An Outline of a Theory of Three-Way Decisions

Feeling of hand deformation as a monkey's hand: an experiment on a visual body with discomfort and its algebraic analysis

While there are many studies in which body ownership can be transferred to a virtual body, there are few experimental studies of how subjects feel about their own bodies being deformed since a real body cannot be deformed. Here, we propose such an experimental setup, in which a twisted hand is diagonally viewed from behind, which is called a "monkey's hand." Although the subject cannot see the thumb hidden behind his or her arm, he or she feels that the monkey's hand has an ambiguous thumb that functionally never exists but structurally exists. This ambiguity is consistent with experimental results on proprioceptive drift, by which the deformation of the hand is measured. The ambiguity of the presence and absence of the thumb is finally analyzed with a specific algebraic structure called a lattice. This can help us understand disownership as being different from the absence of ownership.

Threat assessment of aerial targets based on improved GRA-TOPSIS method and three-way decisions

Target threat assessment is a critical aspect of information warfare and can offer valuable auxiliary support to combat command decision-making. Aiming to address the shortcomings of three decision-making methods in air combat target assessment, such as the inability to effectively handle uncertain situation information and quantitatively rank the decision-making targets according to their importance, a dynamic intuitionistic fuzzy decision model based on the improved GRA-TOPSIS method and three-way decisions is proposed. First, the target attribute weight is obtained by cosine intuitionistic fuzzy entropy algorithm; then, a novel intuitionistic fuzzy distance measure is introduced, and grey incidence analysis and TOPSIS are used to build the conditional probability for three-way decisions that fully utilize the existing information and reflect the consistency of dynamic change trend; finally, the comprehensive loss function matrix is constructed and the threat classification results are obtained using the decision rules. The example analysis shows that the proposed method can not only effectively handle complex battlefield situations and dynamic uncertain information, but it can also classify targets, improving the effectiveness and rationality of decision-making and providing a reference basis for scientific command decision-making.

Network rule extraction under the network formal context based on three-way decision

Knowledge discovery combined with network structure is an emerging field of network data analysis and mining. Three-way concept analysis is a method that can fit the human mind in uncertain decisions and analysis. In reality, when three-way concept analysis is placed in the background of a network, not only the three-way rules need to be obtained, but also the network characteristic values of these rules should be obtained, which is of great significance for concept cognition in the network. This paper mainly combines complex network analysis with the formal context of three-way decision. Firstly, the network formal context of three-way decision (NFC3WD) is proposed to unify the two studies mentioned above into one data framework. Then, the network weaken-concepts of three-way decision (NWC3WD) and their corresponding sub-networks are studied. Therefore, we can not only find out the network weaken-concepts but also know the average influence of the sub-network, as well as the influence difference within the sub-network. Furthermore, the concept logic of network and the properties of its operators are put forward, which lays a foundation for designing the algorithm of rule extraction. Subsequently, the bidirectional rule extraction algorithm and reduction algorithm based on confidence degree are also explored. Meanwhile, these algorithms are applied to the diagnosis examples of COVID-19 from which we can not only get diagnostic rules, but also know the importance of the population corresponding to these diagnostic rules in the network through network eigenvalues. Finally, experimental analysis is made to show the superiority of the proposed method.

Concept learning consistency under three-way decision paradigm

Concept Mining is one of the main challenges both in Cognitive Computing and in Machine Learning. The ongoing improvement of solutions to address this issue raises the need to analyze whether the consistency of the learning process is preserved. This paper addresses a particular problem, namely, how the concept mining capability changes under the reconsideration of the hypothesis class. The issue will be raised from the point of view of the so-called Three-Way Decision (3WD) paradigm. The paradigm provides a sound framework to reconsider decision-making processes, including those assisted by Machine Learning. Thus, the paper aims to analyze the influence of 3WD techniques in the Concept Learning Process itself. For this purpose, we introduce new versions of the Vapnik-Chervonenkis dimension. Likewise, to illustrate how the formal approach can be instantiated in a particular model, the case of concept learning in (Fuzzy) Formal Concept Analysis is considered.

Concept Formation and Quantum-like Probability from Nonlocality in Cognition

Human decision-making is relevant for concept formation and cognitive illusions. Cognitive illusions can be explained by quantum probability, while the reason for introducing quantum mechanics is based on ad hoc bounded rationality (BR). Concept formation can be explained in a set-theoretic way, although such explanations have not been extended to cognitive illusions. We naturally expand the idea of BR to incomplete BR and introduce the key notion of nonlocality in cognition without any attempts on quantum theory. We define incomplete bounded rationality and nonlocality as a binary relation, construct a lattice from the relation by using a rough-set technique, and define probability in concept formation. By using probability defined in concept formation, we describe various cognitive illusions, such as the guppy effect, conjunction fallacy, order effect, and so on. It implies that cognitive illusions can be explained by changes in the probability space relevant to concept formation.

