Granular Computing and Decision-Making

Starting from well-known studies by Kahmenan and Tversky, researchers have found many examples when our decision making seems to be irrational. In this chapter, we show that this seemingly irrational decision making can be explained if we take into account that human abilities to process information are limited; as a result, instead of the exact values of different quantities, we operate with granules that contain these values. On several examples, we show that optimization under such granularity restriction indeed leads to observed human decision making. Thus, granularity helps explain seemingly irrational human decision making.

This chapter describes a comprehensive granular model for decision making with complex data. This granular model first uses information decomposition to form a horizontal set of granules for each of the data instances. Each granule is a partial view of the corresponding data instance; and aggregately all the partial views of that data instance provide a complete representation for the instance. Then, the decision making based on the original data can be divided and distributed to decision making on the collection of each partial view. The decisions made on all partial views will then be aggregated to form a final global decision. Moreover, on each partial view, a sequential M+1 way decision making (a simple extension of Yao’s 3-way decision making) can be carried out to reach a local decision. This chapter further categorizes stock price predication problem using the proposed decision model and incorporates the MLVS model for biological sequence classification into the proposed decision model. It is suggested that the proposed model provide a general framework to address the complexity and volume challenges in big data analytics.

In this article, we attempt to provide a review of the idea of granularity in economic decision making. The review will cover the perspectives from different disciplines, including psychology, cognitive science, complex science, and behavioral and experimental economics. Milestones along this road will be reviewed and discussed, such as Barry Schwartz’s paradox of choice, George Miller’s magic number seven, Gerd Gingerenzer’s fast and frugal heuristics, and Richard Thaler’s nudges. Recent findings from human-subject experiments on the effects of granularity on decision making will also be reviewed, accompanied by various learning models frequently used in agent-based computational economics, such as reinforcement learning and evolutionary computation. These reviews are purported to advance our thinking on the long-ignored granularity in economics and the subsequent implications for public policy-making, such as retirement plans. It, of course, remains to be examined whether the good use of the idea of granularity can enhance the quality of decision making.

Reaching acceptable agreement among decision makers before selecting the suitable alternatives is an important issue in multi-attribute group decision making (MAGDM) process. The aim of this chapter is to present a flexible consensus method in linguistic contexts that adopts a new advice generation scheme by incorporating decision maker’s attitude to achieve agreement at each round of consensus process. Different consensus models for MAGDM problems have been proposed in the literature. However in all of these processes, it is assumed that all the decision makers are equally interested to change their initial opinions. But practically different decision makers may have different levels of confidences in their own opinions and that make their inclinations in changing opinions significantly different to each others’. Moreover, the decision makers who have sufficient agreement levels may not be interested to change their opinions further. This analysis motivates us to develop a new consensus reaching process under linguistic environment wherein decision makers’ opinions will be changed according to the opinion changing indices provided by them and, thus, decision makers’ moral right to modify their opinions will be preserved. Theoretical foundation of the proposed consensus model is laid down and we further implement the consensus algorithm in a linguistic MAGDM problem under dynamic environment. The main contribution of our work is that sovereignty of each decision maker is under consideration in the process of reaching consensus. Finally, a practical example is presented to illustrate the functioning of the proposed method.

Normally, in group decision making problems, groups are composed by individuals or experts with different goals and points of view. For these reasons, they may adopt distinct behaviors in order to achieve their own aims. Nonetheless, in such problems in general, specially those demanding a certain degree of consensus, each expert should comply with a collaboration contract in order to find a common solution for the decision problem.When decision groups are small, all experts usually attempt to fulfill the collaboration contract. However, nowadays technologies such as social media allow to make consensus-driven decisions with larger groups, in which many experts are involved, hence the possibility that some of them try to break the collaboration contract might be greater. In order to prevent the group solution from being biased by these experts, it is necessary to detect and manage their non-cooperative behaviors in this kind of problems. Recent proposals in the literature suggest managing non-cooperative behavior by reducing the importance of expert opinions. These proposals present drawbacks such as, the inability of an expert to recover his/her importance if behavior improves; and the lack of expert’s behavior measures across the time. This chapter introduces a methodology based on fuzzy sets and computing with words, with the aim of identifying and managing those experts whose behavior does not contribute to reach an agreement in consensus reaching processes. Such a methodology is characterized by allowing the importance recovery of experts and taking into account the evolution of their behavior across the time.

