Vemuri, N R and Jayaram, Balasubramaniam
(2014)
The *composition A Novel Generating Method of Fuzzy Implications: An Algebraic Study.
PhD thesis, Indian Institute of Technology Hyderabad.
Abstract
Fuzzy implications are one of the two most important fuzzy logic connectives, the other being
tnorms. They are a generalisation of the classical implication from twovalued logic to the multivalued
setting.
A binary operation I on [0; 1] is called a fuzzy implication if
(i) I is decreasing in the first variable,
(ii) I is increasing in the second variable,
(iii) I(0; 0) = I(1; 1) = 1 and I(1; 0) = 0.
The set of all fuzzy implications defined on [0; 1] is denoted by I.
Fuzzy implications have many applications in fields like fuzzy control, approximate reasoning,
decision making, multivalued logic, fuzzy image processing, etc. Their applicational value necessitates
new ways of generating fuzzy implications that are fit for a specific task. The generating methods
of fuzzy implications can be broadly categorised as in the following:
(M1): From binary functions on [0; 1], typically other fuzzy logic connectives, viz., (S;N), R, QL
implications,
(M2): From unary functions on [0,1], typically monotonic functions, for instance, Yager’s f, g
implications, or from fuzzy negations,
(M3): From existing fuzzy implications.
[error in script]
IITH Creators: 
IITH Creators  ORCiD 

Jayaram, Balasubramaniam  http://orcid.org/0000000173703821 

Item Type: 
Thesis
(PhD)

Uncontrolled Keywords: 
fuzzy implications; TD271 
Subjects: 
Mathematics 
Divisions: 
Department of Mathematics 
Depositing User: 
Team Library

Date Deposited: 
10 Nov 2014 06:25 
Last Modified: 
15 Jul 2019 05:04 
URI: 
http://raiith.iith.ac.in/id/eprint/654 
Publisher URL: 

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