The proof of the abovementioned paper, Case I of item 2) of Proposition 9 is not suitable, although the conclusion of Proposition 9 is correct. Meanwhile, the conditions of <inline-formula><tex-math notation="LaTeX">$O$</tex-math></inline-formula> satisfying <inline-formula><tex-math notation="LaTeX">$O(1,e) = e$</tex-math></inline-formula> or (O6) in Corollary 3 and <inline-formula><tex-math notation="LaTeX">$G$</tex-math></inline-formula> satisfying <inline-formula><tex-math notation="LaTeX">$G(0,e) = e$</tex-math></inline-formula> or (G6) in Corollary 7 are redundant. So, in this paper, first, we show the modification of the incorrect part of Case I of the proof of item 2) of Proposition 9 and express the statement of Proposition 9 by a simpler way than before. In addition, the expression of the statements of Propositions 10, 19, and 20 is shown by a simpler way than before because they are related to Proposition 9. Second, we remove the redundant conditions in Corollaries 3 and 7.
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Corrections to “On Distributive Laws of Uninorms Over Overlap and Grouping Functions”
Semantic Scholar · Mathematics · 2019
Abstract
The proof of the abovementioned paper, Case I of item 2) of Proposition 9 is not suitable, although the conclusion of Proposition 9 is correct. Meanwhile, the conditions of <inline-formula><tex-math notation="LaTeX">$O$</tex-math></inline-formula> satisfying <inline-formula><tex-math notation="LaTeX">$O(1,e) = e$</tex-math></inline-formula> or (O6) in Corollary 3 and <inline-formula><tex-math notation="LaTeX">$G$</tex-math></inline-formula> satisfying <inline-formula><tex-math notation="LaTeX">$G(0,e) = e$</tex-math></inline-formula> or (G6) in Corollary 7 are redundant. So, in this paper, first, we show the modification of the incorrect part of Case I of the proof of item 2) of Proposition 9 and express the statement of Proposition 9 by a simpler way than before. In addition, the expression of the statements of Propositions 10, 19, and 20 is shown by a simpler way than before because they are related to Proposition 9. Second, we remove the redundant conditions in Corollaries 3 and 7.