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Iranian Journal of Fuzzy Systems، جلد ۱۹، شماره ۶، صفحات ۶۱-۷۳
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چکیده فارسی مقاله
کلیدواژه‌های فارسی مقاله
عنوان انگلیسی Pseudo L-algebras
چکیده انگلیسی مقاله We introduce generalized structures of L-algebras, called pseudo L-algebras, which are the multiplication reduct of pseudo hoops and are structures combining two L-algebras with one compatible order. We prove that every pseudo hoop gives rise to a pseudo L-algebra and every pseudo effect algebra gives rise to a pseudo L-algebra. The self-similarity is the most important property of an L-algebra $L$, which guarantees to induce a multiplication on $L$. We introduce a notion of self-similar pseudo L-algebras and prove that a self-similar pseudo L-algebra becomes an L-algebra if and only if the multiplication $odot$ is commutative. We get some interesting results for self-similar pseudo L-algebras: (1) The negative cone $G^-$ of an $ell$-group $G$ can be seen as a self-similar pseudo L-algebra. (2) Every self-similar pseudo L-algebra is a pseudo hoop. Next, we introduce the notion of self-similar closures of pseudo L-algebras and obtain a self-similar closure by a recursive method. Given a pseudo L-algebra $(L, rightarrow, rightsquigarrow ,1)$, we can generate a free semigroup $(A, ast)$ by the set $Lsetminus {1}$. Furthermore, we let $S(L)=Acup{1}$ and define a binary operation $odot$ on $S(L)$. Then we extend the operations $rightarrow$ and $rightsquigarrow$ from $L$ to $S(L)$, and prove that $(S(L), rightarrow, 1)$ and $(S(L), rightsquigarrow, 1)$ are two cycloids, respectively. Furthermore, under some conditions, $(S(L), rightarrow, rightsquigarrow, 1)$ becomes a self-similar pseudo L-algebra. Finally, we introduce the notion of the structure group of pseudo L-algebras, and give an interesting example to show how to extend a pseudo L-algebra $L$ into the pseudo self-similar closure $S(L)$, and furthermore, derive it's structure group $G(L)$.
کلیدواژه‌های انگلیسی مقاله Pseudo L-algebra, self-similar closure of pseudo L-algebra, structure group of pseudo L-algebra, pseudo hoop, $ell$-group
نویسندگان مقاله X. L. Xin |
School of Science, Xi'an Polytechnic University, Xi'an 710048, China

X. F. Yang |
School of Science, Xi'an Polytechnic University, Xi'an 710048, China

Y. C. Ma |
School of Science, Xi'an Polytechnic University, Xi'an 710048, China

نشانی اینترنتی https://ijfs.usb.ac.ir/article_7210_904114994177871109c4da5605b2e7ac.pdf
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