The concept of resolvability of a balanced incomplete block (BIB) design, introduced by Bose (1942), was generalized to $\mu$-resolvability of an incomplete block design by Shrikhande and Raghavarao (1964). As a further generalization of these, the concept of $(\mu_1, \mu_2, \cdots, \mu_t$)-resolvability is here introduced for an incomplete block design. This concept may be useful from both combinatorial and practical points of view. Furthermore, some methods of constructing BIB designs with the generalized concept are discussed with illustrations. One method is based on a finite geometry over a Galois field.