Hoops上的伪赋值

王梅, 辛小龙, 王军涛

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

数学季刊 >

2018 , Vol. 33 >Issue 1: 51 - 60

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.01.006

Hoops上的伪赋值

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School of Mathematics, Northwest University

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.

收稿日期: 2016-09-21

录用日期: 2016-09-21

网络出版日期: 2020-10-09

基金资助

Supported by a grant of National Natural Science Foundation of China(11571281)；

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Implicative Pseudo Valuations on Hoops

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School of Mathematics, Northwest University

Received date: 2016-09-21

Accepted date: 2016-09-21

Online published: 2020-10-09

Supported by

Supported by a grant of National Natural Science Foundation of China(11571281)；

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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

本文引用格式

王梅, 辛小龙, 王军涛 . Hoops上的伪赋值[J]. 数学季刊, 2018 , 33(1) : 51 -60 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.01.006

Abstract

Key words： (implicative) pseudo valuation; hoops

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