Complemental Fuzzy Sets: A Semantic Justification of q-Rung Orthopair Fuzzy Sets

This article introduces complemental fuzzy sets, explains their semantics, and presents a subclass of this model that generalizes intuitionistic fuzzy sets in a novel manner. It also provides practical results that will facilitate their implementation in real situations. At the theoretical level, we...

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Published in:IEEE transactions on fuzzy systems 2023-12, Vol.31 (12), p.4262-4270
Main Author: Alcantud, Jose Carlos R.
Format: Article
Language:English
Subjects:
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aggregation
Boundary conditions
Fuzzy logic
Fuzzy sets
intuitionistic fuzzy set
Probabilistic logic
Semantics
Sugeno's fuzzy complement
Sustainable development
Yager's fuzzy complement
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Summary:This article introduces complemental fuzzy sets, explains their semantics, and presents a subclass of this model that generalizes intuitionistic fuzzy sets in a novel manner. It also provides practical results that will facilitate their implementation in real situations. At the theoretical level, we define a family of \mathfrak {c}-complemental fuzzy sets from each fuzzy negation \mathfrak {c}. We argue that this construction provides semantic justification for all subfamilies of complemental fuzzy sets, which include q-rung orthopair fuzzy sets (when \mathfrak {c} is a Yager's fuzzy complement) and the new family of Sugeno intuitionistic fuzzy sets (when \mathfrak {c} belongs to the class of Sugeno's fuzzy complements). We study fundamental operations and a general methodology for the aggregation of complemental fuzzy sets. Then, we give some specific examples of aggregation operators to illustrate their applicability. On a more practical level, constructive proofs demonstrate that all orthopair fuzzy sets on finite sets that satisfy a mild restriction are Sugeno intuitionistic fuzzy sets, and they are q-rung orthopair fuzzy sets for some q too. These contributions produce a new operational model that semantically justifies, and mathematically contains, "almost all" orthopair fuzzy sets on finite sets.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2023.3280221