Examples of Fuzzy Sets, Hyperfuzzy Sets, and SuperHyperfuzzy Sets in Climate Change and the Proposal of Several New Concepts

Abstract

A fuzzy set generalizes classical set theory by assigning each element a membership value within [0, 1], allowing for the representation of partial or uncertain membership. It is well established that fuzzy sets can be further extended to Hyperfuzzy sets and SuperHyperfuzzy sets. However, as these concepts have been introduced only recently, their practical applications remain largely unexplored. In this paper, we investigate potential applications of Fuzzy sets, Hyperfuzzy sets, and SuperHyperfuzzy sets in the context of climate change and environmental factors. Additionally, we introduce the Forest Fuzzy Set, Forest Hyperfuzzy Set, and Forest SuperHyperfuzzy Set, and explore their possible applications. Furthermore, Hyperfuzzy sets and SuperHyperfuzzy sets are known to be associated with Hyperstructure and SuperHyperstructure concepts. While our primary focus is on the aforementioned extensions, we also provide a brief discussion on TreeStructure and ForestStructure by considering their definitions in the context of Hyperstructure and SuperHyperstructure.