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.

We consider the aggregation operators which are ⊕-additive for commonotone functions. The main result is that any operator is expressed by a kind of general fuzzy integral which uses a family of fuzzy measures connected by a ⊕-additive Cauchy’s equations. In particular, the family of fuzzy measures can be obtained by a ⊕-fitting pseudomultiplication. In this case, the aggregation operator is ex...

In this paper, we investigate the existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor. The notion of ’bounded integral contractor’, introduced by Altman [1], is weaker than Lipschitz condition.

This doubly inequality is known in the literature as Hermite-Hadamard integral inequality for convex mapping.We note that Hadamard’s inequality may be regarded as a refinement of the concept of convexity and it follows easily from Jensen’s inequality. For several recent results concerning the inequality (1) we refer the interested reader to [3,5,6,8,9,11,18,21,22] and the references cited there...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

In this paper, the Henstock integral for fuzzy-number-valued functions in R is defined and some properties of this integral are discussed. Finally, by using the embedding theorem the fuzzy number space E can be embedded into a concrete space, some characterized theorems for this integral are given. AMS Subject Classification: 94D05, 46S40, 47S40, 54A40

In most statistical analysis, inequality or extent of variation in income isrepresented in terms of certain summary measures. But some authors arguedthat the concept of inequality is vague and thus cannot be measured as anexact concept. Therefore, fuzzy set theory provides naturally a useful toolfor such circumstances. In this paper we have introduced a real-valued fuzzymethod of illustrating t...