Some Properties of q-Rung Orthopair Fuzzy Derivatives and Indefinite Integrals

Abstract

Abstract. In this paper, we first present the chain rule and the form invariance of differential for q-rung orthopair fuzzy functions (q-ROFFs). In addi tion, we obtain the general formula of indefinite integrals of q-ROFFs by ordinary differential equations. Next, we give the substitution rule of indefinite i ntegrals for q-ROFFs. Meanwhile, we give some examples to verify above-mentioned formul a, such as the chain rule and the substitution rule.