A Brief Analysis and Interpretation on Arithmetic Operations of Fuzzy Numbers

Fuzzy set theory is a generalized form of crisp set theory where elements are binary inclusion forms. In fuzzy set, it differs with degree of membership for every element in the set. There are several strategies for arithmetic operations on fuzzy numbers. Previous studies show that there are many ap...

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Published in:Results in control and optimization Vol. 13; p. 100312
Main Authors: Mukherjee, Asesh Kumar, Gazi, Kamal Hossain, Salahshour, Soheil, Ghosh, Arijit, Mondal, Sankar Prasad
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2023
Elsevier
Subjects:
Arithmetic operations of fuzzy numbers
Fuzzy sets
Triangular fuzzy number
α–cut set
α–cut set
Fuzzy sets
Arithmetic operations of fuzzy numbers
Triangular fuzzy number
ISSN:2666-7207, 2666-7207
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Abstract Fuzzy set theory is a generalized form of crisp set theory where elements are binary inclusion forms. In fuzzy set, it differs with degree of membership for every element in the set. There are several strategies for arithmetic operations on fuzzy numbers. Previous studies show that there are many approaches, such as the α−cut technique, extension principle, vertex method, etc., to execute arithmetic operations on fuzzy numbers. In this study we perform details analysis and interpretation on arithmetic operations based on the α−cut method in a new way.
AbstractList Fuzzy set theory is a generalized form of crisp set theory where elements are binary inclusion forms. In fuzzy set, it differs with degree of membership for every element in the set. There are several strategies for arithmetic operations on fuzzy numbers. Previous studies show that there are many approaches, such as the α−cut technique, extension principle, vertex method, etc., to execute arithmetic operations on fuzzy numbers. In this study we perform details analysis and interpretation on arithmetic operations based on the α−cut method in a new way.
ArticleNumber 100312
Author Ghosh, Arijit
Mukherjee, Asesh Kumar
Gazi, Kamal Hossain
Salahshour, Soheil
Mondal, Sankar Prasad
Author_xml – sequence: 1
  givenname: Asesh Kumar
  surname: Mukherjee
  fullname: Mukherjee, Asesh Kumar
  organization: Department of Mathematics, Haringhata Mahavidyalaya, Subarnapur, Nadia741249, West Bengal, India
– sequence: 2
  givenname: Kamal Hossain
  orcidid: 0000-0001-7179-984X
  surname: Gazi
  fullname: Gazi, Kamal Hossain
  email: kamalhossain.gazi@makautwb.ac.in
  organization: Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata 741249, West Bengal, India
– sequence: 3
  givenname: Soheil
  surname: Salahshour
  fullname: Salahshour, Soheil
  organization: Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey
– sequence: 4
  givenname: Arijit
  surname: Ghosh
  fullname: Ghosh, Arijit
  organization: Department of Mathematics, St. Xavier's College (Autonomous), Kolkata 700016, India
– sequence: 5
  givenname: Sankar Prasad
  orcidid: 0000-0003-4690-2598
  surname: Mondal
  fullname: Mondal, Sankar Prasad
  organization: Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata 741249, West Bengal, India
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Keywords α–cut set
Fuzzy sets
Arithmetic operations of fuzzy numbers
Triangular fuzzy number
Language English
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Snippet Fuzzy set theory is a generalized form of crisp set theory where elements are binary inclusion forms. In fuzzy set, it differs with degree of membership for...
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SubjectTerms Arithmetic operations of fuzzy numbers
Fuzzy sets
Triangular fuzzy number
α–cut set
Title A Brief Analysis and Interpretation on Arithmetic Operations of Fuzzy Numbers
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