Internally Stable Set in Intuitionistic Fuzzy Graph

Cengiz Kahraman; Alexander Bozhenyuk; Margarita Knyazeva

doi:10.1007/978-3-031-09173-5_65

Internally Stable Set in Intuitionistic Fuzzy Graph

Cengiz Kahraman, Alexander Bozhenyuk^*, Margarita Knyazeva

^*Corresponding author for this work

Department of Industrial Engineering

Southern Federal University

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

2 Citations (Scopus)

Abstract

In this paper, the idea of maximum intuitionistic internally stable vertex subset of graph with fuzzy intuitionistic stability degree is considered. The notion of an internally stable set is introduced as some invariant of an intuitionistic fuzzy graph. Here an intuitionistic fuzzy graph is considered as a pair consisting of a crisp set of vertices and an intuitionistic fuzzy set of undirected edges. The paper considers an approach for finding all maximal intuitionistic internally stable subsets of vertices, as a method extension for calculating all maximal internally stable subsets in a crisp graph. The method that allows estimating all maximal internally stable subsets in a fuzzy graph with the highest degree of stability is considered. An example illustrating the operation of the method for finding the internally stable set of the intuitionistic fuzzy graph is also represented in this article.

Original language	English
Title of host publication	Intelligent and Fuzzy Systems - Digital Acceleration and The New Normal - Proceedings of the INFUS 2022 Conference
Editors	Cengiz Kahraman, Sezi Cevik Onar, Basar Oztaysi, Irem Ucal Sari, A. Cagri Tolga, Selcuk Cebi
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	566-572
Number of pages	7
ISBN (Print)	9783031091728
DOIs	https://doi.org/10.1007/978-3-031-09173-5_65
Publication status	Published - 2022
Event	International Conference on Intelligent and Fuzzy Systems, INFUS 2022 - Izmir, Turkey Duration: 19 Jul 2022 → 21 Jul 2022

Publication series

Name	Lecture Notes in Networks and Systems
Volume	504 LNNS
ISSN (Print)	2367-3370
ISSN (Electronic)	2367-3389

Conference

Conference	International Conference on Intelligent and Fuzzy Systems, INFUS 2022
Country/Territory	Turkey
City	Izmir
Period	19/07/22 → 21/07/22

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Fuzzy subgraph
Intuitionistic fuzzy graph
Intuitionistic separability degree
Invariant
Maximum intuitionistic internally stable subset

Access to Document

10.1007/978-3-031-09173-5_65

Cite this

Kahraman, C., Bozhenyuk, A., & Knyazeva, M. (2022). Internally Stable Set in Intuitionistic Fuzzy Graph. In C. Kahraman, S. Cevik Onar, B. Oztaysi, I. U. Sari, A. C. Tolga, & S. Cebi (Eds.), Intelligent and Fuzzy Systems - Digital Acceleration and The New Normal - Proceedings of the INFUS 2022 Conference (pp. 566-572). (Lecture Notes in Networks and Systems; Vol. 504 LNNS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-09173-5_65

Kahraman, Cengiz ; Bozhenyuk, Alexander ; Knyazeva, Margarita. / Internally Stable Set in Intuitionistic Fuzzy Graph. Intelligent and Fuzzy Systems - Digital Acceleration and The New Normal - Proceedings of the INFUS 2022 Conference. editor / Cengiz Kahraman ; Sezi Cevik Onar ; Basar Oztaysi ; Irem Ucal Sari ; A. Cagri Tolga ; Selcuk Cebi. Springer Science and Business Media Deutschland GmbH, 2022. pp. 566-572 (Lecture Notes in Networks and Systems).

