Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones
The main ideas of F-transform came from representing expert rules. It would be therefore reasonable to expect that the more accurately the membership functions describe human reasoning, the more successful will be the corresponding F-transform formulas. We know that an adequate description of our re...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-08-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/8/3/95 |
| _version_ | 1811202484987756544 |
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| author | Olga Kosheleva Vladik Kreinovich Thach Ngoc Nguyen |
| author_facet | Olga Kosheleva Vladik Kreinovich Thach Ngoc Nguyen |
| author_sort | Olga Kosheleva |
| collection | DOAJ |
| description | The main ideas of F-transform came from representing expert rules. It would be therefore reasonable to expect that the more accurately the membership functions describe human reasoning, the more successful will be the corresponding F-transform formulas. We know that an adequate description of our reasoning corresponds to complicated membership functions—however, somewhat surprisingly, many successful applications of F-transform use the simplest possible triangular membership functions. There exist some explanations for this phenomenon, which are based on local behavior of the signal. In this paper, we supplement these local explanations by a global one: namely, we prove that triangular membership functions are the only one that provide the exact reconstruction of the appropriate global characteristic of the signal. |
| first_indexed | 2024-04-12T02:39:15Z |
| format | Article |
| id | doaj.art-d39fd7b982f749888c18730cb14a72eb |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-04-12T02:39:15Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-d39fd7b982f749888c18730cb14a72eb2022-12-22T03:51:22ZengMDPI AGAxioms2075-16802019-08-01839510.3390/axioms8030095axioms8030095Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local OnesOlga Kosheleva0Vladik Kreinovich1Thach Ngoc Nguyen2Department of Teacher Education, University of Texas at El Paso, El Paso, TX 79968, USADepartment of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USAInstitute of Banking Research and Technology, Banking University of Ho Chi Minh City, 56 Hoang Dieu 2, Thu Duc, Ho Chi Minh City 71010, VietnamThe main ideas of F-transform came from representing expert rules. It would be therefore reasonable to expect that the more accurately the membership functions describe human reasoning, the more successful will be the corresponding F-transform formulas. We know that an adequate description of our reasoning corresponds to complicated membership functions—however, somewhat surprisingly, many successful applications of F-transform use the simplest possible triangular membership functions. There exist some explanations for this phenomenon, which are based on local behavior of the signal. In this paper, we supplement these local explanations by a global one: namely, we prove that triangular membership functions are the only one that provide the exact reconstruction of the appropriate global characteristic of the signal.https://www.mdpi.com/2075-1680/8/3/95F-transformtriangular membership functionoptimal global characteristic |
| spellingShingle | Olga Kosheleva Vladik Kreinovich Thach Ngoc Nguyen Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones Axioms F-transform triangular membership function optimal global characteristic |
| title | Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones |
| title_full | Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones |
| title_fullStr | Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones |
| title_full_unstemmed | Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones |
| title_short | Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones |
| title_sort | why triangular membership functions are successfully used in f transform applications a global explanation to supplement the existing local ones |
| topic | F-transform triangular membership function optimal global characteristic |
| url | https://www.mdpi.com/2075-1680/8/3/95 |
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