does not satisfy (EP), because for x = 0.3, y = 0.5 and z = 0.5 we get I (x, I (y, z)) = 0.7 = 0.5 = I (y, I (x, z)). The corrected last two rows are provided in Table 1 here. In both of these cases the natural negation NI is the classical negation NC(x) = 1 − x. One can easily check that the first function satisfies (I1) and it does not satisfy (EP), because for x = 0.3, y = 1 and z = 0, we ge...

In this work we solve an open problem of U.Höhle [Problem 11, Fuzzy Sets and Systems 145 (2004) 471-479]. We show that the solution gives a characterization of all conditionally cancellative t-subnorms. Further, we give an equivalence condition for a conditionally cancellativite t-subnorm to be a t-norm and hence show that conditionally cancellativite t-subnorms whose natural negations are stro...

Let (X,m, H) be a hereditary m-space. A subset of X is said to θ-H-compact relative if for every cover U by m(θ)-open sets X, there exists finite U0 such that \ ∪ ∈ H. We obtain several properties these sets. Also, we define and investigate two kinds strong forms “θ-H-compact X”.