In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function and a scale transformation is given. Consequences for T-(S-)evaluators are established.
We introduce a fuzzy equality for -observables on an -quantum space which enables us to characterize different kinds of convergences, and to represent them by pointwise functions on an appropriate measurable space.
We have modified the axiomatic system of orness measures, originally introduced by Kishor in 2014, keeping altogether four axioms. By proposing a fuzzy orness measure based on the inner product of lattice operations, we compare our orness measure with Yager's one which is based on the inner product of arithmetic operations. We prove that fuzzy orness measure satisfies the newly proposed four axioms and propose a method to determine OWA operator with given fuzzy orness degree.
The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued integral...