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Journal ArticleDOI

Notes on “Bipolar fuzzy graphs”

01 Sep 2013-Information Sciences (Information Sciences)-Vol. 242, pp 113-121
TL;DR: In this note, it is shown by examples that Definitions 3.1, 5.6, and 5.7 contain some flaws and then the correct versions are provided and a generalized bipolar fuzzy graph is introduced.
About: This article is published in Information Sciences.The article was published on 2013-09-01. It has received 92 citations till now. The article focuses on the topics: Fuzzy classification & Fuzzy mathematics.
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01 Jan 2013

801 citations

Journal ArticleDOI
TL;DR: It is proved that bipolar fuzzy sets and [0,1]2-sets (which have been deeply studied) are actually cryptomorphic mathematical notions and many results which are related to these concepts can be generalized to the case of m-polar fuzzy sets.
Abstract: Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and [0,1](2)-sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion of m-polar fuzzy set (actually, [0,1] (m)-set which can be seen as a generalization of bipolar fuzzy set, where m is an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case of m-polar fuzzy sets. We also give examples to show how to apply m-polar fuzzy sets in real world problems.

215 citations


Cites background from "Notes on “Bipolar fuzzy graphs”"

  • ...The notions of bipolar fuzzy graph (see [4, 45]) and fuzzy graph (see [46, 47]) can be generalized to the convenient (because it allows a computing in computers) and intuitive notion of m-polar fuzzy graph....

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  • ...It is not difficult to verify the following conclusions (some of which generalize the corresponding results in [1, 45])....

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Journal ArticleDOI
TL;DR: A practical example for enterprise resource planning system selection is given to verify the developed approach to solve the bipolar fuzzy multiple attribute decision-making problems and demonstrate its practicality and effectiveness.
Abstract: In this paper, we have investigated the multiple attribute decision-making problems with bipolar fuzzy information. Motivated by the Hamacher operations, we have proposed bipolar fuzzy Hamacher weighted average operator, bipolar fuzzy Hamacher ordered weighted average operator, bipolar fuzzy Hamacher hybrid average operator, bipolar fuzzy Hamacher weighted geometric operator, bipolar fuzzy Hamacher ordered weighted geometric operator, bipolar fuzzy Hamacher hybrid geometric operator. We investigate the characteristics and special cases of these operators. Then, we have utilized these operators to develop some approaches to solve the bipolar fuzzy multiple attribute decision-making problems. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

183 citations

Journal ArticleDOI
TL;DR: This paper presents a meta-analyses of nonlinear Analysis and Applied Mathematics (NAAM) and its applications in telecommunications systems and networks.
Abstract: Guiwu Weia,b, Mao Lua, Fuad E. Alsaadib, Tasawar Hayatc,d and Ahmed Alsaedid aSchool of Business, Sichuan Normal University, Chengdu, P.R. China bCommunications Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia cDepartment of Mathematics, Quaid-I-Azam University 45320, Islamabad, Pakistan dNonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

163 citations

Journal ArticleDOI
TL;DR: This paper defines three new operations on bipolar fuzzy graph, viz. direct product, semi strong product and strong product, and it is proved that any of the products of strong bipolar fuzzy graphs are strongipolar fuzzy graphs.
Abstract: Recently, bipolar fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. In this paper, at first we define three new operations on bipolar fuzzy graphs, viz. direct product, semi strong product and strong product. Likewise, sufficient conditions for each one of them to be complete are given. Also, it is proved that any of the products of strong bipolar fuzzy graphs are strong bipolar fuzzy graphs.

122 citations


Additional excerpts

  • ...These are corrected in [30]....

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References
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Book
01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

52,705 citations

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16,023 citations

Book
01 Jan 1998
TL;DR: This book presents an account of newer topics, including Szemer'edi's Regularity Lemma and its use; Shelah's extension of the Hales-Jewett Theorem; the precise nature of the phase transition in a random graph process; the connection between electrical networks and random walks on graphs; and the Tutte polynomial and its cousins in knot theory.
Abstract: The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader.

3,751 citations

Journal ArticleDOI
TL;DR: Through a human centered design project focused on an information science problem, students will gain experience and a better understanding of the process to develop an innovative solution addressing a societal need.
Abstract: Courses IS 100 Exploring the iSchool with a Human-Centered Lens credit: 1 Hour. (https://courses.illinois.edu/schedule/terms/IS/100/) This course introduces students to the School of Information Sciences (iSchool). Students will explore career and professional development within information sciences, building their leadership and collaborative skills, and building a network within and beyond the iSchool. Through a human centered design project focused on an information science problem, students will gain experience and a better understanding of the process to develop an innovative solution addressing a societal need. Prerequisite: Restricted to Majors Only; First Semester Freshman, Intercollegiate and Off-Campus Transfer Students Only.

1,029 citations

01 Jan 2013

801 citations


Additional excerpts

  • ...…Bipolar fuzzy set Bipolar fuzzy graph Strong bipolar fuzzy graph Self complementary a b s t r a c t In this note, we show by examples that Definitions 3.1, 5.6, and 5.7, Example 5.8, Propositions 5.9 and 5.10, and partial proof of Propositions 5.11 and 5.12 in a previous paper by Akram…...

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