A Small Course on Indistinguishability Operators

This is a short introduction to indistinguishability operators. Section 1 contains the definition of these operators and gives basic reasons for their study. Section 2 explains the two most popular ways to generate them, depending on the way the data are given. Section 3 introduces the idea of extensionality and shows that extensional fuzzy subsets with respect to a T-indistinguishability operator are the only fuzzy observable fuzzy subsets. Two maps that give upper and lower approximations of a fuzzy subset by extensional ones are studied. Perhaps the most interesting section is the last one (Section 4). It contains a number of comments and results that can be useful both to people interested in theoretical research and to people interested in applications. For people not familiarized with t-norms, I recommend the excellent book by Klement, Mesiar, Pap ([33]) or if they are in a hurry to replace ”t-norm” by ”product ” or ”minimum”. More information and results on indistinguishability operators can be found i