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Among the various extensions to the common [0, 1]-valued truth degrees of " traditional " fuzzy set theory, closed intervals of [0, 1] stand out as a particularly appealing and promising choice for representing imperfect information, nicely accommodating and combining the facets of vagueness and uncertainty without paying too much in terms of computational(More)
With the demand for knowledge-handling systems capable of dealing with and distinguishing between various facets of imprecision ever increasing, a clear and formal characterization of the mathematical models implementing such services is quintessen-tial. In this paper, this task is undertaken simultaneously for the definition of implication within two(More)
—Intuitionistic fuzzy sets form an extension of fuzzy sets: while fuzzy sets give a degree to which an element belongs to a set, intuitionistic fuzzy sets give both a membership degree and a nonmembership degree. The only constraint on those two degrees is that their sum must be smaller than or equal to 1. In fuzzy set theory, an important class of(More)
—Traditional rough set theory uses equivalence relations to compute lower and upper approximations of sets. The corresponding equivalence classes either coincide or are disjoint. This behaviour is lost when moving on to a fuzzy T-equivalence relation. However, none of the existing studies on fuzzy rough set theory tries to exploit the fact that an element(More)
Traditionally, membership to the fuzzy-rough lower, resp. upper approximation is determined by looking only at the worst, resp. best performing object. Consequently, when applied to data analysis problems, these approximations are sensitive to noisy and/or outlying samples. In this paper, we advocate a mitigated approach, in which membership to the lower(More)
Inclusion for fuzzy sets was ÿrst introduced by Zadeh in his seminal 1965 paper. Since it was found that the deÿnition of inclusion was not in the true spirit of fuzzy logic, various researchers have set out to deÿne alternative indicators of the inclusion of one fuzzy set into another. Among these alternatives, the indicator proposed by Sinha and Dougherty(More)
In this paper, we propose a nearest neighbour algorithm that uses the lower and upper approximations from fuzzy rough set theory in order to classify test objects, or predict their decision value. It is shown experimentally that our method outperforms other nearest neighbour approaches (classical, fuzzy and fuzzy-rough ones) and that it is competitive with(More)