Data envelopment analysis (DEA) is an effective tool for supporting decision-makers to assess bankruptcy, uncertainty concepts including intervals, and game theory. The bankruptcy problem with the qualitative parameters is an economic problem under uncertainty. Accordingly, we combine the concepts of the DEA game theory and uncertain models as interval linear programming (ILP), which can be app...

We present a size-aware type system for first-order shapely functions. Here, a function is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely functions are matrix multiplication and the Cartesian product of two lists. The type checking problem for the type system is shown to be undecidable in general. We define a n...

Shapely types separate data, represented by lists, from shape, or structure. This separation supports shape polymorphism, where operations are deened for arbitrary shapes, and shapely operations, for which the shape of the result is determined by that of the input, permitting static shape checking. The shapely types are closed under the formation of xpoints, and hence include the usual algebrai...

We present a size-aware type system for first-order shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely function definitions may be matrix multiplication and the Cartesian product of two lists. The type checking problem for the type system is shown to be u...

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the ...

This paper demonstrates the potential for combining the polytypic and monadic programming styles, by introducing a new kind of combinator, called a traversal. The natural setting for defining traversals is the class of shapely data types. This result reinforces the view that shapely data types form a natural domain for polytypism: they include most of the data types of interest, while to exceed...

Data distribution algebras are an abstract notion for the description of parallel programs. Their dynamic execution can be optimized if they are shapely. In this paper we describe a shape analysis which allows compile-time shapeliness-tests. It operates on the structure of algebraic data types and works for arbitrary functional programs rather than only shapely ones. Besides a rst-order calculu...

ion and Control for Shapely Nested Graph Transformation

We introduce the notion of containers as a mathematical formalisation of the idea that many important datatypes consist of templates where data is stored. We show that containers have good closure properties under a variety of constructions including the formation of initial algebras and final coalgebras. We also show that containers include strictly positive types and shapely types but that th...