| Mathematics and Computer Science |
|
|
|
|
| The subadditivity and autocontinuity of the generalized quasi Sugeno integral |
| LI Yanhong |
| Department of Mathematics, Teacher’s College, Easten Liaoning University, Dandong 118003, Liaoning Province，China |
|
|
|
Abstract A generalized quasi Sugeno integral is a new non-additive integral established based on the induction operator and the classical Sugeno fuzzy integral, it is not only a generalization of the traditional Sugeno fuzzy integral, but also has unique integral properties and theoretical value. In this paper, the definition of a generalized quasi Sugeno integral is introduced through an induction operator, and taking the integral as a set function, it is proved that the set function satisfies the subadditivity for the pseudo addition. The upper (lower) autocontinuity and zero additivity (subtractive property) of the generalized quasi Sugeno integral are discussed according to the subadditivity of the specific set function. Furthermore, the implication relation between the autocontinuity and zero additivity of the integral is expounded.
|
|
Received: 07 March 2018
Published: 25 January 2020
|
|
|
广义拟Sugeno积分的次可加性和自连续性
广义拟Sugeno积分是基于诱导算子和经典Sugeno模糊积分建立的新型非可加积分，是对传统Sugeno模糊积分的推广，具有独特的积分性质和理论价值。在K-拟加测度空间上通过诱导算子引入广义拟Sugeno积分定义，并将该积分看作集函数，证明该集函数对任意2个可测集和拟加法满足次可加性。依这种特定集函数的次可加性，获得了广义拟Sugeno积分的上(下)自连续性和零可加(减)性，进而阐述该积分的自连续和零可加(减)的蕴含关系。
关键词：
诱导算子,
广义拟加Sugeno积分,
次可加,
自连续,
零可加
|
|
1 SUGENO M . Theory of Fuzzy Integrals and Its Applications[D]. Tokyo :Tokyo Institute of Technology, 1974.
2 WANG Z Y . The autocontinuity of set-function and the fuzzy integral[J]. Journal of Mathematical Analysis and Applications,1984, 99(1): 195-218.
3 SUGENO M , MUROFUSHI T .Pseudo-additive measures and integrals[J]. Journal of Mathematical Analysis Applications,1987,122(1):197-222.
4 蒋兴忠 . tK-积分和Kt-积分[J]. 四川师范大学学报（自然科学版）, 1993, 16(2): 31-39. JIANG X Z . tk-integral and Kt-integral[J]. Journal of Sichuan Normal University（Natural Science Edition）,1993,16(2):31-39.
5 王贵君,李晓萍 . K-拟可加模糊积分的绝对连续性[J]. 四川师范大学学报（自然科学版）,1998,21(3):251-255. WANG G J , LI X P . Absolution continuity of K-pseudo-additive fuzzy integrals[J].Journal of Sichuan Normal University（ Natural Science Edition）,1998,21(3):251-255.
6 王贵君,李晓萍 . K-拟可加模糊数值积分的自连续性[J].数学杂志,2006,26(6):635-641.DOI:10.3969/j.issn.0255-7797.2006.06.009 WANG G J , LI X P . Autocontinuity of K-quasi-additive fuzzy number valued integrals[J]. Journal of Mathematics, 2006,26(6):635-641. DOI:10.3969/j.issn.0255-7797.2006.06.009
7 李艳红,王贵君 . K-拟可加模糊测度空间上广义Sugeno模糊积分[J].浙江大学学报（理学版），2010，37(4):376-380. DOI:10.3785/j.issn.1008-9497.2010.04.003 LI Y H , WANG G J . Generalized Sugeno fuzzy integrals on K-quasi-additive fuzzy measure space[J]. Journal of Zhejiang University（Science Edition）, 2010,37(4):376-380.DOI:10.3785/j.issn.1008-9497.2010.04.003
8 李艳红 .广义拟Sugeno模糊积分的确界式等价表示[J].浙江大学学报（理学版）,2014,41(2):127-131.DOI:10.3785/j.issn.1008-9497.2014.02.002 LI Y H . Equivalent representations of generalized quasi-Sugeno fuzzy integral in supremum forms[J].Journal of Zhejiang University（Science Edition）, 2014,41(2):127-131.DOI:10.3785/j.issn.1008-9497.2014.02.002
9 张广全 .模糊测度论[M].贵阳:贵州科技出版社, 1994. ZHANG G Q . Fuzzy Measure Theory [M]. Guiyang:Guizhou Science and Technology Press,1994.
10 哈明虎,吴从炘 .模糊测度与模糊积分理论[M].北京:科学出版社,1998. HA M H, WU C X . Fuzzy Measure and Theories of Fuzzy Integral[M]. Beijing: Science Press, 1998.
11 HESSE G , HAGEL R . Die chromatographische Racemattrennung[J]. European Journal of Organic Chemistry, 1976(6):996-1008.DOI:10.1002/jlac.197619760604
12 FRANCOTTE E , WOLF R M , LOHMANN D , et al . Chromatographic resolution of racemates on chiral stationary phases : I. Influence of the supramolecular structure of cellulose triacetate[J]. Journal of Chromatography A, 1985, 347:25-37. DOI:10.1016/S0021-9673(01)95466-4
13 BLASCHKE G . Chromatographic resolution of racemates. New analytical methods(17)[J]. Angewandte Chemie International Edition, 1980, 19(1):13-24. DOI:10.1002/anie.198000131
14 FRANCOTTE E , WOLF R M . Benzoyl cellulose beads in the pure polymeric form as a new powerful sorbent for the chromatographic resolution of racemates[J]. Chirality, 1991, 3(1):43-55.DOI:10.1002/chir.530030109
15 OKAMOTO Y , KAIDA Y , HAYASHIDA H , et al . Tris(1-phenylethylcarbamate)s of cellulose and amylose as useful chiral stationary phases for chromatographic optical resolution[J]. ChemInform, 2010, 22(10):909-912. DOI:10.1246/cl.1990.909 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
