Hoops上的伪赋值

doi:10.13371/j.cnki.chin.q.j.m.2018.01.006

数学季刊 ›› 2018, Vol. 33 ›› Issue (1): 51-60.doi: 10.13371/j.cnki.chin.q.j.m.2018.01.006

Hoops上的伪赋值

School of Mathematics, Northwest University

收稿日期:2016-09-21 接受日期:2016-09-21 出版日期:2018-03-30 发布日期:2020-10-09
作者简介:WANG Mei(1992-), female, native of Changzhi, Shanxi, a Master student of Northwest University, engages in fuzzy set, fuzzy logic; XIN Xiao-long(1955-), male, native of Xi'an, Shaanxi, a professor of Northwest University, Ph.D., engages in logic algebras; WANG Jun-tao(1988-), male, native of Xianyang, Shaanxi, a Ph.D. candidate of Northwest University, engages in fuzzy logic, many-valued logic algebras.
基金资助:
Supported by a grant of National Natural Science Foundation of China(11571281)；

Implicative Pseudo Valuations on Hoops

School of Mathematics, Northwest University

Received:2016-09-21 Accepted:2016-09-21 Online:2018-03-30 Published:2020-10-09
About author:WANG Mei(1992-), female, native of Changzhi, Shanxi, a Master student of Northwest University, engages in fuzzy set, fuzzy logic; XIN Xiao-long(1955-), male, native of Xi'an, Shaanxi, a professor of Northwest University, Ph.D., engages in logic algebras; WANG Jun-tao(1988-), male, native of Xianyang, Shaanxi, a Ph.D. candidate of Northwest University, engages in fuzzy logic, many-valued logic algebras.
Supported by:
Supported by a grant of National Natural Science Foundation of China(11571281)；

摘要/Abstract

摘要： The concept of implicative pseudo valuations on hoops is introduced and some related properties are investigated. As an application of properties of pseudo valuations, we find the relationship between a pseudo valuation and an implicative pseudo valuation and obtain some characterizations of implicative pseudo valuations. In particular, we show that a pseudo valuation on regular hoops is implicative if and only if it satisfies φ(x■x’) = 0.This result will provide a more general algebraic foundation for pseudo valuations theory on algebraic structures based on substructure logic.

关键词: (implicative) pseudo valuation, hoops

Abstract: The concept of implicative pseudo valuations on hoops is introduced and some related properties are investigated. As an application of properties of pseudo valuations, we find the relationship between a pseudo valuation and an implicative pseudo valuation and obtain some characterizations of implicative pseudo valuations. In particular, we show that a pseudo valuation on regular hoops is implicative if and only if it satisfies φ(x■x’) = 0.This result will provide a more general algebraic foundation for pseudo valuations theory on algebraic structures based on substructure logic.

Key words: (implicative) pseudo valuation, hoops

中图分类号:

O153

王梅, 辛小龙, 王军涛. Hoops上的伪赋值[J]. 数学季刊, 2018, 33(1): 51-60.

WANG Mei, XIN Xiao-long, WANG Jun-tao. Implicative Pseudo Valuations on Hoops[J]. Chinese Quarterly Journal of Mathematics, 2018, 33(1): 51-60.

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Hoops上的伪赋值

Implicative Pseudo Valuations on Hoops

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