A comprehensive model and computational methods to improve Situation Awareness in Intelligence scenarios

This paper presents a comprehensive model for representing and reasoning on situations to support decision makers in Intelligence analysis activities. The main result presented in the paper stems from a work of refinement and abstraction of previous results of the authors related to the use of Situation Awareness and Granular Computing for the development of analysis methods and techniques to support Intelligence. This work made it possible to derive the characteristics of the model from previous case studies and applications with real data, and to link the reasoning techniques to concrete approaches used by intelligence analysts such as, for example, the Structured Analytic Techniques. The model allows to represent an operational situation according to three complementary perspectives: descriptive, relational and behavioral. These three perspectives are instantiated on the basis of the principles and methods of Granular Computing, mainly based on the theories of fuzzy and rough sets, and with the help of further structures such as graphs. As regards the reasoning on the situations thus represented, the paper presents four methods with related case studies and applications validated on real data.

A method based on Graph Theory and Three Way Decisions to evaluate critical regions in epidemic diffusion:: An analysis of COVID-19 in Italy

The paper reports the results of an analysis of COVID-19 diffusion in Italy. The analysis was carried out with a new method based on the combined use of a 3 Way Decisions model and graph theory. Specifically, the data about infected people in the Italian regions is assessed by means of an evaluation function which allows the tri-partitioning of Italy and the identification of high, medium or low critical regions. The tri-partition is performed, along the temporal evolution of the COVID-19 diffusion, by calculating two threshold values which take into account the containment actions that, from time to time, the decision makers have implemented. The effects of a containment action are related to a reduction in the centrality value of a region. To estimate the effect of containment actions, we evaluated two approaches. The first is based on a uniform reduction in the centrality values of the regions, the second estimates the effects of containment actions starting from the mobility changes data provided by the Google Community Mobility reports. The results of our evaluation based on real data of the COVID-19 diffusion in Italy are encouraging and represent a good starting point for future extensions of the method.

Attribute reduction of SE-ISI concept lattices for incomplete contexts

Three-way concept analysis in incomplete contexts lays the theory dealing with the data in incomplete contexts, especially three kinds of partially known formal concepts including SE-ISI formal concept, ISE-SI formal concept and ISE-ISI formal concept. Generally speaking, not every attribute is essential in an incomplete context since the purpose of research is different. Thus, we propose four kinds of attribute reduction of SE-ISI concept lattices based on different criteria. Then, we discuss the relationships among the four kinds of attribute reduction, including the relationships among the consistent sets and relationships among the reducts. Finally, based on discernibility matrices and discernibility functions, the approaches to obtaining these attribute reduction are presented.

Spatial and temporal reasoning with granular computing and three way formal concept analysis

This paper presents and evaluates a method to combine time-based granulation and three-way decisions to support decision makers in understanding and reasoning on the learned granular structures conceptualising spatio-temporal events. The method uses an existing approach to discover periodic events in the data, such as periods of intense traffic in a city, and provides an original approach to conceptualize such events to support decision makers in: (i) better comprehending the causes that lead to the repetition of such events and/or (ii) increasing the awareness of their effects and consequences. The formal concept analysis is the central tool of the proposed method. This tool is used as a guide in the phase of time-based granulation, which relies on the principle of justified granularity, and as a support for reasoning and making three-way decisions. The main contribution of the paper is an effective and simple method for time-based granulation of events, their observation, and interpretation to support decision making. The method is described with an illustrative example and evaluated on a real data set on forest fires, showing how to define a spatio-temporal DSS model to support decisions in environmental monitoring problems.

Three-Way Decision for Handling Uncertainty in Machine Learning: A Narrative Review

In this work we introduce a framework, based on three-way decision (TWD) and the trisecting-acting-outcome model, to handle uncertainty in Machine Learning (ML). We distinguish between handling uncertainty affecting the input of ML models, when TWD is used to identify and properly take into account the uncertain instances; and handling the uncertainty lying in the output, where TWD is used to allow the ML model to abstain. We then present a narrative review of the state of the art of applications of TWD in regard to the different areas of concern identified by the framework, and in so doing, we will highlight both the points of strength of the three-way methodology, and the opportunities for further research.