Fuzzy Logic Beyond Traditional "And"- and "Or"-Operations

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow

Publication Date

11-1-2021

Comments

Technical Report: UTEP-CS-21-103

Abstract

In the traditional fuzzy logic, we can use "and"-operations (also known as t-norms) to estimate the expert's degree of confidence in a composite statement A&B based on his/her degrees of confidence d(A) and d(B) in the corresponding basic statements A and B. But what if we want to estimate the degree of confidence in A&B&C in situations when, in addition to the degrees of estimate d(A), d(B), and d(C) of the basic statements, we also know the expert's degrees of confidence in the pairs d(A&B), d(A&C), and d(B&C)? Traditional "and"-operations can provide such an estimate -- but only by ignoring some of the available information. In this paper, we show that, by going beyond the traditional "and"- and "or"-operations, we can find a natural estimate that takes all available information into account -- and thus, hopefully, leads to a more accurate estimate.