Bipolar Fuzzy Planar Graphs
In this chapter, we study the concepts of bipolar fuzzy multisets, bipolar fuzzy multigraphs, strong and complete bipolar fuzzy multigraphs, bipolar fuzzy planar graphs, and bipolar fuzzy dual graphs. We discuss different types of bipolar fuzzy edges, int
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Muhammad Akram Musavarah Sarwar Wieslaw A. Dudek
Graphs for the Analysis of Bipolar Fuzzy Information
Studies in Fuzziness and Soft Computing Volume 401
Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
The series “Studies in Fuzziness and Soft Computing” contains publications on various topics in the area of soft computing, which include fuzzy sets, rough sets, neural networks, evolutionary computation, probabilistic and evidential reasoning, multi-valued logic, and related fields. The publications within “Studies in Fuzziness and Soft Computing” are primarily monographs and edited volumes. They cover significant recent developments in the field, both of a foundational and applicable character. An important feature of the series is its short publication time and world-wide distribution. This permits a rapid and broad dissemination of research results. Indexed by ISI, DBLP and Ulrichs, SCOPUS, Zentralblatt Math, GeoRef, Current Mathematical Publications, IngentaConnect, MetaPress and Springerlink. The books of the series are submitted for indexing to Web of Science.
More information about this series at http://www.springer.com/series/2941
Muhammad Akram Musavarah Sarwar Wieslaw A. Dudek •
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Graphs for the Analysis of Bipolar Fuzzy Information
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Muhammad Akram Department of Mathematics University of the Punjab Lahore, Pakistan
Musavarah Sarwar Department of Mathematics Government College Women University Sialkot, Pakistan
Wieslaw A. Dudek Faculty of Pure and Applied Mathematics Wrocław University of Technology Wrocław, Poland
ISSN 1434-9922 ISSN 1860-0808 (electronic) Studies in Fuzziness and Soft Computing ISBN 978-981-15-8755-9 ISBN 978-981-15-8756-6 (eBook) https://doi.org/10.1007/978-981-15-8756-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains n
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