This paper introduces an extension to the center-of-gravity fuzzy pay-off method, CoG-FPOM by Borges and others from 2018 meant for the valuation of real options by using interval-valued fuzzy numbers. The CoG-FPOM was developed as a response and a remedy to the identified inconsistency with financial theory in the original fuzzy pay-off method for real option valuation (FPOM). The use of interval-valued fuzzy numbers introduced in this paper allows taking into account a higher level of uncertainty and imprecision than is possible with the original CoG-FPOM model. This higher level of uncertainty can be encountered in many application areas. The proposed approach builds on using triangular upper and lower membership functions of fuzzy numbers, which represent expected pay-off distributions. The applicability of the CoG-FPOM in high uncertainty situations is improved by allowing the use of ranges instead of single numbers when inputting values for scenarios. An illustrative numerical application is presented in the context of mergers and acquisitions, where an acquiring company may receive options to abandon that is, rights to divest non-core business units acquired together with the desired parts of a target company. The model outcomes will be discussed and compared with the results from other pay-off-based fuzzy real option valuation models including the original FPOM.