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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/1/45 |
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| Summary: | 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. |
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| ISSN: | 2075-1680 |