Logical aggregation based on interpolative

Explicit inclusion of logic in the process of aggregation (information fu- sion) is very important in real problems from many points of view such as adequacy and transparency. In this paper aggregation is treated as a logi- cal and/or pseudo-logical operation based on interpolative Boolean algebra (IBA). IBA is a real-valued ([0, 1]-valued) realization of Boolean algebra. As classical two-valued realization of Boolean algebra is the base of classical two-valued logic, IBA is the base of real-valued logic.Peer Reviewe

An Automated System for Stock Market Trading Based on Logical Clustering

In this paper a novel clustering-based system for automated stock market trading is introduced. It relies on interpolative Boolean algebra as underlying mathematical framework used to construct logical clustering method which is the central component of the system. The system uses fundamental analysis ratios, more precisely market valuation ratios, as clustering variables to differentiate between undervaluated and overvaluated stocks. To structure investment portfolio, the proposed system uses special weighting formulas which automatically diversify investment funds. Finally, a simple trading simulation engine is developed to test our system on real market data. The proposed system was tested on Belgrade Stock Exchange historical data and was able to achieve a high rate of return and to outperform the BelexLine market index as a benchmark variable. The paper has also provided in-depth analysis of the system’s investment decision making process which reveals some exciting insights

Capacities and Games on Lattices: A Survey of Result

We provide a survey of recent developments about capacities (or fuzzy measures) and ccoperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.capacity, fuzzy measure, game, lattice, Choquet integral,Shapley value

Formalization of Human Categorization Process Using Interpolative Boolean Algebra

Since the ancient times, it has been assumed that categorization has the basic form of classical sets. This implies that the categorization process rests on the Boolean laws. In the second half of the twentieth century, the classical theory has been challenged in cognitive science. According to the prototype theory, objects belong to categories with intensities, while humans categorize objects by comparing them to prototypes of relevant categories. Such categorization process is governed by the principles of perceived world structure and cognitive economy. Approaching the prototype theory by using truth-functional fuzzy logic has been harshly criticized due to not satisfying the complementation laws. In this paper, the prototype theory is approached by using structure-functional fuzzy logic, the interpolative Boolean algebra. The proposed formalism is within the Boolean frame. Categories are represented as fuzzy sets of objects, while comparisons between objects and prototypes are formalized by using Boolean consistent fuzzy relations. Such relations are directly constructed from a Boolean consistent fuzzy partial order relation, which is treated by Boolean implication. The introduced formalism secures the principles of categorization showing that Boolean laws are fundamental in the categorization process. For illustration purposes, the artificial cognitive system which mimics human categorization activity is proposed

SELECTION OF THE BEST CONSULTANT FOR SAP ERP PROJECT USING COMBINED AHP-IBA APPROACH

Abstract: In this paper we propose a combined AHP-IBA model for selecting the best SAP consultant for an SAP ERP project. The goal of the SAP Project Manager is to choose the best consultant, the one who is able to implement standard SAP functionalities with quality and on time.When making a decision on the basis of multiple criteria, the traditional Analytic Hierarchy Process (AHP) method does not take into account the fact that attributes may correlate, assuming that there are no dependencies between them. However, the dependencies of the attributes can often be used to model important knowledge for multiple criteria decision analysis. We propose an extension to the traditional AHP method by applying Interpolative realization of Boolean algebra (IBA), using AHP to determine the criteria weights, and IBA to model the logical interactions among criteria. The research conducted on ERP consultant selection suggests that the decision making process is modelled more accurately if logical interactions between attributes are modelled before applying AH

Fuzzy Interpolation Systems and Applications

Fuzzy inference systems provide a simple yet effective solution to complex non-linear problems, which have been applied to numerous real-world applications with great success. However, conventional fuzzy inference systems may suffer from either too sparse, too complex or imbalanced rule bases, given that the data may be unevenly distributed in the problem space regardless of its volume. Fuzzy interpolation addresses this. It enables fuzzy inferences with sparse rule bases when the sparse rule base does not cover a given input, and it simplifies very dense rule bases by approximating certain rules with their neighbouring ones. This chapter systematically reviews different types of fuzzy interpolation approaches and their variations, in terms of both the interpolation mechanism (inference engine) and sparse rule base generation. Representative applications of fuzzy interpolation in the field of control are also revisited in this chapter, which not only validate fuzzy interpolation approaches but also demonstrate its efficacy and potential for wider applications