Preprint Article Version 1 This version is not peer-reviewed

Why Triangular Membership Functions Are So Efficient in F-Transform Applications: A Global Explanation to Supplement the Existing Local One

Version 1 : Received: 22 April 2019 / Approved: 23 April 2019 / Online: 23 April 2019 (11:01:56 CEST)

How to cite: Kosheleva, O.; Kreinovich, V.; Nguyen, T.N. Why Triangular Membership Functions Are So Efficient in F-Transform Applications: A Global Explanation to Supplement the Existing Local One. Preprints 2019, 2019040253 (doi: 10.20944/preprints201904.0253.v1). Kosheleva, O.; Kreinovich, V.; Nguyen, T.N. Why Triangular Membership Functions Are So Efficient in F-Transform Applications: A Global Explanation to Supplement the Existing Local One. Preprints 2019, 2019040253 (doi: 10.20944/preprints201904.0253.v1).

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.

Subject Areas

F-transform; triangular membership function; optimal global characteristics

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