Framework Of Granular Computing Research Articles

A nonadditive rough set model for long-term clinical efficacy evaluation of chronic diseases in real-world settings

The pursuit of clinical effectiveness in real-world settings is at the core of clinical practice progression. In this study, we address a long-term clinical efficacy evaluation decision-making problem with temporal correlation hybrid attribute characteristics. To address this problem, we propose a novel approach that combines a temporal correlation feature rough set model with machine learning techniques and nonadditive measures. Our proposed approach involves several steps. First, over the framework of granular computing, we construct a temporal correlation hybrid information system, the gradient method is employed to characterize the temporal attributes and the similarity between objects is measured using cosine similarity. Second, based on the similarity of gradient and cosine, we construct a composite binary relation of temporal correlation hybrid information, enabling effective classification of this information. Third, we develop a rough set decision model based on the Choquet integral, which describes temporal correlation decision process. We provide the ranking results of decision schemes with temporal correlation features. To demonstrate the practical applications of our approach, we conduct empirical research using an unlabeled dataset consisting of 3094 patients with chronic renal failure (CRF) and 80,139 EHRs from various clinical encounters. These findings offer valuable support for clinical decision-making. Two main innovations are obtained from this study. First, it establishes general theoretical principles and decision-making methods for temporal correlation and hybrid rough sets. Second, it integrates data-driven clinical decision paradigms with traditional medical research paradigms, laying the groundwork for exploring the feasibility of data-driven clinical decision-making in the field.

A preference-approval structure-based non-additive three-way group consensus decision-making approach for medical diagnosis

The clinical diagnosis decision-making process of integrated traditional Chinese medicine and Western medicine is essentially a type of group decision-making (GDM) problem, which is transparently characterized by the multiformity of data types and the diversity of knowledge structures among experts. However, most existing GDM methods are designed based on single data types and cannot address GDM problems involving multiple data types and diversified attributes. Moreover, the preference-approval structure provides a simple framework to simulate the preference information regarding an individual’s ranking and approval. But it only considers two categories: approval and disapproval, without accounting for the indecision of individuals. In reality, three-way decision (TWD) is common. Given the deficiencies above, this paper puts forward a novel preference-approval structure-based three-way group consensus decision-making approach for a class of GDM problems with the characteristics of incompleteness, multi-granularity, diversity, and compound. To represent the information in these complex GDM problems, we firstly present the concept of incomplete multi-granularity diversified compound decision systems (IMGDCDSs). Secondly, according to the data characteristics, we construct a non-additive TWD model over the framework of granular computing. On the one hand, using the reference point of each attribute, an acquisition method of relative loss functions is given by considering three kinds of states. On the other hand, we present a new fuzzy measure to calculate non-additive conditional probabilities. The above work enriches the existing TWD theory. Based on the three-way classification and ranking results obtained, this paper subsequently defines a preference-approval structure and establishes a new group consensus decision-making approach. Thereby, the TWD model is integrated into preference-approval structures, which further enriches the GDM theory. More importantly, some existing group consensus methods are special cases of our study. Whereafter, we demonstrate the feasibility of the approach using an illustrative example. Finally, the stability and effectiveness of the approach are verified through an empirical study in the context of medical diagnosis.

Valued outranking relation-based heterogeneous multi-decision multigranulation probabilistic rough set and its use in medical decision-making

Regarding to group decision-making, decision makers may express different decision preferences for the same target. Since existing decision-making methods only consider a single decision preference at most, it is difficult to integrate the multi-decision preferences of multiple decision makers effectively. In this paper, we explore a class of heterogeneous multi-attribute group decision-making (MAGDM) problems with multiple decisions. Over the framework of granular computing, we present a new MAGDM method with the aid of the valued outranking relations in the ELECTRE III method. Considering the non-compensability among attributes, we first define a special valued outranking relation on a heterogeneous attribute multi-decision information system, and then present the notion of valued outranking classes. Subsequently, given the fact that the fault tolerance of probability approximations can reduce the vulnerability of decision-making methods, we construct multi-decision multigranulation probabilistic rough sets (MD-MGPRSs) form different perspectives, which extend existing rough set models to a more general situation. After that, we establish a novel MAGDM method, and apply the method to a real medical case to illustrate its applicability. Lastly, the experimental results on seven datasets demonstrate the effectiveness, robustness, and superiority of the method. Our study not only enriches the theoretical research of rough sets, but also extends the application scope of decision-making theory.

