In this paper, we consider a set of new symmetries in the SM, {it diagonal reflection} symmetries $R , m_{u, u}^{*} , R = m_{u, u}, ~ m_{d,e}^{*} = m_{d,e}$ with $R =$ diag $(-1,1,1)$. These generalized $CP$ symmetries predict the Majorana phases to be $alpha_{2,3} /2 sim 0$ or $pi /2$. A realization of reflection symmetries suggests a broken chiral $U(1)_{rm PQ}$ symmetry and a flavored axion. The axion scale is suggested to be $langle theta_{u,d} rangle sim Lambda_{rm GUT} , sqrt{m_{u,d} , m_{c,s}} / v sim 10^{12} , $[GeV]. By combining the symmetries with the four-zero texture, the mass eigenvalues and mixing matrices of quarks and leptons are reproduced well. This scheme predicts the normal hierarchy, the Dirac phase $delta_{CP} simeq 203^{circ},$ and $|m_{1}| simeq 2.5$ or $6.2 , $[meV]. In this scheme, the type-I seesaw mechanism and a given neutrino Yukawa matrix $Y_{ u}$ completely determine the structure of right-handed neutrino mass $M_{R}$. An $u- u$ unification predicts mass eigenvalues to be $ (M_{R1} , , M_{R2} , , M_{R3}) = (O (10^{5}) , , O (10^{9}) , , O (10^{14})) , $[GeV].
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