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958. XOR Numbers: Theory and Application

Invited abstract in session MA-44: Preference Learning 1, stream Multiple Criteria Decision Analysis.

Monday, 8:30-10:00
Room: 20 (building: 324)

Authors (first author is the speaker)

1. Amin Hocine
2. Sergio Ortobelli Lozza
University of Bergamo

Abstract

We often find ourselves struggling to determine the truth, hesitating due to our ignorance. In such circumstances, the exclusive disjunction (XOR, for short) is commonly used to express our uncertainty, in contexts ranging from daily life, like "It was either Adam or John—but I couldn't determine which," to more professional scenarios, such as "Global growth is projected to be 3% in 2024, or it may weaken to 2.7% depending on prevailing economic conditions." The primary objective of this paper is to propose a framework to address the uncertainty inherent in such expressions by raising a pivotal inquiry: how to quantify this uncertainty without resorting to oversimplification that leads to the loss of crucial details essential for understanding the problem under consideration? Attempting to address this question leads to the concept of 'xorness' and the 'XOR number.' In particularly, xorness is defined as a state of uncertainty stemming from hesitation, in which multiple objects (such as numbers in our context) are mutually exclusive, indeterminate, and none of them is dominating. This exploration proposes the 'XOR number' as an approach to quantify xorness, recognizing that the multiple options itself represents a choice. This investigation extends to arithmetic operations, metric spaces, and the ordering of XOR numbers. Multiple criteria decision analysis is employed to demonstrate the applicability of the proposed framework.

Keywords

Status: accepted

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