Fuzzy Hypergraphs and Related Extensions by Muhammad Akram & Anam Luqman

Author:Muhammad Akram & Anam Luqman
Language: eng
Format: epub
ISBN: 9789811524035
Publisher: Springer Singapore

Proof

. Suppose is a q-rung orthopair fuzzy transversal of . For any , which satisfies , and . Hence, , because is a transversal.

. Let , for all and , , which implies that is a transversal of .

. This part can be proved trivially.

Theorem 6.5

Let be a q-rung orthopair fuzzy hypergraph. For each such that and for all , the fundamental sequence of .

Proof

Let the fundamental sequence of be and , for . Consider a mapping defined by

Thus, from the definition of , we have and the Definition 6.13 implies that , for all . Since is a q-rung orthopair fuzzy transversal of and , for all , is a q-rung orthopair fuzzy transversal. Now and minimality of both implies that . Hence, . Thus, , therefore we have .

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