**Appendix**


$$
\lambda\_r(E\_j) = \max \{ \lambda\_r(E\_j), \lambda\_r(E\_k), \dots \}.
$$

**Table A1.** Adjacency matrix.


**Algorithm A2:** Method for construction of fuzzy column hypergraph

1. Begin 2. Follow steps 2 and 3 of Algorithm A1. 3. **do** *i* from 1 → *n* 4. Take a vertex *xi* from first *ith* row. 5. value1 = <sup>∞</sup>, value2 = <sup>∞</sup>, num = 0 6. **do** *j* from 1 → *n* 7. **if** (*xij* > 0) **then** 8. *xj* belongs to the hyperedge *Ei*. 9. num = num + 1 10. value1 = value1 ∧ *μ*(*xj*) 11. value2 = value2 ∧ *xij* 12. **end if** 13. **end do** 14. **if** (num > 1) **then** 15. *<sup>λ</sup>cl*(*Ei*) = value1 × value2, where *Ei* is a hyperedge. 16. **end if** 17. **end do** 18. If for some *i*, *supp*(*Ei*) = *supp*(*Ek*), *k* ∈ {*j* + 1, *j* + 2, . . . , *n*} then,

> *<sup>λ</sup>cl*(*Ei*) = max{*<sup>λ</sup>cl*(*Ej*), *<sup>λ</sup>cl*(*Ek*),...}.

> > #»

**Algorithm A3:** Construction of fuzzy competition hypergraph


	- If *xij* > 0 then (*xj*, *xij*) belongs to the fuzzy out neighbourhood N +(*xi*).

6.


*<sup>λ</sup>c*(*Ei*)=[*μ*(*xi*1) ∧ *<sup>μ</sup>*(*xi*2) ∧ ... ∧ *μ*(*xir* )] × *h* -N +(*xi*1) ∩ N +(*xi*2) ∩ ... ∩ N +(*xir* ). . **Algorithm A4:** Construction of fuzzy double competition hypergraph


