implications, coimplications and left semi-uninorms on a complete lattice

نویسندگان

yuan wang

college of information engineering, yancheng teachers university, jiangsu 224002, people's republic of china keming tang

college of information engineering, yancheng teachers university, jiangsu 224002, people's republic of china zhudeng wang

school of mathematics and statistics, yancheng teachers university, jiangsu 224002, people's republic of china

چکیده

in this paper, we firstly show that the $n$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $n$-dual operation. as a dual result, the $n$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge$-distributive left semi-uninorm, is the right residual implication induced by its $n$-dual operation. then, we demonstrate that the $n$-dual operations of the left semi-uninorms induced by an implication and a coimplication, which satisfy the neutrality principle, are the left semi-uninorms. finally, we reveal the relationships between conjunctive right arbitrary $vee$-distributive left semi-uninorms induced by implications and disjunctive right arbitrary $wedge$-distributive left semi-uninorms induced by coimplications, where both implications and coimplications satisfy the neutrality principle.

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عنوان ژورنال:
iranian journal of fuzzy systems

جلد ۱۴، شماره ۱، صفحات ۱۱۵-۱۳۰

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