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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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/153902 |
| Acceso en línea: | http://hdl.handle.net/10366/153902 |
| Access Level: | acceso abierto |
| Palabra clave: | Yager’s fuzzy complement, Sugeno’s fuzzy complement, intuitionistic fuzzy set, q-rung orthopair fuzzy set, aggregation 11 Lógica |
| Sumario: | 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 c-complemental fuzzy sets from each fuzzy negation c. We argue that this construction provides semantic justification for all subfamilies of complemental fuzzy sets, which include q-rung orthopair fuzzy sets (when c is a Yager’s fuzzy complement) and the new family of Sugeno intuitionistic fuzzy sets (when 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. |
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