• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.209-212
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• 2007

Non-additive measures and their corresponding Choquet integrals are very useful tools which are used in both insurance and financial markets. In both markets, it is important to to update prices to account for additional information. The update price is represented by the Choquet integral with respect to the conditioned non-additive measure. In this paper, we consider a price functional H on interval-valued risks defined by interval-valued Choquet integral with respect to a non-additive measure. In particular, we prove that if an interval-valued pricing functional H satisfies the properties of monotonicity, comonotonic additivity, and continuity, then there exists an two non-additive measures ${\mu}_1,\;{\mu}_2$ such that it is represented by interval-valued choquet integral on interval-valued risks.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.451-454
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• 2007

Non-additive measures and their corresponding Choquet integrals are very useful tools which are used in both insurance and financial markets. In both markets, it is important to update prices to account for additional information. The update price is represented by the Choquet integral with respect to the conditioned non-additive measure. In this paper, we consider a price functional H on interval-valued risks defined by interval-valued Choquet integral with respect to a non-additive measure. In particular, we prove that if an interval-valued pricing functional H satisfies the properties of monotonicity, comonotonic additivity, and continuity, then there exists an two non-additive measures ${\mu}1,\;{\mu}2$ such that it is represented by interval-valued choquet integral on interval-valued risks.

• Proceedings of the Korean Radioactive Waste Society Conference
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• 2004.06a
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• pp.188-188
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• 2004

In the present study, a multicriteria decision-making (MCDM) problem of ranking of important radionuclide release scenarios in a low and intermediate radioactive waste repository is to treat on the basis of non-additive fuzzy measures and fuzzy integral theory. Ranking of important scenarios can lead to the provision of more effective safety measure in a design stage of the repository. The ranking is determined by a relative degree of appropriateness of scenario alternatives.(omitted)

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.71-75
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• 2009

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; $$\Phi((C)\;{\int}\;fd{\mu})\;{\leq}\;(C)\;\int\;\Phi(f)d{\mu},$$ where f is Choquet integrable, ${\Phi}\;:\;[0,\;\infty)\;\rightarrow\;[0,\;\infty)$ is convex, $\Phi(\alpha)\;\leq\;\alpha$ for all $\alpha\;{\in}\;[0,\;{\infty})$ and ${\mu}_f(\alpha)\;{\leq}\;{\mu}_{\Phi(f)}(\alpha)$ for all ${\alpha}\;{\in}\;[0,\;{\infty})$. Furthermore, we give some examples assuring both satisfaction and dissatisfaction of Jensen type inequality for the Choquet integral.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.555-558
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• 2003

The Choquet-Stieltjes integral is defined. It is shown that the Choquet -Stieltjes integral is rep-resented by a Choquet integral. As an application of the theorem above, it is shown that Choquet expected utility model for decision under uncertainty and rank dependent utility model for decision under .risk are respectively same as their simplified version.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.195-198
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• 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
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• v.17 no.6
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• pp.749-753
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• 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.

• The Journal of Advanced Prosthodontics
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• v.7 no.4
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• pp.294-302
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• 2015

PURPOSE. The purpose of this study was to verify the clinical-feasibility of additive manufacturing by comparing the accuracy of four different manufacturing methods for metal coping: the conventional lost wax technique (CLWT); subtractive methods with wax blank milling (WBM); and two additive methods, multi jet modeling (MJM), and micro-stereolithography (Micro-SLA). MATERIALS AND METHODS. Thirty study models were created using an acrylic model with the maxillary upper right canine, first premolar, and first molar teeth. Based on the scan files from a non-contact blue light scanner (Identica; Medit Co. Ltd., Seoul, Korea), thirty cores were produced using the WBM, MJM, and Micro-SLA methods, respectively, and another thirty frameworks were produced using the CLWT method. To measure the marginal and internal gap, the silicone replica method was adopted, and the silicone images obtained were evaluated using a digital microscope (KH-7700; Hirox, Tokyo, Japan) at 140X magnification. Analyses were performed using two-way analysis of variance (ANOVA) and Tukey post hoc test (${\alpha}=.05$). RESULTS. The mean marginal gaps and internal gaps showed significant differences according to tooth type (P<.001 and P<.001, respectively) and manufacturing method (P<.037 and P<.001, respectively). Micro-SLA did not show any significant difference from CLWT regarding mean marginal gap compared to the WBM and MJM methods. CONCLUSION. The mean values of gaps resulting from the four different manufacturing methods were within a clinically allowable range, and, thus, the clinical use of additive manufacturing methods is acceptable as an alternative to the traditional lost wax-technique and subtractive manufacturing.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.350-354
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• 2009

Y. R$\acute{e}$ball$\acute{e}$[Fuzzy Sets and Systems, vol.157, pp.3025-2039, 2006] discussed the representation of necessity measure through the Choquet integral criterian. He also considered a decision maker who ranks necessity measures related with Choquet integral representation. Our motivation of this paper is that a decision maker have an "ambiguity" necessity measure to present preferences. In this paper, we discuss the representation of interval-valued necessity measures through the Choquet integral criterian.

• Journal of Korean Society of Transportation
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• v.21 no.1
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• pp.103-113
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• 2003

This paper shows alternative route search and preference route search for the traffic route search, and proposes the use of the fuzzy non-additive controller by the application of AHP(analytic hierarchy process). It is different from classical route search and notices thinking method of human. Appraisal element, weight of route is extracted from basic of the opinion gathering for the driving expert and example of route model was used for the finding of practice utility. Model evaluation was performed attribute membership function making of estimate element, estimate value setting, weight define by the AHP, non additive presentation of weight according to $\lambda$-fuzzy measure and Choquet fuzzy integral. Finally, alternative route search was possible to real time traffic route search for the well variable traffic environment, and preference route search showed reflection of traffic route search disposition for the driver individual. This paper has five important meaning. (1)The approach is similar to the driver's route selection decision process. (2)The approach is able to control of route appraisal criteria for the multiple attribute. (3)The approach makes subjective judgement objective by a non additive. (4)The approach shows dynamic route search for the alternative route search. (5)The approach is able to consider characteristics of individual drivers attributed for the preference route search.