Next Article in Journal
On the Additively Weighted Harary Index of Some Composite Graphs
Previous Article in Journal
Dialectical Multivalued Logic and Probabilistic Theory
Article Menu
Issue 1 (March) cover image

Export Article

Open AccessArticle
Mathematics 2017, 5(1), 17;

Certain Concepts of Bipolar Fuzzy Directed Hypergraphs

Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
Author to whom correspondence should be addressed.
Academic Editor: Lokenath Debnath
Received: 15 December 2016 / Revised: 17 February 2017 / Accepted: 22 February 2017 / Published: 4 March 2017
Full-Text   |   PDF [6873 KB, uploaded 4 March 2017]   |  


A hypergraph is the most developed tool for modeling various practical problems in different fields, including computer sciences, biological sciences, social networks and psychology. Sometimes, given data in a network model are based on bipolar information rather than one sided. To deal with such types of problems, we use mathematical models that are based on bipolar fuzzy (BF) sets. In this research paper, we introduce the concept of BF directed hypergraphs. We describe certain operations on BF directed hypergraphs, including addition, multiplication, vertex-wise multiplication and structural subtraction. We introduce the concept of B = ( m + , m ) -tempered BF directed hypergraphs and investigate some of their properties. We also present an algorithm to compute the minimum arc length of a BF directed hyperpath. View Full-Text
Keywords: bipolar fuzzy (BF) directed hypergraphs; B-tempered BF directed hypergraphs; BF shortest hyperpath bipolar fuzzy (BF) directed hypergraphs; B-tempered BF directed hypergraphs; BF shortest hyperpath

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Akram, M.; Luqman, A. Certain Concepts of Bipolar Fuzzy Directed Hypergraphs. Mathematics 2017, 5, 17.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top