Optimization theory for n-set functions

A New Di erential Formalism for Optimization of Set Functions

In many practical problems we must optimize a set function i e nd a set a for which f a max where f is a function de ned on the class of sets Such problems appear in design in image processing in game theory etc In particular if we use statistical methods i e random sets to solve the corresponding set related practical problems then at the end we get a probability distribution on the class of a...

K-epiderivatives for set-valued functions and optimization

A New Diierential Formalism for Optimization of Set Functions

In many practical problems, we must optimize a set function, i.e., nd a set a for which f(a) ! max, where f is a function deened on the class of sets. Such problems appear in design, in image processing, in game theory, etc. In particular, if we use statistical methods (i.e., random sets) to solve the corresponding set-related practical problems, then, at the end, we get a probability distribut...

ON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES

Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...

A Set Theory with Support for Partial Functions

Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special machinery for reasoning about partial functions. For instance, there is no direct way of handling the application of a function to an argument outside its domain as in partial logic. There is also no utilization of lambda-notation and sorts or types as in...