How to Describe Conditions Like 2-out-of-5 in Fuzzy Logic: a Neural Approach

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Nguyen Hoang Phuong, Thang Long UniversityFollow

Publication Date

3-2020

Comments

Technical Report: UTEP-CS-20-19

To appear in Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII)

Abstract

In many medical applications, we diagnose a disease and/or apply a certain remedy if, e.g., two out of five conditions are satisfied. In the fuzzy case, i.e., when we only have certain degrees of confidence that each of n statement is satisfied, how do we estimate the degree of confidence that k out of n conditions are satisfied? In principle, we can get this estimate if we use the usual methodology of applying fuzzy techniques: we represent the desired statement in terms of "and" and "or", and use fuzzy analogues of these logical operations. The problem with this approach is that for large $n$, it requires too many computations. In this paper, we derive the fastest-to-compute alternative formula. In this derivation, we use the ideas from neural networks.