Using Gradual Numbers to Analyze Non-Monotonic Functions of Fuzzy Intervals
Elizabeth Untiedt, Weldon Lodwick
TL;DR
This paper introduces a novel approach combining gradual numbers and optimization to evaluate any differentiable function on fuzzy intervals without requiring monotonicity, expanding the analysis capabilities for fuzzy interval functions.
Contribution
It presents a new method that integrates gradual numbers with optimization techniques to analyze non-monotonic functions of fuzzy intervals.
Findings
Enables evaluation of non-monotonic functions on fuzzy intervals.
Extends existing methods beyond monotonic functions.
Provides a framework for differentiable fuzzy interval analysis.
Abstract
Gradual numbers have been introduced recently as a means of extending standard interval computation methods to fuzzy intervals. The literature treats monotonic functions of fuzzy intervals. In this paper, we combine the concepts of gradual numbers and optimization, which allows for the evaluation of any differentiable function on fuzzy intervals, with no monotonicity requirement.
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Taxonomy
TopicsFuzzy Systems and Optimization · Fuzzy Logic and Control Systems · Multi-Criteria Decision Making