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abstract = "In this paper, the idea of maximum intuitionistic internally stable vertex subset of graph with fuzzy intuitionistic stability degree is considered. The notion of an internally stable set is introduced as some invariant of an intuitionistic fuzzy graph. Here an intuitionistic fuzzy graph is considered as a pair consisting of a crisp set of vertices and an intuitionistic fuzzy set of undirected edges. The paper considers an approach for finding all maximal intuitionistic internally stable subsets of vertices, as a method extension for calculating all maximal internally stable subsets in a crisp graph. The method that allows estimating all maximal internally stable subsets in a fuzzy graph with the highest degree of stability is considered. An example illustrating the operation of the method for finding the internally stable set of the intuitionistic fuzzy graph is also represented in this article.",

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author = "Cengiz Kahraman and Alexander Bozhenyuk and Margarita Knyazeva",

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Kahraman, C, Bozhenyuk, A & Knyazeva, M 2022, Internally Stable Set in Intuitionistic Fuzzy Graph. in C Kahraman, S Cevik Onar, B Oztaysi, IU Sari, AC Tolga & S Cebi (eds), Intelligent and Fuzzy Systems - Digital Acceleration and The New Normal - Proceedings of the INFUS 2022 Conference. Lecture Notes in Networks and Systems, vol. 504 LNNS, Springer Science and Business Media Deutschland GmbH, pp. 566-572, International Conference on Intelligent and Fuzzy Systems, INFUS 2022, Izmir, Turkey, 19/07/22. https://doi.org/10.1007/978-3-031-09173-5_65

Internally Stable Set in Intuitionistic Fuzzy Graph. / Kahraman, Cengiz; Bozhenyuk, Alexander; Knyazeva, Margarita.
Intelligent and Fuzzy Systems - Digital Acceleration and The New Normal - Proceedings of the INFUS 2022 Conference. ed. / Cengiz Kahraman; Sezi Cevik Onar; Basar Oztaysi; Irem Ucal Sari; A. Cagri Tolga; Selcuk Cebi. Springer Science and Business Media Deutschland GmbH, 2022. p. 566-572 (Lecture Notes in Networks and Systems; Vol. 504 LNNS).

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

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AU - Kahraman, Cengiz

AU - Bozhenyuk, Alexander

AU - Knyazeva, Margarita

PY - 2022

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N2 - In this paper, the idea of maximum intuitionistic internally stable vertex subset of graph with fuzzy intuitionistic stability degree is considered. The notion of an internally stable set is introduced as some invariant of an intuitionistic fuzzy graph. Here an intuitionistic fuzzy graph is considered as a pair consisting of a crisp set of vertices and an intuitionistic fuzzy set of undirected edges. The paper considers an approach for finding all maximal intuitionistic internally stable subsets of vertices, as a method extension for calculating all maximal internally stable subsets in a crisp graph. The method that allows estimating all maximal internally stable subsets in a fuzzy graph with the highest degree of stability is considered. An example illustrating the operation of the method for finding the internally stable set of the intuitionistic fuzzy graph is also represented in this article.

AB - In this paper, the idea of maximum intuitionistic internally stable vertex subset of graph with fuzzy intuitionistic stability degree is considered. The notion of an internally stable set is introduced as some invariant of an intuitionistic fuzzy graph. Here an intuitionistic fuzzy graph is considered as a pair consisting of a crisp set of vertices and an intuitionistic fuzzy set of undirected edges. The paper considers an approach for finding all maximal intuitionistic internally stable subsets of vertices, as a method extension for calculating all maximal internally stable subsets in a crisp graph. The method that allows estimating all maximal internally stable subsets in a fuzzy graph with the highest degree of stability is considered. An example illustrating the operation of the method for finding the internally stable set of the intuitionistic fuzzy graph is also represented in this article.

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KW - Intuitionistic separability degree

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Y2 - 19 July 2022 through 21 July 2022

ER -

Kahraman C, Bozhenyuk A, Knyazeva M. Internally Stable Set in Intuitionistic Fuzzy Graph. In Kahraman C, Cevik Onar S, Oztaysi B, Sari IU, Tolga AC, Cebi S, editors, Intelligent and Fuzzy Systems - Digital Acceleration and The New Normal - Proceedings of the INFUS 2022 Conference. Springer Science and Business Media Deutschland GmbH. 2022. p. 566-572. (Lecture Notes in Networks and Systems). doi: 10.1007/978-3-031-09173-5_65

Internally Stable Set in Intuitionistic Fuzzy Graph

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