## Keywords (4)

Publications
Fuzzy integrals and linearity

# Fuzzy integrals and linearity,10.1016/j.ijar.2007.05.013,International Journal of Approximate Reasoning,Radko Mesiar,Andrea Mesiarová

Fuzzy integrals and linearity
Linearity and generalized linearity of fuzzy integrals are studied. For continuous from below fuzzy integrals, linearity leads to the Lebesgue integral while the comonotone linearity results to the Choquet integral with respect to a selfdual fuzzy measure m. Similar results in the case of idempotent linearity are presented. Some open problems were stated, too. Finally, pseudo-linearity related to two types of semirings is discussed.
Journal: International Journal of Approximate Reasoning - IJAR , vol. 47, no. 3, pp. 352-358, 2008
View Publication
 The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
 ( www.sciencedirect.com ) ( linkinghub.elsevier.com ) ( www.informatik.uni-trier.de )

## Citation Context (3)

• ...Clearly, we have Su = I Min and Sh = IProd , where the pseudomultiplications Min and Prod are given (as usual) by Min(a, b) = min(a, b) and Prod(a, b )= a · b. Note that, the nonlinearity of the Sugeno integral Su (see, e.g., [37], [46]) implies that universal integrals are also nonlinear, in general...

### Erich-Peter Klement, et al. A Universal Integral as Common Frame for Choquet and Sugeno Integral

• ...It is well known that Sugeno integral is a type of nonlinear integral [7], i.e., for general case,...

### H. Román-Flores, et al. Extended Chebyshev type inequality for Sugeno integral

• ...Clearly, we have Su = IMin and Sh = IProd, where the pseudo-multiplications Min and Prod are given (as usual) by Min(a, b )= min(a, b) and Prod(a, b )= a · b. Note that the nonlinearity of the Sugeno integral Su (see, e.g., [38], [47]) implies that universal integrals are also nonlinear, in general...

Sort by:

## Citations (19)

### Generalized Lebesgue integral(Citations: 1)

Journal: International Journal of Approximate Reasoning - IJAR , vol. 52, no. 3, pp. 427-443, 2011

### General Barnes-Godunova-Levin type inequalities for Sugeno integral(Citations: 1)

Journal: Information Sciences - ISCI , vol. 181, no. 6, pp. 1072-1079, 2011

### Effect of ω-3 fatty acids on life span

Unknown
Journal: Nutrition , vol. 27, no. 3, pp. 333-333, 2011

### General Minkowski type inequalities for Sugeno integrals(Citations: 18)

Journal: Fuzzy Sets and Systems - FSS , vol. 161, no. 5, pp. 708-715, 2010

### A Universal Integral as Common Frame for Choquet and Sugeno Integral(Citations: 10)

Journal: IEEE Transactions on Fuzzy Systems - TFS , vol. 18, no. 1, pp. 178-187, 2010