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유주한,정성관,최원영,이우성,You, Ju-Han,Jung, Sung-Gwan,Choi, Won-Young,Lee, Woo-Sung 한국조경학회 2006 韓國造景學會誌 Vol.34 No.5
This study was carried out to provide guidance to environmental policy makers when deciding which assessment fields (biotic, abiotic, qualitative, functional) should have priority for ecological preservation and to develop an objective and scientific methodology by introducing the engineering concept of the fuzzy integral. The grant of weights was used the eigenvalues calculated by factor analysis, and the converted values of indicators were obtained in multiplying the arithmetic values and eigenvalues. The results of the appropriateness and reliability of assessment fields were examined over 0.6, and the results showed that the design of questionnaire presented no great problems. When the fuzzy integral was calculated to determine the rankings at ${\lambda}$=1, 2, 3, 4, 5, respectively, they were 0.646, 0.630, 0.943, 1.423, and 1.167 for the biotic field, 1.298, 1.400, 0.901, 0.580, and 1.456 for the abiotic field, 0.714, 0.674, 0.346, 0.674, and 1.610 in the qualitative field and 1.000, 0.973, 0.943, 1.024, and 1.008 in the functional field. The sensitivity to ${\lambda}$ value showed that ${\lambda}=4$ was the most suitable. In comparison with ${\lambda}=0$ (the arithmetic mean), the range of change was narrow. Because the range for ${\lambda}=4$ was narrower than my other values, ${\lambda}=4$ was sure to be available in ranking-decision. The fuzzy integral is expected to be a method for analyzing and filtering human thoughts. In the future, in order to overcome linguistic uncertainty and subjectivity, other fuzzy integral models including Sugeno's method, AHP, and so forth should be used.
Hamzeh Agahi,Radko Mesiar,Mehran Motiee 한국통계학회 2016 Journal of the Korean Statistical Society Vol.45 No.3
Working with real phenomena, one often faces situations where additivity assumption is unavailable. Non-additive measures and Choquet integral are attracting much attention from scientists in many different areas such as financial economics, economic modelling, probability theory and statistics. Hoeffding’s and Bernstein’s inequalities are two powerful tools that can be applied in many studies of the asymptotic behaviour of inference problems in probability theory, model selection, stochastic processes and economic modelling. One thing that seems missing is the developments of Hoeffding’s and Bernstein’s inequalities for sums of random variables in non-additive cases. The purposes of this paper are to extend Hoeffding’s and Bernstein’s inequalities for sums of random variables from probability measure space to non-additive measure space, and then establish two complete convergence theorems for more general form.
장이채(Lee-Chae Jang),김태균(Taekyun Kim) 한국지능시스템학회 2007 한국지능시스템학회논문지 Vol.17 No.6
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.
장이채(Lee-Chae Jang),김태균(Taekyun Kim) 한국지능시스템학회 2007 한국지능시스템학회 학술발표 논문집 Vol.17 No.2
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.