On the distributive equation of implication based on a continuous t-norm and a continuous Archimedean t-conorm
In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equation of implication I(T(x,y),z) = S (I(x,z),I(y,z)). In detail, by means of the sections of /, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(T(x,y),z) - S(I(x,z),I(y,z)), when T is a continuous but not Archimedean triangular norm, S is a continuous and Archimedean triangular conorm and I is an unknown function. This obtained characterizations indicate that there are no continuous solutions, for the previous functional equation, satisfying the boundary conditions of implications. However, under the assumptions that I is continuous except the point (1,1), we get its complete characterizations.
Fuzzy connectives Fuzzy implication Distribu-tive equations of implications Functional Equations T-norm
Feng Qin Ping-Chong Yang
College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, 330063, P.R. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330063, P.R. Ch
国际会议
上海
英文
2267-2271
2011-10-15（万方平台首次上网日期，不代表论文的发表时间）