Multi-Criteria Group Decision Making (MCGDM) is a decision tool which is able to find a unique agreement from a group of decision makers (DMs) by evaluating various conflicting criteria. However, most multi-criteria decision making techniques utilizing a group of DMs (MCGDM) do not effectively deal with the large number of possibilities inherent in a domain with a variety of possibilities, different judgments, and ideas on opinions. In recent years, there has been a growing interest in developing MCGDM using type-2 fuzzy systems which provide a framework to handle the encountered uncertainties in decision making models. In addition, fuzzy logic is regarded as an appropriate methodology for decision making systems which are able to simultaneously handle numerical data and linguistic knowledge. In this paper, we will aim to modify the fuzzy logic theories based multi-criteria group decision making models to employ a suite of type-2 fuzzy logic systems in order to provide answers to the problems that are encountered in the real experts’ decision. In the proposed framework, we will present a MCGDM method based on interval type-2 fuzzy logic combined with intuitionistic fuzzy evaluation (from intuitionistic fuzzy sets). This combination handles the linguistic uncertainties by the interval type-2 membership function and simultaneously computes the non-membership degree from the intuitionistic evaluation. However, the interval values with hesitation index cannot fully represent the uncertainty distribution associated with the decision makers. Hence, we will present a final component of our framework employing general type-2 fuzzy logic based approach for MCGDM which is more suited for higher levels of uncertainties. In order to optimally find the type-2 fuzzy sets parameters (including interval type-2 and general type-2), we have employed the Big Bang Big Crunch (BB-BC) optimisation method. In order to validate the efficiency of the proposed systems in handling various DMs’ behaviour and opinion, we will present comparisons which were performed on two different real world decision making problems. As will be shown in the various experiment sections, we found that the proposed type-2 MCGDM based system better agrees with the users’ decision compared to type-1 fuzzy expert system and existing type-1 fuzzy MCDMs including the Fuzzy Logic based TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution). In addition, we will show how the different type-2 fuzzy logic based MCGDM systems compare to each other when increasing the level of uncertainties where the general type-2 MCGDM will outperform the MCGDM based interval type-2 fuzzy logic combined with intuitionistic fuzzy evaluation which will outperform the MCGDM based on interval type-2 fuzzy sets. Hence, this work can be regarded as a step towards producing higher ordered fuzzy logic approach for MCGDM (HFL-MCGDM) which could be applied to complex problems with high uncertainties to produce automated decisions much closer to the group of human experts.

This chapter describes the use of influence diagrams in the risk assessment and proposes their extension to the group decision making using fuzzy logic, sequential approach and multi-criteria evaluation. Instead of classical Bayesian networks using conditional probability tables that are often difficult or impossible to obtain, a verbal expression of probabilistic uncertainty, represented by fuzzy sets is used in this approach. Influence diagrams are modeling the multistage decision processes and the interrelations among different chance and value nodes as well, enabling the iterative approach to the risk assessment. After the first, independent assessment of the group of experts, this preliminary risk grade is the input in the second step where the adapted risk grade has been adopted based on known evaluations, and interaction among decision makers. The different risk components and decision maker’s attitudes are considered by ordered weighted averages (OWA) operators. This inference engine is illustrated through the assessment of risk caused by improper drug storage in pharmaceutical cold chain by the group of experts in the iterative assessment process.

This chapter presents a new dynamic model for consensus reaching under fuzziness that uses randomness in the modeling of the individual process iterations. Repeating the process multiple times leads to many singular (different) consensus process paths. The imprecision of the overall result, the resulting different consensus outcomes, is captured by introducing a simple process to form an overall distribution of the outcomes. The model uses a random term that is drawn from a uniform distribution to introduce randomness in the consensus reaching process, and allows for the modeling of real-world behavioral aspects of negotiations, such as negotiator “power” issues by tuning the “amount” of randomness used for each negotiation participant. The new model is numerically illustrated.

In this chapter, firstly, according to the problem of the consistency of reciprocal judgment matrix, two kinds of consistency recursive iterative adjustment algorithms were given.Secondly, according to the consistency problem of the fuzzy complementary judgment matrix, the definition of the scale transition matrix of the fuzzy complementary judgment matrix was given, then one method of additive consistency recursive iterative adjustment algorithms about the fuzzy complementary judgment matrix was given.Thirdly, the definition of additive consistent intuitionistic fuzzy complementary judgement matrix was given, then the addition and subtraction algorithms of intuitionistic fuzzy value representing the relative importance degree in the matrix were given, and the definition of the scale transition matrix of intuitionistic fuzzy complementary judgement matrix was given, then additive consistency recursive iterative adjustment algorithms about the intuitionistic fuzzy complementary judgement matrix was given.Meanwhile, the priority vectors formula of intuitionistic fuzzy complementary judgment matrix was introduced in this paper.Lastly, based on additive consistency recursive iterative adjustment algorithms about the intuitionistic fuzzy complementary judgement matrix, the steps of intuitionistic fuzzy analytic hierarchy process were introduced, then the method was applied in actual examples, and the effectiveness was verified.

