Interval Ranges of Fuzzy Sets Induced by Arithmetic Operations Using Gradual Numbers

Wu introduced the interval range of fuzzy sets. Based on this, he defined a kind arithmetic sets using gradual number and From point view soft computing, this definition provides new way handling operations The is an important characterization set. also useful for analyses applications arithmetic. In paper, we present general conclusions crucial problems related to ranges induced by These indicate that corresponding in previous works should be modified: firstly, give properties composites finite Then, discuss relationship between domain set its set, above results, intersection group their resulting obtained compositions Furthermore, construct examples show even under conditions stronger than work, there are still various possibilities resulted sets,