minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. also related inequalities to minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. several examples are given to illustrate the validity of theorems. some results on chebyshev and minkowski type inequalities are obtained.

Non-additive entropy measures are important for many applications. We study Havrda and Charvat entropy for record values and have shown that this characterizes the underlying distribution function uniquely. Also the non-additive entropy of record values has been derived in case of some specific distributions. Further we propose a generalized residual entropy measure for record value.

In non-additive measure and integration (or fuzzy measure and integral) one tries to generalise the issues of product measure and conditional expectation from the additive theory. In the discrete case successful attempts have been made via the max-min additive representation of the monotone measure and the corresponding integrals. The present paper intends to find, for arbitrary monotone measur...

In this paper, we study monotone set functions defined as the composition of an additive measure with a strictly increasing function. This function is unary operator in continuous-valued logic, called tau function, and it generator function-based parametric mapping. We provide necessary sufficient condition for equality two that are induced by different functions. Using its properties, introduc...

In this paper, Lebesgue decomposition type theorems for non-additive measure are shown under the conditions of null-additivity, converse null-additivity, weak null-additivity and σ-null-additivity, etc.. In our discussion, the monotone continuity of set function is not required.

In this paper, the well-known Egoroff’s theorem in classical measure theory is established on monotone non-additive measure spaces. Taylor’s theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient condition for the Egoroff’s theorem i...