Bijective transformations of fuzzy implications – An algebraic perspective

Vemuri, N R and Jayaram, Balasubramaniam (2016) Bijective transformations of fuzzy implications – An algebraic perspective. Fuzzy Sets and Systems, 291. pp. 3-17. ISSN 0165-0114

[img]
Preview
Text (Author version pre-print)
FSS-D-15-0049-R1.pdf - Accepted Version

Download (331kB) | Preview

Abstract

Bijective transformations play an important role in generating fuzzy implications from fuzzy implications. In [Representations through a Monoid on the set of Fuzzy Implications, Fuzzy Sets and Systems, 247, 51–67], Vemuri and Jayaram proposed a monoid structure on the set of fuzzy implications, which is denoted by II, and using the largest subgroup SS of this monoid discussed some group actions on the set II. In this context, they obtained a bijective transformation which ultimately led to hitherto unknown representations of the Yager's families of fuzzy implications, viz., f-, g -implications. This motivates us to consider whether the bijective transformations proposed by Baczyński & Drewniak and Jayaram & Mesiar, in different but purely analytic contexts, also possess any algebraic connotations. In this work, we show that these two bijective transformations can also be seen as being obtained from some group actions of SS on II. Further, we consider the most general bijective transformation that generates fuzzy implications from fuzzy implications and show that it can also be obtained as a composition of group actions of SS on II. Thus this work tries to position such bijective transformations from an algebraic perspective.

[error in script]
IITH Creators:
IITH CreatorsORCiD
Jayaram, Balasubramaniamhttp://orcid.org/0000-0001-7370-3821
Item Type: Article
Uncontrolled Keywords: Bijective transformation; Fuzzy implications; Group action; Equivalence relation; Conjugacy classes; Special property
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 17 Aug 2015 04:22
Last Modified: 20 Sep 2017 07:24
URI: http://raiith.iith.ac.in/id/eprint/1859
Publisher URL: https://doi.org/10.1016/j.fss.2015.08.003
OA policy: http://www.sherpa.ac.uk/romeo/issn/0165-0114/
Related URLs:

Actions (login required)

View Item View Item
Statistics for RAIITH ePrint 1859 Statistics for this ePrint Item