Center-of-gravity fuzzy systems based on normal fuzzy implications
In this paper, the construction and approximation problem of a single input and single output (SISO) fuzzy system with normal implication and center-of-gravity defuzzifier is discussed. First, the method of a non-singleton fuzzifier for the input variable and the concept of an adaptive universe for...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2011-05, Vol.61 (9), p.2879-2898 |
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| container_title | Computers & mathematics with applications (1987) |
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| creator | Yuan, Xue-hai Liu, Zeng-liang Stanley Lee, E. |
| description | In this paper, the construction and approximation problem of a single input and single output (SISO) fuzzy system with normal implication and center-of-gravity defuzzifier is discussed. First, the method of a non-singleton fuzzifier for the input variable and the concept of an adaptive universe for the output fuzzy set are proposed. Then, by using this method and this concept of an adaptive universe, SISO fuzzy systems based on center-of-gravity defuzzifier and normal implications such as the Kleene–Dienes implication or the Lukasiewicz implication are constructed. The constructed fuzzy systems have the general form
S
¯
(
x
)
=
A
i
∗
(
x
)
f
(
x
i
)
+
A
i
+
1
∗
(
x
)
f
(
x
i
+
1
)
, with
A
i
∗
(
x
)
+
A
i
+
1
∗
(
x
)
=
1
, and, furthermore, they are universal approximators. The sufficient conditions for the proposed fuzzy systems to be universal approximators are also obtained. To illustrate the universal property, an example is also given. |
| doi_str_mv | 10.1016/j.camwa.2011.03.074 |
| format | Article |
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S
¯
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x
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(
x
)
f
(
x
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, and, furthermore, they are universal approximators. The sufficient conditions for the proposed fuzzy systems to be universal approximators are also obtained. To illustrate the universal property, an example is also given.</description><identifier>ISSN: 0898-1221</identifier><identifier>EISSN: 1873-7668</identifier><identifier>DOI: 10.1016/j.camwa.2011.03.074</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Adaptive universe ; Approximation ; Center-of-gravity defuzzifier ; Construction ; Fuzzy ; Fuzzy logic ; Fuzzy set theory ; Fuzzy systems ; Mathematical analysis ; Non-singleton fuzzifier ; Normal implication ; Universal approximation ; Universe</subject><ispartof>Computers & mathematics with applications (1987), 2011-05, Vol.61 (9), p.2879-2898</ispartof><rights>2011 Elsevier Ltd</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c381t-ba84c935b4f371a03939e570b0bbca5086704ad27f1d678fe76457d97e2aa10c3</citedby><cites>FETCH-LOGICAL-c381t-ba84c935b4f371a03939e570b0bbca5086704ad27f1d678fe76457d97e2aa10c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.camwa.2011.03.074$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids></links><search><creatorcontrib>Yuan, Xue-hai</creatorcontrib><creatorcontrib>Liu, Zeng-liang</creatorcontrib><creatorcontrib>Stanley Lee, E.</creatorcontrib><title>Center-of-gravity fuzzy systems based on normal fuzzy implications</title><title>Computers & mathematics with applications (1987)</title><description>In this paper, the construction and approximation problem of a single input and single output (SISO) fuzzy system with normal implication and center-of-gravity defuzzifier is discussed. First, the method of a non-singleton fuzzifier for the input variable and the concept of an adaptive universe for the output fuzzy set are proposed. Then, by using this method and this concept of an adaptive universe, SISO fuzzy systems based on center-of-gravity defuzzifier and normal implications such as the Kleene–Dienes implication or the Lukasiewicz implication are constructed. The constructed fuzzy systems have the general form
S
¯
(
x
)
=
A
i
∗
(
x
)
f
(
x
i
)
+
A
i
+
1
∗
(
x
)
f
(
x
i
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1
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, with
A
i
∗
(
x
)
+
A
i
+
1
∗
(
x
)
=
1
