Matrix expression of finite BZMVdM-algebra-Reference-Cited by-同舟云学术

Matrix expression of finite BZMVdM-algebra

Published:2022-07-21 Issue:3 Volume:43 Page:3469-3478
ISSN:1064-1246
Container-title:Journal of Intelligent & Fuzzy Systems
language:
Short-container-title:IFS

Author:

Yue Shufang¹,Li Ying¹,Zhao Jianli¹

Affiliation:

1. Research Center of Semi-tensor Product of Matrices: Theory and Applications, College of Mathematical Sciences, Liaocheng University, Shandong, P.R. China

Abstract

In this paper, we provide a systematic characterization of finite BZMVdM-algebra by using semi-tensor product of matrices. The abstract operation law about logic of the finite algebra is transformed into the simple operation of concrete logical matrices. In addition, we study some properties of BZMVdM-algebra, such as homomorphism, isomorphism, and the product of the BZMVdM-algebra. Through logical matrix operation, the direct verifiable conditions for detecting the above properties are given.

Publisher

IOS Press

Subject

Artificial Intelligence,General Engineering,Statistics and Probability

Reference10 articles.

1. Cattaneo G. , Giuntini R. and Pilla R. , BZMVdM algebras and stonian MV-algebras (applications to fuzzy sets and rough approximations), Fuzzy Sets and Systems 108(2) (1999).

2. Algebraic Analysis of Many Valued Logics, (2);Chang;Transactions of the American Mathematical Society,1958

3. An Algebraic Approach to Shadowed Sets;Cattaneo;Electronic Notes in Theoretical Computer Science,2003

4. Relations Between BZMVdM-Algebra and Other Algebras;Gao;Journal of Southwest Jiaotong University,2003

5. Completeness and normal form of multi-valued logical functions;Cheng;Journal of the Franklin Institute,2020