Analytical Properties of Credibilistic Expectation Functions
The expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical prop...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/294183 |
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| author | Shuming Wang Bo Wang Junzo Watada |
| author_facet | Shuming Wang Bo Wang Junzo Watada |
| author_sort | Shuming Wang |
| collection | DOAJ |
| description | The expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical properties of credibilistic expectation functions of fuzzy variables that lie in three aspects. First, some continuity theorems on the continuity and semicontinuity conditions are proved for the expectation functions. Second, a differentiation formula of the expectation function is derived which tells that, under certain conditions, the derivative of the fuzzy expectation function with respect to the parameter equals the expectation of the derivative of the fuzzy function with respect to the parameter. Finally, a law of large numbers for fuzzy variable sequences is obtained leveraging on the Chebyshev Inequality of fuzzy variables. Some examples are provided to verify the results obtained. |
| format | Article |
| id | doaj-art-1e2050728b18492ab864037e2cbdb7ac |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-1e2050728b18492ab864037e2cbdb7ac2025-02-03T01:12:38ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/294183294183Analytical Properties of Credibilistic Expectation FunctionsShuming Wang0Bo Wang1Junzo Watada2Department of Industrial & Systems Engineering, National University of Singapore, Block E1A No. 05-19, 1 Engineering Drive 2, 117576, SingaporeGraduate School of Information, Production & Systems, Waseda University, Hibikino 2-7, Wakamatsu-ku, Kitakyshu, Fukuoka, JapanGraduate School of Information, Production & Systems, Waseda University, Hibikino 2-7, Wakamatsu-ku, Kitakyshu, Fukuoka, JapanThe expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical properties of credibilistic expectation functions of fuzzy variables that lie in three aspects. First, some continuity theorems on the continuity and semicontinuity conditions are proved for the expectation functions. Second, a differentiation formula of the expectation function is derived which tells that, under certain conditions, the derivative of the fuzzy expectation function with respect to the parameter equals the expectation of the derivative of the fuzzy function with respect to the parameter. Finally, a law of large numbers for fuzzy variable sequences is obtained leveraging on the Chebyshev Inequality of fuzzy variables. Some examples are provided to verify the results obtained.http://dx.doi.org/10.1155/2014/294183 |
| spellingShingle | Shuming Wang Bo Wang Junzo Watada Analytical Properties of Credibilistic Expectation Functions The Scientific World Journal |
| title | Analytical Properties of Credibilistic Expectation Functions |
| title_full | Analytical Properties of Credibilistic Expectation Functions |
| title_fullStr | Analytical Properties of Credibilistic Expectation Functions |
| title_full_unstemmed | Analytical Properties of Credibilistic Expectation Functions |
| title_short | Analytical Properties of Credibilistic Expectation Functions |
| title_sort | analytical properties of credibilistic expectation functions |
| url | http://dx.doi.org/10.1155/2014/294183 |
| work_keys_str_mv | AT shumingwang analyticalpropertiesofcredibilisticexpectationfunctions AT bowang analyticalpropertiesofcredibilisticexpectationfunctions AT junzowatada analyticalpropertiesofcredibilisticexpectationfunctions |