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. Axioms2019, 8, 95.
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.
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. Axioms2019, 8, 95.
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.
Abstract
The main ideas of F-transform came from representing expert rules. It would be therefore re reasonable to expect that the more accurately the membership functions describe human reasoning, the more efficient will be the corresponding F-transform formulas. We know that an adequate description of our reasoning corresponds to complicated membership functions -- however, somewhat surprisingly, most efficient 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 this local explanation by a global one: namely, we prove that triangular membership functions are the only one that provide the accurate description of appropriate global characteristics of the signal.
Keywords
F-transform; triangular membership function; optimal global characteristics
Subject
Computer Science and Mathematics, Computer Science
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
