The *-composition -A Novel Generating Method of Fuzzy Implications: An Algebraic Study

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.  Preview
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Abstract

Fuzzy implications are one of the two most important fuzzy logic connectives, the other being t-norms. They are a generalisation of the classical implication from two-valued 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.

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IITH Creators:
IITH CreatorsORCiD
Jayaram, Balasubramaniamhttp://orcid.org/0000-0001-7370-3821
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 View Item