Rings of Typed Ordered Fuzzy Numbers
Matthew Kukla, Rachel Traylor
TL;DR
This paper introduces a mathematical framework for rings of typed ordered fuzzy numbers, including methods to convert improper fuzzy numbers into proper ones within the same type, enhancing their algebraic structure.
Contribution
It constructs rings of typed ordered fuzzy numbers with common component functions and develops operations to convert improper fuzzy numbers into proper ones of the same type.
Findings
Established a ring structure for typed ordered fuzzy numbers.
Developed conversion operations for improper to proper fuzzy numbers.
Enhanced algebraic manipulation of fuzzy numbers within this framework.
Abstract
We construct rings of typed ordered fuzzy numbers whose component functions are of a common form. As this ring also contains improper fuzzy numbers (OFNs whose membership "functions" are actually just relations), we develop a set of operations to convert an improper fuzzy number to a proper one of the same type.
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Taxonomy
TopicsFuzzy Systems and Optimization · Multi-Criteria Decision Making · Fuzzy Logic and Control Systems