*Article* **A New Method to Decision-Making with Fuzzy Competition Hypergraphs**

#### **Musavarah Sarwar 1, Muhammad Akram 2,\* and Noura Omair Alshehri 3**


Received: 23 July 2018; Accepted: 12 September 2018; Published: 16 September 2018

**Abstract:** Hypergraph theory is the most developed tool for demonstrating various practical problems in different domains of science and technology. Sometimes, information in a network model is uncertain and vague in nature. In this paper, our main focus is to apply the powerful methodology of fuzziness to generalize the notion of competition hypergraphs and fuzzy competition graphs. We introduce various new concepts, including fuzzy column hypergraphs, fuzzy row hypergraphs, fuzzy competition hypergraphs, fuzzy *k*-competition hypergraphs and fuzzy neighbourhood hypergraphs, strong hyperedges, *k*th strength of competition and symmetric properties. We design certain algorithms for constructing different types of fuzzy competition hypergraphs. We also present applications of fuzzy competition hypergraphs in decision support systems, including predator–prey relations in ecological niche, social networks and business marketing.

**Keywords:** fuzzy competition hypergraph; fuzzy *k*-competition hypergraph; fuzzy open neighbourhood; fuzzy closed neighbourhood; ecological niches

**MSC:** 05C65; 05C85; 68R10; 03E72
