The planning process: structure of verbal descriptions

The success of physical sciences led the social scientists to adopt the 'mathematics' that accompanied the development of physical sciences to be the mode of their disciplines and they developed the habit of dressing up their rather imprecise concepts in the language of numbers and calculus. Very few social scientists are aware that, if they are to imitate the procedures of modern physics, they must begin with a critical account of the quantitative notions and the means adopted for collecting and measuring them. We can follow the procedures of physical sciences if we have the equivalent of the so-called 'physics' of physical sciences which provides appropriate dimension-conversion formulae for the aggregation of measurements, etc. In the absence of an elaborated 'physics', social scientists have to restrict themselves, at least at the very beginning, to the qualitative aspect of the system under consideration. A way to do this is to confine their measurements to a 'homogeneous set of logical values', in particular, the set (true, false}. In other words, they should put 'structure before measure'. This paper presents a method of constructing the structure of an object - feature relation based on the so-called verbal descriptions of a phenomenon. The object - feature map λ: M -»- N from a set of perceived objects to a set of descriptive features is analyzed mathematically, and it forms a Galois lattice, if we interpret the mapping of a set of objects by λ as a process of extracting the common features possessed by the objects. Each element of the Galois lattice is of the form ( A, B ), with B = λ( A), and it is generated dynamically through an interaction of λ and λ -1 , the inverse relation of λ. The mapping λ extracts the features common to a set of objects A and λ -1 will pick all the objects which have λ( A) as part of their common features. The internal relation that organizes the objects is a tolerance relation σ, σ = λ -1 λ, and a tolerance class of objects is a set of objects A such that σ( A) = A . The theory is constructive and an algorithm to generate the Galois lattice is presented.