On forming joint variables in computing with words

Abstract

We discuss Zadeh’s idea of computing with words and emphasize its perspective that information provides a restriction on the values variables can assume. We describe the role that the constraint-based semantics plays in translating natural language statements into formal mathematical objects. One task that arises in using this approach is the formulation of joint restrictions on multiple variables from individual information about each of the variables. Our interest here is to extend the capability of the framework of computing with words in the task of forming joint variables with the introduction of the idea of perceived relatedness between variables, a concept closely related to the idea of correlation. We are particularly interested in role that knowledge about perceived relatedness between variables can play in further restricting the possible values of joint then that simple provided by the individual constraints. We look at the problem of joining various types of uncertain variables, possibilistic, probabilistic and Dempster-Shafer belief structures.

Keywords:

• computing with words
• fuzzy sets
• possibility theory
• restriction
• approximate reasoning

Acknowledgement

This work has been supported by a Multidisciplinary University Research Initiative (MURI) grant (Number W911NF-09-1-0392) for “Unified Research on Network-based Hard/Soft Information Fusion”, issued by the US Army Research Office (ARO). This work has also been supported by an ONR grant. We gratefully appreciate this support.”