17 research outputs found

    On the Minkowski-H\"{o}lder type inequalities for generalized Sugeno integrals with an application

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    In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-H\"{o}lder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi in General Minkowski type and related inequalities for seminormed fuzzy integrals, Sahand Communications in Mathematical Analysis 1 (2014) 9--20 is not true. Next, we study the Minkowski-H\"{o}lder inequality for the lower Sugeno integral and the class of μ\mu-subadditive functions introduced in On Chebyshev type inequalities for generalized Sugeno integrals, Fuzzy Sets and Systems 244 (2014) 51--62. The results are applied to derive new metrics on the space of measurable functions in the setting of nonadditive measure theory. We also give a partial answer to the open problem 2.22 posed by Borzov\'a-Moln\'arov\'a and et al in The smallest semicopula-based universal integrals I: Properties and characterizations, Fuzzy Sets and Systems 271 (2015) 1--17.Comment: 19 page

    An equivalent condition to the Jensen inequality for the generalized Sugeno integral.

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    For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given

    Representation of maxitive measures: an overview

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    Idempotent integration is an analogue of Lebesgue integration where σ\sigma-maxitive measures replace σ\sigma-additive measures. In addition to reviewing and unifying several Radon--Nikodym like theorems proven in the literature for the idempotent integral, we also prove new results of the same kind.Comment: 40 page

    Nejednakosti za integrale bazirane na neaditivnim merama

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    Klasi£ne integralne nejednakosti vezane za Lebegov integral uop²tene su za integrale bazirane na neaditivnim merama. U ovoj tezi dokazana je Bervaldova nejednakost za Sugenov integral. Data je nejednakost koju zadovoljava univerzalni integral, £ije su posledice nejednakosti ebi²eva i Minkovskog. Uop²tenja nejednakosti Jensena, ebi²eva, Holdera i Minkovskog dokazane su za pseudo-integral i data je njihova primena u pseudo-verovatno- ¢i. Sli£no kao u klasi£noj teoriji mere pokazane nejednakosti za pseudointegral su primenjene prilikom uop²tavanja klasi£nog Lp prostor
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