Recent Advances in Decision Making

This chapter presents the application of Computational Intelligence (CI) paradigms for supporting decision making processes. First, the three main CI techniques, i.e., evolutionary computing, fuzzy computing, and neural computing, are introduced. Then, a review of recent applications of CI-based systems for decision making in various domains is presented. The contribution of each chapter included in this book is also described. A summary of concluding remarks is presented at the end of the chapter.

In this paper we discuss the ranking of alternatives represented by elements of Atanassov’s intuitionistic fuzzy sets, to be called A-IFSs, for short. That is, alternatives are elements of the universe of discourse with a degree of membership and a degree of non-membership assigned. First, we show disadvantages of some approaches known from the literature, including a straightforward method based on the calculation of distances from the ideal positive alternative which can be viewed as a counterpart of the approach in the traditional fuzzy setting. Instead, we propose an approach which takes into account not only the amount of information related to an alternative (expressed by a distance from an ideal positive alternative) but also the reliability of information represented by an alternative meant as how sure the information is.

Fuzzy systems have been successfully used in the area of controllers for a long time. The Mamdani method is one of the most popular inference systems for practical applications. The main problem of Mamdani-type inference system and other fuzzy logic based controllers is how to gain the fuzzy rules the inference system based on. Several approaches have been proposed for automatic rule base identification. The bacterial type evolutionary algorithms have been successfully applied for solving this task. These algorithms are based on the Pseudo-Bacterial Genetic Algorithm and are supplied with operations and methods (e.g. the Levenberg-Marquardt method) to complete their task more efficiently. The goal is to create more accurate fuzzy rule bases from input-output data sets as quickly as possible. In this work, we summarize the bacterial type evolutionary algorithms used for fuzzy rule base identification.

Data mining, also known as knowledge discovery in databases, is the process of extracting desirable knowledge or interesting patterns from existing databases. As a specific form of knowledge, association reflects semantics in terms of relationships among attributes in databases, and has been widely studied recently. This chapter focuses on dealing with uncertainty in discovering association rules (AR) and functional dependencies (FD), and provides an overview of our efforts on association rules with fuzzy taxonomies (FAR), on implication-based fuzzy quantitative association rules (ARsi), and on functional dependencies with partial degrees of satisfaction (FD_d).

We first formulate the problem of decision making under uncertainty. The importance of the representation of our knowledge about the uncertainty in formulating a decision process is pointed out. We provide a brief discussion of the case of probabilistic uncertainty. Next, in considerable detail, we discuss the case of decision making under ignorance. For this case the fundamental role of the attitude of the decision maker is noted and its subjective nature is emphasized. Next the case in which a Dempster-Shafer belief structure is used to model our knowledge of the uncertainty is considered. Here we also emphasize the subjective choices the decision maker must make in formulating a decision function. The case in which the uncertainty is represented by a monotonic set measure is then investigated. We then return to the Dempster-Shafer belief structure and show its relationship to the set measure. This relationship allows us to get a deeper understanding of the formulation the decision function used Dempster- Shafer framework. We discuss how this deeper understanding allows a decision analyst to better make the subjective choices needed in the formulation of the decision function. Finally we provide a generalized framework for decision-making in the face of Dempster-Shafer type uncertainty.

The fundamental feature of human-friendly decision-making models (such as those encountered in complex medical problems, economical or political systems, technical diagnostic of physical systems, etc.) is predominantly concerned with interpretability of resulting constructs. Interpretability comes hand in hand with the granular nature of conceptual entities which are sought as the generic building blocks of such decision models and directly support a logic nature of their processing. From the system development perspective, the interpretability begs for solutions to the fundamental problems which need to be fully addressed with this regard. These concern: (a) a construction of information granules (both one-dimensional as well as multivariable structures), and (b) exploitation of logic operators and aggregation operators that are carefully adjusted to cope with available experimental data.

In this study, we concentrate on the two design problems identified above and show how they could be efficiently handled by making use of the carefully crafted methodology of fuzzy sets. The design of information granules is discussed in the setting of fuzzy clustering where we envision an incorporation of the machinery of user feedback so that the information granules are formed both on a basis of available experimental evidence (numeric data) whose processing is cast in the framework of a navigation setup formed by the user/designer realized through the formation of the relevance feedback loop. The construction of logic operators aimed at the logic aggregation of information granules builds upon the available data while adhering to the principles of logic computing. Given this character of processing, we will be referring to these constructs as statistically grounded logic aggregators.

Managerial decision-making is a complex procedure which combines information both in numerical as well as in linguistic form. In this paper, we present a general decision-making methodology which utilizes several intelligent soft-computing techniques, namely the theory of evaluative linguistic expressions, perception-based logical deduction and fuzzy transform. These techniques fulfil the above requirement and so, we are convinced that they can effectively fulfil the needs of managers and provide them with a tool that can help them to obtain a relevant decision. The methodology is demonstrated on an example.

We present how the conceptually and numerically simple concept of a fuzzy linguistic database summary can be a very powerful tool for gaining much insight into the essence of data that may be relevant for a business activity. The use of linguistic summaries provides tools for the verbalization of data analysis (mining) results which, in addition to the more commonly used visualization e.g. via a GUI, graphical user interface, can contribute to an increased human consistency and ease of use. The results (knowledge) derived are in a simple, easily comprehensible linguistic form which can be effectively and efficiently employed for supporting decision makers via the data driven decision support system paradigm. Two new relevant aspects of the analysis are also outlined which was first initiated by the authors. First, following Kacprzyk and Zadrożny (2009a) comments are given on an extremely relevant aspect of scalability of linguistic summarization of data, using their new concept of a conceptual scalability that is crucial for large applications. Second, following Kacprzyk and Zadrożny (2009b) it is further considered how linguistic data summarization is closely related to some types of solutions used in natural language generation (NLG), which can make it possible to use more and more effective and efficient tools and techniques developed in this another rapidly developing area. An application for a computer retailer is outlined.

Computation intelligence paradigms including artificial neural networks, fuzzy systems, evolutionary computing techniques, intelligent agents and so on provide a basis for human like reasoning in medical systems. Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed in our practical model concerning a medical application. The approximate reasoning system presented in this work considers evaluation of a risk in the situation when physicians weigh necessity of the operation on a patient. The patient’s clinical symptom levels, pathologically heightened, indicate the presence of a disease possible to recover by surgery. We wish to evaluate the extension of the operation danger by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.