What is “linguistic decision making” exactly?

Consider the following problem.

Five experts are asked to grade a candidate for tenure based on work in three categories: research, service, and teaching. In each category, the experts assign a grade from a list: very poor, poor, fair, good, or very good. From these evaluations, how does one come up with a single recommendation? To add to the complications, one cannot assume that each expert has the same criteria for each grade, nor can one assume that each expert is equally reliable. The goal of this book is to describe a set of tools and procedures that can be applied in this situation.

The book starts with the notion of a linguistic evaluation scale, of which the list given above is an example. Such a scale may be given an additive or multiplicative structure. Thus, if you think of “fair” as neutral (zero if you will), then for an additive scale, evaluations of poor and good add to fair. The notion of a multiplicative scale is similar. For this review, we will only consider additive evaluations, to simplify the narrative. Given an additive linguistic scale, one can then define ways of aggregating these values. These aggregated methods may involve weightings of the linguistic values, so that poor may be worse than (negative good). The author introduces several ways to do this.

The next step is to introduce the notion of a linguistic preference relation. Suppose that one has a number of different alternatives and that each pair of alternatives is ranked according to a linguistic evaluation scale whose middle value represents neutrality. The resulting matrix of values is called a linguistic preference relation.

For an additive linguistic scale, the resulting matrix must be antisymmetric. The author describes how the linguistic preference matrices of several decision makers can be combined into a single matrix. An important notion introduced here is that of the degree of deviation between two linguistic preference relations. As the name suggests, the degree of deviation measures the closeness of two preference relations. It can be used to weight or adjust the opinion of an expert relative to the others.

A really interesting section discusses incomplete linguistic preference relations. These occur when the expert does not assign values to all the entries in the matrix. An important and eminently practical result shows that under certain circumstances, essentially when enough of the “right” pairs of values are given, the missing values can be filled in. The book gives a number of worked examples to show how this is done. Indeed, this pattern of introducing a concept and following it with a worked example is used throughout the book.

The concept of the linguistic preference relation can be extended to what the author calls “uncertain linguistic relations.” Here, instead of a specific value for each preference between alternatives, one has a range of linguistic values, for example [poor,fair].

The final chapter of the book ties together the basic ideas in a discussion of decision making in the case where one has several attributes that are part of the evaluative process, as, for example, in the tenure decision outlined at the start of the review. The many techniques introduced earlier in the book are applied to yield a set of decision procedures. These allow for weighting experts differently, adjusting the weights accorded to each linguistic value, and setting criteria for accepting the judgment. These various weights can be further adjusted during the process, if this is necessary to arrive at a decision that meets the judgment criterion.

Because of the way the book is structured, with concepts introduced in a formal way and examples restricted to the current context, it is not always clear in what direction the book is going. Only in the examples at the end of the third chapter and in chapter 4 do the methods appear in the context of applications. Readers need to have faith that the material is leading toward applications. By the end of the book, they will be rewarded.

The writing is quite dense with a large amount of terminology introduced quite rapidly. It makes sense to read through the book once quickly enough to get to the later material, perhaps confining oneself to the material on additive linguistic scales. After acquiring an overall sense of the structure of linguistic decision making, readers can return to the earlier material for closer study. The book can also serve as a reference for techniques for working with multi-expert, multi-attribute decision making in those cases where the valuations are qualitative rather than metric.

Readers should determine for themselves whether the methods described here can yield decisions about which they can feel comfortable. For some readers, the process may appear too mechanical. The book is a valuable resource for anyone interested in formalizing a linguistic decision-making process. The few misprints can easily be corrected by the reader.