From [0,1]-Based Logic to Interval Logic (From Known Description of All Possible [0,1]-Based Logical Operations to a Description of All Possible Interval-Based Logical Operations)

Authors

Hung T. Nguyen
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

8-2002

Comments

UTEP-CS-01-04c.

Published in Notes on Intuitionistic Fuzzy Sets (NIFS), 2002, Vol. 8, No. 3, pp. 75-94.

Abstract

Since early 1960s, we have a complete description of all possible [0,1]-based logical operations, namely of "and"-operations (t-norms) and of "or"-operations (t-conorms). In some real-life situations, intervals provide a more adequate way of describing uncertainty, so we need to describe interval-based logical operations. Usually, researchers followed a pragmatic path and simply derived these operations from the [0,1]-based ones. From the foundational viewpoint, it is desirable not to a priori restrict ourselves to such derivative operations but, instead, to get a description of all interval-based operations which satisfy reasonable properties.

Such description is presented in this paper. It turns out that all such operations can be described as the result of applying interval computations to the corresponding [0,1]-based ones.