Affiliations: [a] Instituto Metrópole Digital, Universidade Federal do Rio Grande do Norte, Campus Universitário, 59072-970 Natal-RN, Brazil | [b] Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Campus Universitário s/n, 59072-970 Natal-RN, Brazil | [c] Departamento de Ciências Exatas, Universidade Federal da Paraíba, 58297-000, Rio Tinto-PB, Brazil | [d] Departamento de Ciências Exatas e Tecnológicas, Universidade Estadual de Santa Cruz, Campus Soane Nazaré de Andrade, Km 16 Rodovia Ilhéus-Itabuna, 45662-900 Ilhéus-BA, Brazil | [e] Departamento de Matemática, Universidade Federal do Pará, Av. Augusto Corrêa s/n, Marco, 66093-380 Belem-PA, Brazil
Correspondence:
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Correspondence to: Ivanosca A. da Silva, Instituto Metrópole Digital, Universidade Federal do Rio Grande do Norte, CampusUniversitário, 59072-970 Natal-RN, Brazil. E-mail: [email protected].
Abstract: This paper considers the concept of pseudo-uninorm which is a natural generalization of the concept of pseudo t-norm for uninorms and presents the relationship between pseudo-uninorms on the unit interval and their natural extension according to Atanassov’s intuitionistic framework, showing how to obtain, in a canonical manner, Atanassov’s intuitionistic pseudo-uninorms from pseudo-uninorms. Moreover, we also show that the automorphisms on the unit interval and on L
* (the intuitionistic valued lattice) are in one-to-one correspondence and how automorphisms on L
* act on Atanassov’s intuitionistic pseudo-uninorms. It is also proved the commutation between the action of automorphisms and the canonical construction of pseudo-uninorms on L
* commute. Moreover, we generalize the usual generation of fuzzy negations from t-norms in order to construct fuzzy negations from pseudo-uninorms and, subsequently, generalize this construction for L
* and relate these two constructions. Finally, we use pseudo-uninorms to obtain a class of weighted average operator and applies it in multiple attribute group decisionmaking problems.
