q-Rung orthopair fuzzy inequality derived from equality and operation

The q-rung orthopair fuzzy set is an extension of fuzzy set, whose remarkable characteristic is that the sum of q power of membership degree, non-membership degree and hesitation degree is equal to 1. Inequalities on q-rung orthopair fuzzy set are of importance in theory of uncertainty. In this paper, firstly, some q-rung orthopair fuzzy inequalities are constructed based on the equality in definition. Then, their inequalities are proved by well-known inequalities, including Rearrangement, Mean, Chebyshev, Nesbitt, Power-Mean, Cauchy, Carlson, Wei-Wei dual, Hölder, Minkowski, Jensen, Tangent, Schur, Muirhead, Vasc or their mix forms. Finally, we derive other q-rung orthopair fuzzy inequalities based on some existing operations, which provides a new basis for the q-rung orthopair fuzzy inequalities.