Abstract
In this article, we introduce the ∗-fuzzy (L+)p spaces for 1≤p<∞ on triangular norm-based ∗-fuzzy measure spaces and show that they are complete ∗-fuzzy normed space and investigate some properties in these space. Next, we prove Chebyshev’s inequality and Hölder’s inequality in ∗-fuzzy (L+)p spaces.
Highlights
IntroductionThe standard analysis, based on sigma-additive measures and Lebesgue–Stieltjess integral, including several integral inequalities, has been generalized in the past decades into set-valued analysis, including set-valued measures, integrals, and related inequalities
We use a new model of the fuzzy measure theory (∗-fuzzy measure) which is a dynamic generalization of the classical measure theory
The ∗-fuzzy measure theory has been motivated by defining new additivity property using triangular norms
Summary
The standard analysis, based on sigma-additive measures and Lebesgue–Stieltjess integral, including several integral inequalities, has been generalized in the past decades into set-valued analysis, including set-valued measures, integrals, and related inequalities. Some subsequent generalizations are based on fuzzy sets [1,2] and include fuzzy measures, fuzzy integrals and several fuzzy integral inequalities. We use a new model of the fuzzy measure theory (∗-fuzzy measure) which is a dynamic generalization of the classical measure theory. Our model of the fuzzy measure theory created by replacing the non-negative real range and the additivity of classical measures with fuzzy sets and triangular norms. The ∗-fuzzy measure theory has been motivated by defining new additivity property using triangular norms.
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