• Honam Mathematical Journal
• /
• v.30 no.1
• /
• pp.171-183
• /
• 2008

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.

• Communications of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.227-234
• /
• 2007

At first, we consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. In this paper we investigate some properties and structural characteristics of the monotone interval-valued set function defined by an interval-valued Choquet integral.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.18 no.3
• /
• pp.311-315
• /
• 2008

We introduce nonnegative interval-valued set functions and nonnegative measurable interval-valued Junctions. 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 [17]. We also obtained absolutely continuity of them in [9]. In this paper, we investigate some characterizations of the monotone interval-valued set function defined by the interval-valued Choquet integral, and such as subadditivity, superadditivity, null-additivity, converse-null-additivity.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2007.11a
• /
• pp.195-198
• /
• 2007

In this paper, we consider Lebesgue-type theorems in non-additive measure theory and then investigate interval-valued Choquet integrals and interval-valued fuzzy integral with respect to a additive monotone set function. Furthermore, we discuss the equivalence among the Lebesgue's theorems, the monotone convergence theorems of interval-valued fuzzy integrals with respect to a monotone set function and find some sufficient condition that the monotone convergence theorem of interval-valued Choquet integrals with respect to a monotone set function holds.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.6
• /
• pp.749-753
• /
• 2007

In this paper, we consider Lebesgue-type theorems in non-additive measure theory and then investigate interval valued Choquet integrals and interval-valued fuzzy integral with respect to a additive monotone set function. Furthermore, we discuss the equivalence among the Lebesgue's theorems, the monotone convergence theorems of interval-valued fuzzy integrals with respect to a monotone set function and find some sufficient condition that the monotone convergence theorem of interval-valued Choquet integrals with respect to a monotone set function holds.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.13 no.1
• /
• pp.83-90
• /
• 2013

Intervals can be used in the representation of uncertainty. In this regard, we consider monotone interval-valued set functions and the Choquet integral. This paper investigates characterizations of monotone interval-valued set functions and provides applications of the Choquet integral with respect to monotone interval-valued set functions, on the space of measurable functions with the Hausdorff metric.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2003.05a
• /
• pp.9-13
• /
• 2003

In this paper, we will define comonotonically additive interval-valued functionals which are generalized comonotonically additive real-valued functionals in Shcmeildler[14] and Narukawa[12], and study some properties of them. And we also investigate some relations between comonotonically additive interval-valued functionals and interval-valued Choquet integrals on a suitable function space cf.[19,10,11,13].

• Communications for Statistical Applications and Methods
• /
• v.27 no.3
• /
• pp.365-376
• /
• 2020

Interval-valued data, a type of symbolic data, is given as an interval in which the observation object is not a single value. It can also occur frequently in the process of aggregating large databases into a form that is easy to manage. Various regression methods for interval-valued data have been proposed relatively recently. In this paper, we introduce a nonparametric regression model using the kernel function and a nonlinear regression model for the interval-valued data. We also propose applying the local linear regression model, one of the nonparametric methods, to the interval-valued data. Simulations based on several distributions of the center point and the range are conducted using each of the methods presented in this paper. Various conditions confirm that the performance of the proposed local linear estimator is better than the others.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.14 no.1
• /
• pp.33-38
• /
• 2004

In this paper, we will define comonotonically additive interval-valued functionals which are generalized comonotonically additive real-valued functionals in Schmeidler[14] and Narukawa[12], and prove some properties of them. And we also investigate some relations between comonotonically additive interval-valued functionals and interval-valued Choquet integrals on a suitable function space, cf.[9,10,11,13].

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.4
• /
• pp.287-295
• /
• 2010

Based on the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as interval-valued in tuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy numbers, and the information about attribute weights is partially known. Anumerical example is used to illustrate the applicability of the proposed approach.