THE AUTOCONTINUITY OF MONOTONE INTERVAL-VALUED SET FUNCTIONS DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL

- Journal title : Honam Mathematical Journal
- Volume 30, Issue 1, 2008, pp.171-183
- Publisher : The Honam Mathematical Society
- DOI : 10.5831/HMJ.2008.30.1.171

Title & Authors

THE AUTOCONTINUITY OF MONOTONE INTERVAL-VALUED SET FUNCTIONS DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL

Jang, Lee-Chae;

Jang, Lee-Chae;

Abstract

In a previous work [18], the authors investigated autocontinuity, converse-autocontinuity, uniformly autocontinuity, uniformly converse-autocontinuity, and fuzzy multiplicativity of monotone set function defined by Choquet integral([3,4,13,14,15]) instead of fuzzy integral([16,17]). We consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. Then the interval-valued Choquet integral determines a new nonnegative monotone interval-valued set function which is a generalized concept of monotone set function defined by Choquet integral in [18]. These integrals, which can be regarded as interval-valued aggregation operators, have been used in [10,11,12,19,20]. In this paper, we investigate some characterizations of monotone interval-valued set functions defined by the interval-valued Choquet integral such as autocontinuity, converse-autocontinuity, uniform autocontinuity, uniform converse-autocontinuity, and fuzzy multiplicativity.

Keywords

monotone interval-valued set functions;interval-valued functions;fuzzy measures;Choquet integrals;

Language

English

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