• Title, Summary, Keyword: Measure theory

### Uncertainty in the dempster-shafer Theory - A Critical Re-examination

• Klir, George J.;Ramer, Arthur
• Journal of the Korean Institute of Intelligent Systems
• /
• v.1 no.2
• /
• pp.4-45
• /
• 1991
• Measures of two types of uncertainty that coexist in the Dempster-Shafer theory are overivewed. A measure of one type of uncertainty, which expresses nonspecificity of evidential claims, is well justified on both intuitive and mathermatical grounds. Proposed measures of the other types of uncertainty, which attempt to capture conflicts among evidential claims, are shown to have some deficiencies. To alleviate these deficiencies, a new measure is proposed. This measure, which is called a measure of discord, is not only satisfactory on intuitive grounds, but has alos desirable mathematical properties. A measure of total uncertainty, which is defined as the sum of nonspecificity and discord, is also discussed. The paper focuses on conceptual issues. Mathematical properties of the measure of idscord are only stated ; their proofs are given in a companion paper.

### INTEGRATION WITH RESPECT TO ANALOGUE OF WIENER MEASURE OVER PATHS IN WIENER SPACE AND ITS APPLICATIONS

• Ryu, Kun-Sik
• Bulletin of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.131-149
• /
• 2010
• In 1992, the author introduced the definition and the properties of Wiener measure over paths in Wiener space and this measure was investigated extensively by some mathematicians. In 2002, the author and Dr. Im presented an article for analogue of Wiener measure and its applications which is the generalized theory of Wiener measure theory. In this note, we will derive the analogue of Wiener measure over paths in Wiener space and establish two integration formulae, one is similar to the Wiener integration formula and another is similar to simple formula for conditional Wiener integral. Furthermore, we will give some examples for our formulae.

### A New Approach to Risk Comparison via Uncertain Measure

• Li, Shengguo;Peng, Jin
• Industrial Engineering and Management Systems
• /
• v.11 no.2
• /
• pp.176-182
• /
• 2012
• This paper presents a new approach to risk comparison in uncertain environment. Based on the uncertainty theory, some uncertain risk measures and risk comparison rules are proposed. Afterward the bridges are built between uncertain risk measures and risk comparison rules. Finally, several comparable examples are given.

### Information Quantification Application to Management with Fuzzy Entropy and Similarity Measure

• Wang, Hong-Mei;Lee, Sang-Hyuk
• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.4
• /
• pp.275-280
• /
• 2010
• Verification of efficiency in data management fuzzy entropy and similarity measure were discussed and verified by applying reliable data selection problem and numerical data similarity evaluation. In order to calculate the certainty or uncertainty fuzzy entropy and similarity measure are designed and proved. Designed fuzzy entropy and similarity are considered as dissimilarity measure and similarity measure, and the relation between two measures are explained through graphical illustration. Obtained measures are useful to the application of decision theory and mutual information analysis problem. Extension of data quantification results based on the proposed measures are applicable to the decision making and fuzzy game theory.

### Information Management by Data Quantification with FuzzyEntropy and Similarity Measure

• Siang, Chua Hong;Lee, Sanghyuk
• Journal of the Korea Convergence Society
• /
• v.4 no.2
• /
• pp.35-41
• /
• 2013
• Data management with fuzzy entropy and similarity measure were discussed and verified by applying reliable data selection problem. Calculation of certainty or uncertainty for data, fuzzy entropy and similarity measure are designed and proved. Proposed fuzzy entropy and similarity are considered as dissimilarity measure and similarity measure, and the relation between two measures are explained through graphical illustration.Obtained measures are useful to the application of decision theory and mutual information analysis problem. Extension of data quantification results based on the proposed measures are applicable to the decision making and fuzzy game theory.

### HOMEOMORPHISMS WITH VARIOUS MEASURE SHADOWING

• BAGHERZAD, M.R.;KIM, SANG JIN
• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.3
• /
• pp.483-489
• /
• 2015
• In this paper we introduce two notions of measure shadowing for homeomorphsims, and study the relationship between them.

### A Study on the Development of the Scale for Measuring Perception of Equity in Marital Relationship (한국부부간 공평성 인지척도 개발에 관한연구)

• 박정희
• Journal of Korean Home Management Association
• /
• v.16 no.2
• /
• pp.107-122
• /
• 1998
• It has been suggested that equity theory a social psychological theory concerned with the fairness in casual relationships should be applicable to marital relationships. This study describes the development of the scale for measuring perception of equity which measure the level of equity in marital relationships among Korean couples. PES(Perception of Equity Scale) is composed of two subscales; detailed measure of equity(DME) and global measure of equity(GME). The PES which include items from two areas of concern for intimates-pschological-emotional concern day-to-day concern-are describes. As results of test reliability of areas of DME range from .86 to .88 and reliability of GME is .92. And there are primarily evidences of construct validity of PES. Therefore PES is very reasonable scale to measure of equity/inequity perception in married couples. Finally analyzing of the level of equity in this sample husbands and wives has generally equitable relationships with their partn rs. Another findings suggest that husbands are overbenefited of their patners through marriage whereas wives are not.

### Psychological Well-being Measurement: A Comparative Study of Korean and American Adults

• An Jeong-shin;Lambert Michael C.;Han Gyoung-hae;Cha Seung-eun
• International Journal of Human Ecology
• /
• v.5 no.2
• /
• pp.13-29
• /
• 2004
• Ryff's(1989) psychological well-being measure is used to assess and sometimes compare Korean and American adults, however, there is no information regarding whether its dimensions are psychometrically invariant across, whether its items provide sufficient information for, and whether each item measures identical trait levels in, the two nations. Confirmatory factor analysis on response 1,696 Korean and 3,669 American adults, gave to the measure revealed lack of fit and absence of factorial invariance across the two nations. Item response theory revealed significant variance for items on each factor across two countries that most items yielded limited psychometric information. And that each item measure different trait levels, suggesting that in its present form, the measure might lead to misleading results for, and across the two nations.

### A Study on the Perception of Equity & the Decision-Making Styles: Application of Summated/Global Measure (도시 주부의 공평성 인지와 의사결정 유형에 관한 연구: 합산적/총체적 측정방법의 적용)

• 이정우;강기연
• Journal of the Korean Home Economics Association
• /
• v.38 no.5
• /
• pp.41-54
• /
• 2000
• While equity theory started as a theory focusing upon the relationship between employee and employer, over the years the theory has been expanded to various other types of relationships including marital relationships. The present research among 251 housewives examines the perception of equity and the decision-making styles from the perspective of equity theory. The perception of equity was measured by the revised TUW scales and the Walster's global measure. Also, decision-making styles was assessed by means of the 'final-say' scale In line with the predictions, the results clearly showed that the perception of equity was a strong predictor variable to the joint decision-making.

### HEAT EQUATION IN WHITE NOISE ANALYSIS

• KimLee, Jung-Soon
• Journal of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.541-555
• /
• 1996
• The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.