Two versions of the generalized sign test and the signed-rank test for interval-valued data (both for one-sample and paired two-sample problem) are proposed. These two versions correspond to different possible views on the interval outcomes of the experiment—either the epistemic or the ontic one. Each view yields its own approach to data analysis which results in different test construction and the way of carrying on the statistical inference.

The probabilistic version of the inclusion–exclusion principle is generalized for IF-events. Two versions of the generalized formula, corresponding to different t-conorms applied for defining the union of IF-events are shown.

Classical statistical tests may be sensitive to violations of the fundamental model assumptions inherent in the derivation and construction of these tests. It is obvious that such violations are much more probable in the presence of vague data. Thus nonparametric tests seem to be promising statistical tools. In the present paper, a distribution-free statistical test for the so-called “many-one problem” with vague data is suggested. This test is a generalization of the k-sample median test. In our approach, we utilize the necessity index of strict dominance, suggested by Dubois and Prade. © 2009 Wiley Periodicals, Inc.

The traditional query languages used in database management systems require precise and unambiguous queries only. Fuzzy querying was introduced to relax this rigidity and allow the user more natural information retrieval. In this article we suggest how to enrich fuzzy querying by the use of IF-sets. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 587–597, 2007.

The problem of the interval defuzzification of fuzzy numbers is discussed. A new continuous operator is suggested and investigated.