ISSN :2582-9793

Why Cauchy Membership Functions: Reliability

Original Research (Published On: 28-May-2022 )
Why Cauchy Membership Functions: Reliability
DOI : 10.54364/AAIML.2022.1125

Anca Ralescu

Adv. Artif. Intell. Mach. Learn., 2 (2):385-393

Anca Ralescu : University of Cincinnati

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DOI: 10.54364/AAIML.2022.1125

Article History: Received on: 02-Apr-22, Accepted on: 27-May-22, Published on: 28-May-22

Corresponding Author: Anca Ralescu

Email: ralescal@ucmail.uc.edu

Citation: Anca Ralescu (2022). Why Cauchy Membership Functions: Reliability. Adv. Artif. Intell. Mach. Learn., 2 (2 ):385-393

          

Abstract

    

An important, often decisive step in designing a fuzzy system is the elicitation of the membership functions for the fuzzy sets used. Most often the membership functions are obtained from data, that is, in a training-like manner. They are expected to match or be at least compatible with those obtained from experts knowledgeable of the domain and the problem being addressed. In cases when neither are possible, e.g., insu_cient data or unavailability of experts, we are faced with the question of hypothesizing the membership function. We have previously argued in favor of Cauchy membership functions (thus named because their expressionis similar to that of the Cauchy distributions) and supported this choice from the point of view of e_ciency - that is, how easy is to train such functions. This paper looks at the same family of membership functions from the point of view of reliability.

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