Some Properties Of The Random Membership Functions And The Combination Rules Via Random Set Formulation

In this thesis, the concept of random membership function is introduced. Thefuzzy degree is no more a determinant number, but a random variable. Random mem-bership function have more information than non-random membership function. Somediscussions about the properties of random membership function are presented, and theexamples show the reasonability of the the random membership function. From the re-lationship of the random set and random membership function, various combinationrules from stochastic point of view can be constructed.