A concrete reformulation of fuzzy arithmetic

作者：

Highlights：

• Fuzzy arithmetic (FA) is essential to tackling approximate reasoning problems.

• Recent progresses in FA have relied on increasingly advanced mathematical concepts.

• Here, we employ a different approach, of offering a simple and concrete FA framework.

• The framework possesses concrete elements for building various types of FA operators.

• We describe key ideas for extending the framework to the type-2 fuzzy setting.

摘要

•Fuzzy arithmetic (FA) is essential to tackling approximate reasoning problems.•Recent progresses in FA have relied on increasingly advanced mathematical concepts.•Here, we employ a different approach, of offering a simple and concrete FA framework.•The framework possesses concrete elements for building various types of FA operators.•We describe key ideas for extending the framework to the type-2 fuzzy setting.

论文关键词：Fuzzy arithmetic,Fuzzy sets,Type-2 fuzzy sets,Fuzzy numbers,Type-2 fuzzy numbers,Approximate reasoning

论文评审过程：Received 26 July 2019, Revised 19 June 2020, Accepted 30 July 2020, Available online 7 August 2020, Version of Record 10 February 2021.

论文官网地址：https://doi.org/10.1016/j.eswa.2020.113818