Semi-Overlap Functions on Complete Lattices, Semi-Θ-Ξ Functions, and Inflationary MTL Algebras
As new kinds of aggregation functions, overlap functions and semi overlap functions are widely applied to information fusion, approximation reasoning, data classification, decision science, etc. This paper extends the semi-overlap function on [0, 1] to the function on complete lattices and investiga...
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2024-11-01
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| Online Access: | https://www.mdpi.com/2075-1680/13/11/799 |
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| author | Xingna Zhang Eunsuk Yang Xiaohong Zhang |
| author_facet | Xingna Zhang Eunsuk Yang Xiaohong Zhang |
| author_sort | Xingna Zhang |
| collection | DOAJ |
| description | As new kinds of aggregation functions, overlap functions and semi overlap functions are widely applied to information fusion, approximation reasoning, data classification, decision science, etc. This paper extends the semi-overlap function on [0, 1] to the function on complete lattices and investigates the residual implication derived from it; then it explores the construction of a semi-overlap function on complete lattices and some fundamental properties. Especially, this paper introduces a more generalized concept of the ‘semi-Θ-Ξ function’, which innovatively unifies the semi-overlap function and semi-grouping function. Additionally, it provides methods for constructing and characterizing the semi-Θ-Ξ function. Furthermore, this paper characterizes the semi-overlap function on complete lattices and the semi-Θ-Ξ function on [0, 1] from an algebraic point of view and proves that the algebraic structures corresponding to the inflationary semi-overlap function, the inflationary semi-Θ-Ξ function, and residual implications derived by each of them are inflationary MTL algebras. This paper further discusses the properties of inflationary MTL algebra and its relationship with non-associative MTL algebra, and it explores the connections between some related algebraic structures. |
| format | Article |
| id | doaj-art-82d83893b7ad4c54b355107bd5c8a533 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-82d83893b7ad4c54b355107bd5c8a5332024-11-26T17:50:57ZengMDPI AGAxioms2075-16802024-11-01131179910.3390/axioms13110799Semi-Overlap Functions on Complete Lattices, Semi-Θ-Ξ Functions, and Inflationary MTL AlgebrasXingna Zhang0Eunsuk Yang1Xiaohong Zhang2School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, ChinaRm 417, Center for Humanities & Social Sciences, Department of Philosophy & Institute of Critical Thinking and Writing, Jeonbuk National University, Jeonju 54896, Republic of KoreaSchool of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, ChinaAs new kinds of aggregation functions, overlap functions and semi overlap functions are widely applied to information fusion, approximation reasoning, data classification, decision science, etc. This paper extends the semi-overlap function on [0, 1] to the function on complete lattices and investigates the residual implication derived from it; then it explores the construction of a semi-overlap function on complete lattices and some fundamental properties. Especially, this paper introduces a more generalized concept of the ‘semi-Θ-Ξ function’, which innovatively unifies the semi-overlap function and semi-grouping function. Additionally, it provides methods for constructing and characterizing the semi-Θ-Ξ function. Furthermore, this paper characterizes the semi-overlap function on complete lattices and the semi-Θ-Ξ function on [0, 1] from an algebraic point of view and proves that the algebraic structures corresponding to the inflationary semi-overlap function, the inflationary semi-Θ-Ξ function, and residual implications derived by each of them are inflationary MTL algebras. This paper further discusses the properties of inflationary MTL algebra and its relationship with non-associative MTL algebra, and it explores the connections between some related algebraic structures.https://www.mdpi.com/2075-1680/13/11/799aggregation functionscomplete latticessemi-overlap functionssemi-Θ-Ξ functionsresidual implicationinflationary MTL algebras |
| spellingShingle | Xingna Zhang Eunsuk Yang Xiaohong Zhang Semi-Overlap Functions on Complete Lattices, Semi-Θ-Ξ Functions, and Inflationary MTL Algebras Axioms aggregation functions complete lattices semi-overlap functions semi-Θ-Ξ functions residual implication inflationary MTL algebras |
| title | Semi-Overlap Functions on Complete Lattices, Semi-Θ-Ξ Functions, and Inflationary MTL Algebras |
| title_full | Semi-Overlap Functions on Complete Lattices, Semi-Θ-Ξ Functions, and Inflationary MTL Algebras |
| title_fullStr | Semi-Overlap Functions on Complete Lattices, Semi-Θ-Ξ Functions, and Inflationary MTL Algebras |
| title_full_unstemmed | Semi-Overlap Functions on Complete Lattices, Semi-Θ-Ξ Functions, and Inflationary MTL Algebras |
| title_short | Semi-Overlap Functions on Complete Lattices, Semi-Θ-Ξ Functions, and Inflationary MTL Algebras |
| title_sort | semi overlap functions on complete lattices semi θ ξ functions and inflationary mtl algebras |
| topic | aggregation functions complete lattices semi-overlap functions semi-Θ-Ξ functions residual implication inflationary MTL algebras |
| url | https://www.mdpi.com/2075-1680/13/11/799 |
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