Rule based classification is a popular approach for decision making. It is also achievable that multiple rule based classifiers work together for group decision making by using ensemble learning approach. This kind of expert system is referred to as ensemble rule based classification system by means of a system of systems. In machine learning, an ensemble learning approach is usually adopted in order to improve overall predictive accuracy, which means to provide highly trusted decisions. This chapter introduces basic concepts of ensemble learning and reviews Random Prism to analyze its performance. This chapter also introduces an extended framework of ensemble learning, which is referred to as Collaborative and Competitive Random Decision Rules (CCRDR) and includes Information Entropy Based Rule Generation (IEBRG) and original Prism in addition to PrismTCS as base classifiers. This is in order to overcome the identified limitations of Random Prism. Each of the base classifiers mentioned above is also introduced with respects to its essence and applications. An experimental study is undertaken towards comparative validation between the CCRDR and Random Prism. Contributions and Ongoing and future works are also highlighted.

An academic library, as a service organization, has to maintain a level of service quality that, satisfying its users, will assure funding for its existence and development. To do so, the general manager, which is in charge of distributing the funding, asks to the staff of the library about their opinions in the allocation of the budget. An important issue here is the level of agreement achieved among the staff before making a decision. In this paper,we propose a group decision making method based on granular computing aiding to the general manager to decide about funding distribution according to the staff’s opinions. Assuming fuzzy preference relations to represent the preferences of the staff, a concept of a granular fuzzy preference relation is developed, where each pairwise comparison is formed as an information granule instead of a single numeric value. It offers the required flexibility to increase the level of agreement within the staff, using the fact that the most suitable numeric representative of the fuzzy preference relation is selected.

An image conveys multiple meanings depending on the viewing context and the level of granularity at which the viewer perceptually organizes the scene. In image processing, an image can be similarly organized by means of a standardized natural-scene-taxonomy, borrowed from the study of human visual taxometrics. Such a method yields a three-dimensional representation comprised of a hierarchy of nested spatial-taxons. Spatial-taxons are information granules composed of pixel regions that are stationed at abstraction levels within hierarchically-nested scene-architecture. They are similar to the Gestalt psychological designation of figure-ground, but are extended to include foreground, object groups, objects and salient object parts. By using user interaction to determine scene scale and taxonomy structure, image segmentation can be operationalized into a series of iterative two-class fuzzy inferences. Spatial-taxons are segmented from a natural image via a three step process. This chapter provides a gentle introduction to analogous human language and vision information-granules; and decision systems, modeled on fuzzy natural vision-based reasoning, that exploit techniques for measuring human consensus about spatial-taxon structure. A system based on natural vision-based reasoning is highly non-linear and dynamical. It arrives at an end-point spatial-taxon by adjusting to human input as it iterates. Human input determines the granularity of the query and consensus regarding spatial-taxon regions. The methods of concept algebra developed for computing with words [42] [48] are applied to spatial-taxons. Tools from the study of chaotic systems, such as tools for avoiding iteration problems, are explained in the context of fuzzy inference.

Group decision making (GDM) has become a necessity to seek a solution to real life complex problems. The complexity of the problem is due to multiple aspects of any problem such as social, political and economical that is perceived differently by multiple actors (members) due to their diverse, often conflicting evaluation system. In order to reach consensus in the group, members tend to change their opinions guided by the views of other members in the group. In this paper, we have given a methodology that obtains group’s consensus view by finding the shift in the members’ opinions as dictated by group’s dynamics i.e. their importance and support in the group. The members’ preferences for the alternatives are elicited using linguistic terms by comparing pairs of alternatives. Also, importance values of a member as perceived by others in the group are taken in linguistic terms. We have developed a Fuzzy Inference System that gives a rule base for the likely shift in the members’ opinions given the group dynamics. The methodology proceeds iteratively to calculate likely shift in the members’ opinions till the time consensus in the group reaches a predefined threshold value.

This study presents an optimization method in fuzzy decision making of air quality management. The optimization method presented in this chapter gives the mathematical representation to find the equilibrium point. How to obtain and express these optimal data depends on the fuzzy optimization techniques. The methodology and algorithm of fuzzy decision making process by interactive multi-objective approach and iterative optimization method are described, with the application in the process of air quality management. This paper also provides the interactive multi-objective model and iterative calculation method for the application of air quality management. First, the comparison of model output and field monitoring results was discussed, and then the experimental outcome of interactive fuzzy optimum model was presented. Secondly, the comparison of optimum decision from different decision makers was considered, and the experimental outcome of iterative fuzzy optimum model was presented. The combined approach of interactive and iterative method for fuzzy optimization model makes the decision of air quality management more accurate and pragmatic.