Similarity of Overlap Functions and Robustness of Fuzzy Reasoning
The overlap function has been extensively utilized across various fields. In this paper, we introduce the concepts of the similarity and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></seman...
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2025-01-01
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| author | Songsong Dai Qiuchen Ruan |
| author_facet | Songsong Dai Qiuchen Ruan |
| author_sort | Songsong Dai |
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| description | The overlap function has been extensively utilized across various fields. In this paper, we introduce the concepts of the similarity and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-equality of overlap functions to measure the degree of similarity between two overlap functions. Subsequently, we examine the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-equality of several operations on overlap functions, including meet, join, and weighted sum, to assess how these operations maintain the similarity. Finally, we discuss the robustness of fuzzy reasoning for FMP, FMT, and FHS models based on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-equality of the overlap functions. |
| format | Article |
| id | doaj-art-33623130ed7a48a0875177de884c62a7 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-33623130ed7a48a0875177de884c62a72025-01-24T13:22:15ZengMDPI AGAxioms2075-16802025-01-011414510.3390/axioms14010045Similarity of Overlap Functions and Robustness of Fuzzy ReasoningSongsong Dai0Qiuchen Ruan1School of Electronics and Information Engineering, Taizhou University, Taizhou 318000, ChinaSchool of Electronics and Information Engineering, Taizhou University, Taizhou 318000, ChinaThe overlap function has been extensively utilized across various fields. In this paper, we introduce the concepts of the similarity and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-equality of overlap functions to measure the degree of similarity between two overlap functions. Subsequently, we examine the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-equality of several operations on overlap functions, including meet, join, and weighted sum, to assess how these operations maintain the similarity. Finally, we discuss the robustness of fuzzy reasoning for FMP, FMT, and FHS models based on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-equality of the overlap functions.https://www.mdpi.com/2075-1680/14/1/45similarityoverlap functionsgrouping functionsrobustnessfuzzy reasoning |
| spellingShingle | Songsong Dai Qiuchen Ruan Similarity of Overlap Functions and Robustness of Fuzzy Reasoning Axioms similarity overlap functions grouping functions robustness fuzzy reasoning |
| title | Similarity of Overlap Functions and Robustness of Fuzzy Reasoning |
| title_full | Similarity of Overlap Functions and Robustness of Fuzzy Reasoning |
| title_fullStr | Similarity of Overlap Functions and Robustness of Fuzzy Reasoning |
| title_full_unstemmed | Similarity of Overlap Functions and Robustness of Fuzzy Reasoning |
| title_short | Similarity of Overlap Functions and Robustness of Fuzzy Reasoning |
| title_sort | similarity of overlap functions and robustness of fuzzy reasoning |
| topic | similarity overlap functions grouping functions robustness fuzzy reasoning |
| url | https://www.mdpi.com/2075-1680/14/1/45 |
| work_keys_str_mv | AT songsongdai similarityofoverlapfunctionsandrobustnessoffuzzyreasoning AT qiuchenruan similarityofoverlapfunctionsandrobustnessoffuzzyreasoning |