On the basic solutions to the generalized fuzzy integral equation

✍ Scribed by Wu Congxin; Song Shiji; Wang Haiyan

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 408 KB
• Volume: 95
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(96)00297-7

✦ Synopsis

For the fuzzy measure space (X, &,p), the structure of the basic solutions to the generalized fuzzy integral equation

is considered, where h(x) is taken as a nonnegative measurable kernel function, j E (0, co) is a constant, A denotes the logic multiplication (minimum operator). At first, the existence of the constant basic solution to Eq. ( 1) is investigated, and the solvable sufficient and necessary conditions to the Eq. ( 1) are characterized, then the characteristic functional basic solution to Eq. ( 1) is shown. In addition, two convergent theorems corresponding to the sequences of approximate basic solutions each of which is constituted by the series with the logic addition (maximum operator denoted by V) for the characteristic functions are obtained. 0 1998 Elsevier Science B.V.