Journal: 
                                :iranian journal of fuzzy systems
                            
                        
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                    dechao li 
                    
                    
                    
                        
                    school of mathematics, physics and information science, zhejiang ocean
university, zhoushan, zhejiang, 316022, china and key laboratory of oceanographic big data mining and application of zhejiang province, zhoushan, zhejiang, 316022,
china yongjian xie 
                    
                    
                    
                        
                    college of mathematics and information science, shaanxi normal
university, xi'an, 710062, china 
                    
                    
            
                    
                    
                    it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...