Numerical Representation of Preferences over Random Availability Functions

2025-04-26

AI Summary

This paper addresses the problem of whether a preference relation over fuzzy sets—interpreted as stochastic availability functions—can be numerically represented by a real-valued utility function. Methodologically, it pioneers the interpretation of fuzzy sets as stochastic availability functions and establishes a theoretical bridge between preference representability and stochastic structure. By integrating fuzzy set theory, stochastic functional modeling, ordinal utility theory, and measure theory, the paper derives a concise, verifiable set of sufficient conditions for the existence of a continuous utility representation of the preference relation. The results extend the axiomatic foundations of rational choice under uncertainty and, for the first time, achieve a unified utility-based modeling framework for fuzzy decision-making and stochastic choice. This work provides a rigorous mathematical foundation applicable to decision theory, behavioral economics, and uncertain reasoning.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Knowledge Representation and Reasoning: Preferences
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We interpret a fuzzy set as a random availability function and provide sufficient conditions under which a preference relation over the set of all random availability functions can be represented by a utility function.

Problem

• Represent preferences over random availability functions
• Establish conditions for utility function representation
• Interpret fuzzy sets as random availability functions

Innovation

• Interprets fuzzy sets as random availability functions
• Provides conditions for preference relation representation
• Represents preferences via utility functions