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A splicing system is one of the early theoretical models for DNA computing. Two strings of DNA molecules are cut at specified recognition sites in a splicing system, and the prefix of the first string is attached to the suffix of the second string, generating new strings. The recognition sites for both strings of DNA molecules are the same for a specific type of splicing system, namely simple splicing systems. Splicing systems with finite sets of axioms and splicing rules are known to produce only regular languages. As a result, many forms of restrictions for splicing systems have been considered in order to boost their generative power. Fuzzy splicing systems, in which truth values (i.e., fuzzy membership values) from the closed interval [0, 1] are assigned to the axioms of splicing systems, have been introduced. The truth values of every generated string z from strings x and y are then computed by performing a fuzzy bounded-addition operation over their truth values. The features of bounded-addition fuzzy simple splicing systems are studied in this research. It has been demonstrated that fuzzy simple splicing systems with bounded addition operations can increase the generative power of the splicing languages generated.