Multiconditional Approximate Reasoning with Continuous Piecewise Linear Membership Functions

It is shown that, for some intersection and implication functions, an exact and efficient algorithm exists for the computation of inference results in multiconditional approximate reasoning on domains which are finite intervals of the real numbers, when membership functions are restricted to functions which are continuous and piecewise linear. An implementation of the algorithm is given in the functional programming language Miranda

Twistor space, Minkowski space and the conformal group

It is shown that the conformal group of compactified Minkowski space is isomorphic to a group of rays of semilinear transformations of twistor space. The action of the conformal group on twistor space is given by an explicit realisation of this isomorphism. In this way we determine the transformation of twistor space under space inversion and time inversion

On the determination of factor systems of PUA representations

A method is developed to obtain a complete set of inequivalent factor systems of PUA � representations of a group with a subgroup of index two from the factor systems of this subgroup

On the type and the standardform of induced UA representations

We derive to which of the three types an irreducible UA representation which is obtained with the procedure of generalised induction belongs. We analyse the question whether or not the irreducible induced UA representations are on standardform. The results hold as well for induced PUA representations

On the factor systems of the Shubnikov space groups

The procedure of Backhouse for the determination of a complete set of inequivalent factor systems of the symmorphic Shubnikov space groups of type I is generalized for all Shubnikov space groups of types I and 111. The results are used to obtain a method for the construction of a set of inequivalent factor systems of the Shubnikov space groups of types I1 and IV

Efficient algorithms for approximate reasoning

We present algorithms for approximate reasoning computations, for some intersection and implication functions, which are as efficient as E.H. Mamdani et al.'s (1975) interpolation method. Implementations of the algorithms are given in the functional language Mirand

Induced PUA representations and selection rules

Well known properties of induced unitary representations are generalised for induced PUA representations. They are applied to obtain an expression for the multiplicities in the Clebsch-Gordon series of induced PUA representations. Finally we show how these multiplicities can be used for the determination of selection rules

Static Analysis of Functional Programs

In this paper, the static analysis of programs in the functional programming language Miranda* is described based on two graph models. A new control-flow graph model of Miranda definitions is presented, and a model with four classes of callgraphs. Standard software metrics are applicable to these models. A Miranda front end for Prometrix, ¿, a tool for the automated analysis of flowgraphs and callgraphs, has been developed. This front end produces the flowgraph and callgraph representations of Miranda programs. Some features of the metric analyser are illustrated with an example program. The tool provides a promising access to standard metrics on functional programs

Validation in the Software Metric Development Process

In this paper the validation of software metrics will be examined. Two approaches will be combined: representational measurement theory and a validation network scheme. The development process of a software metric will be described, together with validities for the three phases of the metric development process. Representation axioms from measurement theory are used both for the formal and empirical validation. The differentiation of validities according to these phases unifies several validation approaches found in the software metric's literature

Programmers' performance on structured versus nonstructured function definitions

A control-flow model for functional programs is used in an experimental comparison of the performance of programmers on structured versus nonstructured Miranda function definitions. The performance is taken as a measure of the comprehensibility of functional programs. The experimental set-up is similar to the Scanlan study (1989). However, in the present study, a two-factor repeated measures design is used in the statistical analysis. The control-flow model appears to be useful in the shaping of the experiment. A significantly better performance has been found for structured function definitions on both dependent variables: the time needed to answer questions about the function definitions and the proportion correct answers. Moreover, for structured function definitions, a counter-intuitive result has been obtained: there are significantly fewer errors in larger definitions than in smaller ones