Generating theorems for s-norms and t-norms
The s-norm and t-norm operators are generalization of the union and intersection operators respectively for fuzzy sets. Thus various alternative operators have been proposed by several authors since the introduction of fuzzy sets by Zadeh in 1965. In this paper we give generating theorems for s-n...
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| Format: | Article |
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Penerbit ukm
2008
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| Online Access: | http://journalarticle.ukm.my/1870/ |
| _version_ | 1848809680917233664 |
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| author | Shawkat Mahmoud Rasheed Alkhazaleh, Abdul Razak Salleh , |
| author_facet | Shawkat Mahmoud Rasheed Alkhazaleh, Abdul Razak Salleh , |
| author_sort | Shawkat Mahmoud Rasheed Alkhazaleh, |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | The s-norm and t-norm operators are generalization of the union and intersection operators
respectively for fuzzy sets. Thus various alternative operators have been proposed by several
authors since the introduction of fuzzy sets by Zadeh in 1965. In this paper we give generating
theorems for s-norms and t-norm, namely given an s-norm we can generate a class of s-norms
and t-norms, and given a t-norm we can generate a class of t-norms and s-norms. We also give
bijective generating theorems for s-norms and t-norms. Given two bijective functions on [0, 1]
under certain conditions, from an s-norm, we generate an s-norm and a t-norm, and from a
t-norm we generate a t-norm and an s-norm |
| first_indexed | 2025-11-14T23:18:28Z |
| format | Article |
| id | ukm-1870 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T23:18:28Z |
| publishDate | 2008 |
| publisher | Penerbit ukm |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ukm-18702011-06-15T08:00:57Z http://journalarticle.ukm.my/1870/ Generating theorems for s-norms and t-norms Shawkat Mahmoud Rasheed Alkhazaleh, Abdul Razak Salleh , The s-norm and t-norm operators are generalization of the union and intersection operators respectively for fuzzy sets. Thus various alternative operators have been proposed by several authors since the introduction of fuzzy sets by Zadeh in 1965. In this paper we give generating theorems for s-norms and t-norm, namely given an s-norm we can generate a class of s-norms and t-norms, and given a t-norm we can generate a class of t-norms and s-norms. We also give bijective generating theorems for s-norms and t-norms. Given two bijective functions on [0, 1] under certain conditions, from an s-norm, we generate an s-norm and a t-norm, and from a t-norm we generate a t-norm and an s-norm Penerbit ukm 2008-07 Article PeerReviewed Shawkat Mahmoud Rasheed Alkhazaleh, and Abdul Razak Salleh , (2008) Generating theorems for s-norms and t-norms. Journal of Quality Measurement and Analysis, 4 (1). pp. 231-242. ISSN 1823-5670 http://www.ukm.my/~ppsmfst/jqma/index.html |
| spellingShingle | Shawkat Mahmoud Rasheed Alkhazaleh, Abdul Razak Salleh , Generating theorems for s-norms and t-norms |
| title | Generating theorems for s-norms and t-norms |
| title_full | Generating theorems for s-norms and t-norms |
| title_fullStr | Generating theorems for s-norms and t-norms |
| title_full_unstemmed | Generating theorems for s-norms and t-norms |
| title_short | Generating theorems for s-norms and t-norms |
| title_sort | generating theorems for s-norms and t-norms |
| url | http://journalarticle.ukm.my/1870/ http://journalarticle.ukm.my/1870/ |