Algebraic Structure of Adjoint Triples Generating a Weak Negation on the Unit Interval

作者: M. Eugenia Cornejo , Jesús Medina , Eloísa Ramírez-Poussa

DOI: 10.1007/978-3-030-52705-1_25

关键词:

摘要: This paper presents a theoretical research about the relationship between weak negations and adjoint negations. Adjoint are generalization of residuated built from implications an triple. Specifically, this work shows how to build triples on unit interval such that their coincide with given negation. Moreover, algebraic structure formed by these is also investigated.

参考文章(41)
Cristina Alcalde, Ana Burusco, Juan Carlos Díaz, Ramón Fuentes-González, Jesús Medina-Moreno, Fuzzy property-oriented concept lattices in morphological image and signal processing international conference on artificial neural networks. pp. 246- 253 ,(2013) , 10.1007/978-3-642-38682-4_28
Enric Trillas, Sobre funciones de negación en la teoría de conjuntos difusos. Stochastica. ,vol. 3, pp. 47- 60 ,(1979)
M. Eugenia Cornejo, Jesús Medina, Eloisa Ramírez-Poussa, Multi-adjoint algebras versus non-commutative residuated structures International Journal of Approximate Reasoning. ,vol. 66, pp. 119- 138 ,(2015) , 10.1016/J.IJAR.2015.08.003
A. Pradera, G. Beliakov, H. Bustince, B. De Baets, A review of the relationships between implication, negation and aggregation functions from the point of view of material implication Information Sciences. ,vol. 329, pp. 357- 380 ,(2016) , 10.1016/J.INS.2015.09.033
Chris Cornelis, Jesús Medina, Nele Verbiest, Multi-adjoint fuzzy rough sets: Definition, properties and attribute selection International Journal of Approximate Reasoning. ,vol. 55, pp. 412- 426 ,(2014) , 10.1016/J.IJAR.2013.09.007
Jesús Medina, Manuel Ojeda-Aciego, Jorge Ruiz-Calviño, Formal concept analysis via multi-adjoint concept lattices Fuzzy Sets and Systems. ,vol. 160, pp. 130- 144 ,(2009) , 10.1016/J.FSS.2008.05.004
Ginés Moreno, Jaime Penabad, Carlos Vázquez, Beyond multi-adjoint logic programming International Journal of Computer Mathematics. ,vol. 92, pp. 1956- 1975 ,(2015) , 10.1080/00207160.2014.975218
Francesc Esteva, Lluís Godo, Petr Hájek, Mirko Navara, Residuated fuzzy logics with an involutive negation Archive for Mathematical Logic. ,vol. 39, pp. 103- 124 ,(2000) , 10.1007/S001530050006
Juan Carlos Díaz, Jesús Medina, Multi-adjoint relation equations: Definition, properties and solutions using concept lattices Information Sciences. ,vol. 253, pp. 100- 109 ,(2013) , 10.1016/J.INS.2013.07.024
Roberto Cignoli, Francesc Esteva, Lluís Godo, Franco Montagna, On a class of left-continuous t -norms Fuzzy Sets and Systems. ,vol. 131, pp. 283- 296 ,(2002) , 10.1016/S0165-0114(01)00215-9