Fuzzy Number Addition with the Application of Horizontal Membership Functions
Joint Authors
Piegat, Andrzej
Pluciński, Marcin
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-06-23
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
The paper presents addition of fuzzy numbers realised with the application of the multidimensional RDM arithmetic and horizontal membership functions (MFs).
Fuzzy arithmetic (FA) is a very difficult task because operations should be performed here on multidimensional information granules.
Instead, a lot of FA methods use α-cuts in connection with 1-dimensional classical interval arithmetic that operates not on multidimensional granules but on 1-dimensional intervals.
Such approach causes difficulties in calculations and is a reason for arithmetical paradoxes.
The multidimensional approach allows for removing drawbacks and weaknesses of FA.
It is possible thanks to the application of horizontal membership functions which considerably facilitate calculations because now uncertain values can be inserted directly into equations without using the extension principle.
The paper shows how the addition operation can be realised on independent fuzzy numbers and on partly or fully dependent fuzzy numbers with taking into account the order relation and how to solve equations, which can be a difficult task for 1-dimensional FAs.
American Psychological Association (APA)
Piegat, Andrzej& Pluciński, Marcin. 2015. Fuzzy Number Addition with the Application of Horizontal Membership Functions. The Scientific World Journal،Vol. 2015, no. 2015, pp.1-16.
https://search.emarefa.net/detail/BIM-1078707
Modern Language Association (MLA)
Piegat, Andrzej& Pluciński, Marcin. Fuzzy Number Addition with the Application of Horizontal Membership Functions. The Scientific World Journal No. 2015 (2015), pp.1-16.
https://search.emarefa.net/detail/BIM-1078707
American Medical Association (AMA)
Piegat, Andrzej& Pluciński, Marcin. Fuzzy Number Addition with the Application of Horizontal Membership Functions. The Scientific World Journal. 2015. Vol. 2015, no. 2015, pp.1-16.
https://search.emarefa.net/detail/BIM-1078707
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1078707