, and, furthermore, they are universal approximators. The sufficient conditions for the proposed fuzzy systems to be universal approximators are also obtained. To illustrate the universal property, an example is also given.</description><subject>Adaptive universe</subject><subject>Approximation</subject><subject>Center-of-gravity defuzzifier</subject><subject>Construction</subject><subject>Fuzzy</subject><subject>Fuzzy logic</subject><subject>Fuzzy set theory</subject><subject>Fuzzy systems</subject><subject>Mathematical analysis</subject><subject>Non-singleton fuzzifier</subject><subject>Normal implication</subject><subject>Universal approximation</subject><subject>Universe</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAURS0EEqXwC1gysiS8Fye2MzBAxZdUiQVmy3FekKskLnZa1P56Au3M9IZ3z5XuYewaIUNAcbvKrOm_TZYDYgY8A1mcsBkqyVMphDplM1CVSjHP8ZxdxLgCgILnMGMPCxpGCqlv089gtm7cJe1mv98lcRdH6mNSm0hN4odk8KE33fHr-nXnrBmdH-IlO2tNF-nqeOfs4-nxffGSLt-eXxf3y9RyhWNaG1XYipd10XKJBnjFKyol1FDX1pSghITCNLlssRFStSRFUcqmkpQbg2D5nN0cetfBf20ojrp30VLXmYH8JmoUEvm0U_Apyg9RG3yMgVq9Dq43YacR9K8xvdJ_xvSvMQ1cT8Ym6u5A0bRi6yjoaB0NlhoXyI668e5f_gcDXXWf</recordid><startdate>20110501</startdate><enddate>20110501</enddate><creator>Yuan, Xue-hai</creator><creator>Liu, Zeng-liang</creator><creator>Stanley Lee, E.</creator><general>Elsevier Ltd</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20110501</creationdate><title>Center-of-gravity fuzzy systems based on normal fuzzy implications</title><author>Yuan, Xue-hai ; Liu, Zeng-liang ; Stanley Lee, E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c381t-ba84c935b4f371a03939e570b0bbca5086704ad27f1d678fe76457d97e2aa10c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Adaptive universe</topic><topic>Approximation</topic><topic>Center-of-gravity defuzzifier</topic><topic>Construction</topic><topic>Fuzzy</topic><topic>Fuzzy logic</topic><topic>Fuzzy set theory</topic><topic>Fuzzy systems</topic><topic>Mathematical analysis</topic><topic>Non-singleton fuzzifier</topic><topic>Normal implication</topic><topic>Universal approximation</topic><topic>Universe</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yuan, Xue-hai</creatorcontrib><creatorcontrib>Liu, Zeng-liang</creatorcontrib><creatorcontrib>Stanley Lee, E.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yuan, Xue-hai</au><au>Liu, Zeng-liang</au><au>Stanley Lee, E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Center-of-gravity fuzzy systems based on normal fuzzy implications</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2011-05-01</date><risdate>2011</risdate><volume>61</volume><issue>9</issue><spage>2879</spage><epage>2898</epage><pages>2879-2898</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>In this paper, the construction and approximation problem of a single input and single output (SISO) fuzzy system with normal implication and center-of-gravity defuzzifier is discussed. First, the method of a non-singleton fuzzifier for the input variable and the concept of an adaptive universe for the output fuzzy set are proposed. Then, by using this method and this concept of an adaptive universe, SISO fuzzy systems based on center-of-gravity defuzzifier and normal implications such as the Kleene–Dienes implication or the Lukasiewicz implication are constructed. The constructed fuzzy systems have the general form
S
¯
(
x
)
=
A
i
∗
(
x
)
f
(
x
i
)
+
A
i
+
1
∗
(
x
)
f
(
x
i
+
1
)
, with
A
i
∗
(
x
)
+
A
i
+
1
∗
(
x
)
=
1
, and, furthermore, they are universal approximators. The sufficient conditions for the proposed fuzzy systems to be universal approximators are also obtained. To illustrate the universal property, an example is also given.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.camwa.2011.03.074</doi><tpages>20</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0898-1221 |
| ispartof | Computers & mathematics with applications (1987), 2011-05, Vol.61 (9), p.2879-2898 |
| issn | 0898-1221 1873-7668 |
| language | eng |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Adaptive universe Approximation Center-of-gravity defuzzifier Construction Fuzzy Fuzzy logic Fuzzy set theory Fuzzy systems Mathematical analysis Non-singleton fuzzifier Normal implication Universal approximation Universe |
| title | Center-of-gravity fuzzy systems based on normal fuzzy implications |
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