Proportional Fuzzy Set Extensions and Their Operations

Cengiz Kahraman

doi:10.1007/978-3-031-70018-7_85

Proportional Fuzzy Set Extensions and Their Operations

Cengiz Kahraman^*

^*Corresponding author for this work

Department of Industrial Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Following the initial introduction of fuzzy sets by Zadeh (1965), extensions of regular fuzzy sets have been documented in the literature. Among these expansions are type-2 fuzzy sets, intuitionistic fuzzy sets, image fuzzy sets, and neutrosophic sets. One issue with standard fuzzy set extensions is that they require experts to provide decimal values for an element's membership, non-membership, and indecision degrees, which might be difficult to ascertain. Assigning membership degrees for three or more digits will make this more challenging. Rather, it will be simpler to ascertain the degrees of membership, non-membership, and indecision using proportional relations between the degrees of parameters of a fuzzy set extension. We introduce the basic operations of proportional intuitionistic fuzzy sets, proportional Pythagorean fuzzy sets, proportional picture fuzzy sets, proportional spherical fuzzy sets, and proportional neutrosophic sets.

Original language	English
Title of host publication	Intelligent and Fuzzy Systems - Intelligent Industrial Informatics and Efficient Networks Proceedings of the INFUS 2024 Conference
Editors	Cengiz Kahraman, Sezi Cevik Onar, Selcuk Cebi, Basar Oztaysi, Irem Ucal Sari, A. Cagrı Tolga
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	775-782
Number of pages	8
ISBN (Print)	9783031700170
DOIs	https://doi.org/10.1007/978-3-031-70018-7_85
Publication status	Published - 2024
Event	International Conference on Intelligent and Fuzzy Systems, INFUS 2024 - Canakkale, Turkey Duration: 16 Jul 2024 → 18 Jul 2024

Publication series

Name	Lecture Notes in Networks and Systems
Volume	1088 LNNS
ISSN (Print)	2367-3370
ISSN (Electronic)	2367-3389

Conference

Conference	International Conference on Intelligent and Fuzzy Systems, INFUS 2024
Country/Territory	Turkey
City	Canakkale
Period	16/07/24 → 18/07/24

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Keywords

Extensions of fuzzy sets
intuitionistic fuzzy sets
picture fuzzy sets
proportional fuzzy sets

Access to Document

10.1007/978-3-031-70018-7_85

Cite this

Kahraman, C. (2024). Proportional Fuzzy Set Extensions and Their Operations. In C. Kahraman, S. Cevik Onar, S. Cebi, B. Oztaysi, I. Ucal Sari, & A. C. Tolga (Eds.), Intelligent and Fuzzy Systems - Intelligent Industrial Informatics and Efficient Networks Proceedings of the INFUS 2024 Conference (pp. 775-782). (Lecture Notes in Networks and Systems; Vol. 1088 LNNS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-70018-7_85

Kahraman, Cengiz. / Proportional Fuzzy Set Extensions and Their Operations. Intelligent and Fuzzy Systems - Intelligent Industrial Informatics and Efficient Networks Proceedings of the INFUS 2024 Conference. editor / Cengiz Kahraman ; Sezi Cevik Onar ; Selcuk Cebi ; Basar Oztaysi ; Irem Ucal Sari ; A. Cagrı Tolga. Springer Science and Business Media Deutschland GmbH, 2024. pp. 775-782 (Lecture Notes in Networks and Systems).

@inproceedings{0202d627adbc4cec8c104c25565a63d8,

title = "Proportional Fuzzy Set Extensions and Their Operations",

abstract = "Following the initial introduction of fuzzy sets by Zadeh (1965), extensions of regular fuzzy sets have been documented in the literature. Among these expansions are type-2 fuzzy sets, intuitionistic fuzzy sets, image fuzzy sets, and neutrosophic sets. One issue with standard fuzzy set extensions is that they require experts to provide decimal values for an element's membership, non-membership, and indecision degrees, which might be difficult to ascertain. Assigning membership degrees for three or more digits will make this more challenging. Rather, it will be simpler to ascertain the degrees of membership, non-membership, and indecision using proportional relations between the degrees of parameters of a fuzzy set extension. We introduce the basic operations of proportional intuitionistic fuzzy sets, proportional Pythagorean fuzzy sets, proportional picture fuzzy sets, proportional spherical fuzzy sets, and proportional neutrosophic sets.",

keywords = "Extensions of fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, proportional fuzzy sets",

author = "Cengiz Kahraman",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; International Conference on Intelligent and Fuzzy Systems, INFUS 2024 ; Conference date: 16-07-2024 Through 18-07-2024",

year = "2024",

doi = "10.1007/978-3-031-70018-7_85",

language = "English",

isbn = "9783031700170",

series = "Lecture Notes in Networks and Systems",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "775--782",

editor = "Cengiz Kahraman and {Cevik Onar}, Sezi and Selcuk Cebi and Basar Oztaysi and {Ucal Sari}, Irem and Tolga, {A. Cagrı}",

