An information retrieval (IR) system (IRs) (search engine) is said to be efficient, to the degree that always evaluates each object in the information base (database, document base, web,...) like the expert. The ability of IRs's is to retrieve mostly all relevant objects (measured by the recall), and only the (most) relevant objects (measured by the precision) from the collection queried.
Recall and precision measures provide the classical measure of the retrieval efficiency. They measure the degree to which the query answer (the set of documents that retrieved by IRs as response to the user query). Where, the query answer is the set of relevant documents in the information based queried.
Retrieving most relevant documents to the user query in IRs was one of the most important methods of World Wide Web (WWW) search engines used in the world now. So the searchers aim to use genetic programming (GP) and fuzzy optimization to optimize the user search query in the Boolean IRs model and in the fuzzy IRs model; and to use more Boolean operators (AND, OR, XOR, OF, and NOT) instead of using the standard operators (AND, OR, and NOT), and to use weights for terms and for Boolean operators. Weights are used to give the users more relaxation in defining how much the importance of the terms and of the Boolean operators is. The terms and the Boolean operators' weights are used in fuzzy IRs model. In addition, it investigates extensions of the classical measurement of effectiveness in IRs, precision; recall and harmonic mean.
The researchers use harmonic mean measure as an objective function which uses both measures precision and recall at once for evaluating the results of the two IRs models to grow up the precision-recall relationship curve.
This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to max−∗ fuzzy relational equations and an inequality constraint, where ∗ is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy max−∗ relational equation and an inequality constraint, where ∗ is the t-norm or mean. The authors present results that generalize this outcome, so the linear optimization problem can be used with any continuous increasing operation with a zero element where ∗ includes in particular the previously studied operations. Moreover, operation ∗ does not need to be a t-norm nor a pseudo-t-norm. Due to the fact that optimal solutions are constructed from the greatest and minimal solutions of a max−∗ relational equation or inequalities, this article presents a method to compute them. We note that the linear optimization problem is valid for both minimization and maximization problems. Therefore, for the optimization problem, we present results to find the largest and the smallest value of the objective function. To illustrate this problem a numerical example is provided.