Name
Title | ||
|---|---|---|
(fI,ω)-implications and distributivity of implications on L over t-representable t-norms: The case of strict and nilpotent t-norms |
Abstract | ||
|---|---|---|
In this paper, a new class of intuitionistic fuzzy implications (IFIs) known as (fI,ω)-implications is introduced which is a generalized form of Yager’s f-implications in intuitionistic fuzzy environment (IFE). The basic properties of these implications are discussed in detail. It is shown that (fI,ω)-implications are not only the generalizations of Yager’s f-implications, but also the generalizations of R-, (S,N)- and QL-implications in IFE. The distributivity equations II(T(u,v),w)=S(II(u,w),II(v,w)) and II(u,T1(v,w))=T2(II(u,v),II(u,w)) over t-representable t-norms and t-conorms generated from nilpotent and strict t-norms in IF set theory are discussed. Also, we solve the open problems concerning characterize all of the correct solutions of the distributive equation II(u,T1(v,w))=T2(II(u,v),II(u,w)) when t-norms are strict and nilpotent. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.ins.2019.11.051 | Information Sciences |
Keywords | Field | DocType |
Intuitionistic fuzzy implicator,fI−Generators,ω−Generators,Distributivity equations | Discrete mathematics,Distributive property,Set theory,Generalization,Fuzzy logic,Distributivity,Mathematics,Nilpotent | Journal |
Volume | ISSN | Citations |
513 | 0020-0255 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vishnu Singh | 1 | 7 | 1.79 |
| Shiv Prasad Yadav | 2 | 117 | 15.90 |