booktitle = "Intelligent and Fuzzy Systems - Intelligent Industrial Informatics and Efficient Networks Proceedings of the INFUS 2024 Conference",

address = "Germany",

}

Kahraman, C 2024, Proportional Fuzzy Set Extensions and Their Operations. in C Kahraman, S Cevik Onar, S Cebi, B Oztaysi, I Ucal Sari & AC Tolga (eds), Intelligent and Fuzzy Systems - Intelligent Industrial Informatics and Efficient Networks Proceedings of the INFUS 2024 Conference. Lecture Notes in Networks and Systems, vol. 1088 LNNS, Springer Science and Business Media Deutschland GmbH, pp. 775-782, International Conference on Intelligent and Fuzzy Systems, INFUS 2024, Canakkale, Turkey, 16/07/24. https://doi.org/10.1007/978-3-031-70018-7_85

Proportional Fuzzy Set Extensions and Their Operations. / Kahraman, Cengiz.
Intelligent and Fuzzy Systems - Intelligent Industrial Informatics and Efficient Networks Proceedings of the INFUS 2024 Conference. ed. / Cengiz Kahraman; Sezi Cevik Onar; Selcuk Cebi; Basar Oztaysi; Irem Ucal Sari; A. Cagrı Tolga. Springer Science and Business Media Deutschland GmbH, 2024. p. 775-782 (Lecture Notes in Networks and Systems; Vol. 1088 LNNS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Proportional Fuzzy Set Extensions and Their Operations

AU - Kahraman, Cengiz

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024

Y1 - 2024

N2 - Following the initial introduction of fuzzy sets by Zadeh (1965), extensions of regular fuzzy sets have been documented in the literature. Among these expansions are type-2 fuzzy sets, intuitionistic fuzzy sets, image fuzzy sets, and neutrosophic sets. One issue with standard fuzzy set extensions is that they require experts to provide decimal values for an element's membership, non-membership, and indecision degrees, which might be difficult to ascertain. Assigning membership degrees for three or more digits will make this more challenging. Rather, it will be simpler to ascertain the degrees of membership, non-membership, and indecision using proportional relations between the degrees of parameters of a fuzzy set extension. We introduce the basic operations of proportional intuitionistic fuzzy sets, proportional Pythagorean fuzzy sets, proportional picture fuzzy sets, proportional spherical fuzzy sets, and proportional neutrosophic sets.

AB - Following the initial introduction of fuzzy sets by Zadeh (1965), extensions of regular fuzzy sets have been documented in the literature. Among these expansions are type-2 fuzzy sets, intuitionistic fuzzy sets, image fuzzy sets, and neutrosophic sets. One issue with standard fuzzy set extensions is that they require experts to provide decimal values for an element's membership, non-membership, and indecision degrees, which might be difficult to ascertain. Assigning membership degrees for three or more digits will make this more challenging. Rather, it will be simpler to ascertain the degrees of membership, non-membership, and indecision using proportional relations between the degrees of parameters of a fuzzy set extension. We introduce the basic operations of proportional intuitionistic fuzzy sets, proportional Pythagorean fuzzy sets, proportional picture fuzzy sets, proportional spherical fuzzy sets, and proportional neutrosophic sets.

KW - Extensions of fuzzy sets

KW - intuitionistic fuzzy sets

KW - picture fuzzy sets

KW - proportional fuzzy sets

UR - http://www.scopus.com/inward/record.url?scp=85203598760&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-70018-7_85

DO - 10.1007/978-3-031-70018-7_85

M3 - Conference contribution

AN - SCOPUS:85203598760

SN - 9783031700170

T3 - Lecture Notes in Networks and Systems

SP - 775

EP - 782

BT - Intelligent and Fuzzy Systems - Intelligent Industrial Informatics and Efficient Networks Proceedings of the INFUS 2024 Conference

A2 - Kahraman, Cengiz

A2 - Cevik Onar, Sezi

A2 - Cebi, Selcuk

A2 - Oztaysi, Basar

A2 - Ucal Sari, Irem

A2 - Tolga, A. Cagrı

PB - Springer Science and Business Media Deutschland GmbH

T2 - International Conference on Intelligent and Fuzzy Systems, INFUS 2024

Y2 - 16 July 2024 through 18 July 2024

ER -

Kahraman C. Proportional Fuzzy Set Extensions and Their Operations. In Kahraman C, Cevik Onar S, Cebi S, Oztaysi B, Ucal Sari I, Tolga AC, editors, Intelligent and Fuzzy Systems - Intelligent Industrial Informatics and Efficient Networks Proceedings of the INFUS 2024 Conference. Springer Science and Business Media Deutschland GmbH. 2024. p. 775-782. (Lecture Notes in Networks and Systems). doi: 10.1007/978-3-031-70018-7_85

Proportional Fuzzy Set Extensions and Their Operations

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this