Extensions of Ordinary Fuzzy Sets: A Comparative Literature Review

Cengiz Kahraman*, Basar Oztaysi, Irem Otay, Sezi Cevik Onar

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Citations (Scopus)

Abstract

Fuzzy sets extensions have been often used in the modeling of problems including vagueness and impreciseness in order to better define the membership functions together with the hesitancy of decision makers. More than 20 different extensions of ordinary fuzzy sets have appeared in the literature after the introductions of ordinary fuzzy sets by Zadeh (1965). These sets involve interval-type fuzzy sets, type-2 fuzzy sets, hesitant fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets, q-rung orthopair fuzzy sets, spherical fuzzy sets, picture fuzzy sets, fermatean fuzzy sets, etc. Mainly, these extensions can be divided into two classes: extensions with two independent membership parameters and extensions with three independent membership parameters. In this paper, we briefly classify these extensions and present some comparative graphical illustrations.

Original languageEnglish
Title of host publicationIntelligent and Fuzzy Techniques
Subtitle of host publicationSmart and Innovative Solutions - Proceedings of the INFUS 2020 Conference
EditorsCengiz Kahraman, Sezi Cevik Onar, Basar Oztaysi, Irem Ucal Sari, Selcuk Cebi, A. Cagri Tolga
PublisherSpringer
Pages1655-1665
Number of pages11
ISBN (Print)9783030511555
DOIs
Publication statusPublished - 2021
EventInternational Conference on Intelligent and Fuzzy Systems, INFUS 2020 - Istanbul, Turkey
Duration: 21 Jul 202023 Jul 2020

Publication series

NameAdvances in Intelligent Systems and Computing
Volume1197 AISC
ISSN (Print)2194-5357
ISSN (Electronic)2194-5365

Conference

ConferenceInternational Conference on Intelligent and Fuzzy Systems, INFUS 2020
Country/TerritoryTurkey
CityIstanbul
Period21/07/2023/07/20

Bibliographical note

Publisher Copyright:
© 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

  • Extensions
  • Fuzzy sets
  • Intuitionistic fuzzy sets
  • Picture fuzzy sets
  • Pythagorean fuzzy sets
  • q-rung orthopair fuzzy sets
  • Spherical fuzzy sets

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