Axiom turns out to be a special case when the product t-norm is considered and other sim...

This paper provides an algebraic characterization of mathematical structures formed by cartesian products of fuzzy relations with sup-min composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom was given by G. Schmidt and T. Strohlein, and cartesian products of Boolean relation algebras were investigated by B. J onsson and A....

In this paper, we present a general framework for the study of interval type-2 rough fuzzy sets by using both constructive and axiomatic approaches. First, several concepts and properties of interval type-2 fuzzy sets are introduced. Then, a pair of lower and upper interval type-2 rough fuzzy approximation operators with respect to a crisp binary relation is proposed. Classical representations ...

If one of the axioms in ring, namely inverse axiom addition operation, is omitted, it will produce another algebraic structure, a semiring. Analogous to there are zero elements, ideal (left/right) semiring, and cross product semiring ideal. The analog fuzzy has (left/right), associated with membership value. This paper discuss cross-product two (more) ideals from Furthermore, always be But conv...

In the paper we consider non-Archimedean fuzziness and probabilities. The idea of non-Archimedean multiple-validities is that (1) the set of values for the vagueness and probability is uncountable infinite and (2) this set is not wellordered. For the first time the non-Archimedean logical multiple-validity was proposed in [13], [14]. We propose non-Archimedean fuzziness that is defined on an in...

In the previous work we accomplished the problem of defining fuzzy dependency as well as projection and join operators which allow us to decompose a database in such a way that this process is fuzzy loss less. The definition of rules-based fuzzy dependency did not satisfy the transitivity axiom, which is crucial to obtaining the completeness of the counterpart of Armstrong axioms for fuzzy depe...

If m = 2, i.e., P = (p, 1 − p) and Q = (q, 1 − q), we also write DKL(p‖q). The Kullback-Leibler divergence provides a measure of distance between the distributions P and Q: it represents the expected loss of efficiency if we encode an m-letter alphabet with distribution P with a code that is optimal for distribution Q. We can now state the general form of the Chernoff Bound: Theorem 1.1. Let X1...