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Why Use a Fuzzy Partition in F-Transform?
Open AccessArticle

Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones

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Department of Teacher Education, University of Texas at El Paso, El Paso, TX 79968, USA
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Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA
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Institute of Banking Research and Technology, Banking University of Ho Chi Minh City, 56 Hoang Dieu 2, Thu Duc, Ho Chi Minh City 71010, Vietnam
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Author to whom correspondence should be addressed.
Axioms 2019, 8(3), 95; https://doi.org/10.3390/axioms8030095
Received: 22 April 2019 / Revised: 1 August 2019 / Accepted: 2 August 2019 / Published: 5 August 2019
(This article belongs to the Special Issue Fuzzy Transforms and Their Applications)
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. View Full-Text
Keywords: F-transform; triangular membership function; optimal global characteristic F-transform; triangular membership function; optimal global characteristic
MDPI and ACS Style

Kosheleva, O.; Kreinovich, V.; Nguyen, T.N. Why Triangular Membership Functions Are Successfully Used in F-Transform Applications: A Global Explanation to Supplement the Existing Local Ones. Axioms 2019, 8, 95.

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