Information structures in a multiset-valued information system with application to uncertainty measurement

Information system (IS) is a significant model in the field of artificial intelligence. Information structure is not only a research direction in the field of granular computing (GrC), but also an important method to study an IS. A multiset-valued information system (MVIS) refers to an IS where information values are multisets. A MVIS can be seen as a model that is the result of information fusion of multiple categorical ISs. This model helps deal with missing values in the dataset. This paper studies information structures in a MVIS on the view of GrC and consider their application for uncertainty measurement (UM). First of all, some notions of multisets and probability distribution sets (PDSs) are proposed. Naturally, relationships between multisets and PDSs are researched. Then, the concept of a MVIS based on the notion of multisets is given, and the internal structure of a MVIS is revealed by an incomplete information system (IIS). Furthermore, tolerance relations in a MVIS are defined by using Hellinger distance, and tolerance classes are obtained to construct the information structures of a MVIS. Considering the association of information structures, relationships between information structures are raised from the two aspects of dependence and separation. Moreover, some properties between information structures are provided by using information distance and inclusion degree. Finally, four UMs as the applications of information structures are investigated, and comprehensive experiments on several datasets demonstrate the feasibility and superiority of the proposed measures. These results will be helpful for establishing a framework of GrC in a MVIS and studying UM.

Designing of higher order information granules through clustering heterogeneous granular data

This study is devoted to the generalization of information granules by forming higher order, namely, order-2 information granules. Information granules are semantically meaningful entities, which play a central role in knowledge representation and system modeling in the framework of Granular Computing. The encountered information granules could exhibit significant heterogeneity because of the diversified formal formalisms. To facilitate an effective generalization of heterogeneous granular data when using clustering algorithms, an efficient scheme has been proposed to form a unified representation of various types of granular data by using Possibility–necessity measures. Once the clustering process has been completed in the possibility–necessity feature space, the higher order information granules come as results of decoding by involving the possibility–necessity metrics and fuzzy relational calculus. The extent to which the higher order information granules are supported by the granular data present at a lower level of hierarchy is quantified in terms of the membership degrees obtained in the clustering process. Experimental studies concerning a series of publicly available datasets coming from UCI and KEEL machine learning repositories are carried out in this study.

A rule-based granular model development for interval-valued time series

As one type of time series, interval-valued time series (ITS) is encountered frequently in many fields such as finance, environment, agriculture and so on since it can describe the uncertainty and variability of observed variables. The modeling of ITS is an ongoing issue pursued by researchers. In this paper, a novel rule-based granular ITS model is proposed by considering the interval-valued data as interval information granules in the framework of granular computing (GrC). The development of the proposed granular model consists of three components with progressive relationship, that is, the generation of granular prototypes, the formation of initial granular model and the refinement of the initial granular model. Further, the detail computation of reasoning of the corresponding granular model is also given. The resulting granular models have not only interpretability but also an ability to process ITS containing linguistic variables. Numerical experiments on six financial datasets and two meteorological datasets from real world reveal the impact of the parameter involved in the proposed method on the resulting granular model, and also exhibit that the resulting granular model is superior to seven existing competitive models including interval Holt one, multi-output support vector regression one and interval arithmetic-based multilayer perceptron one etc.

Hierarchical Axiomatic Fuzzy Set Granulation for Financial Time Series Clustering

Financial time series are generally high-dimensional, nonstationary, and exhibit heteroscedasticity. To derive a suitable way to cluster financial time series, these characteristics have to be taken into consideration. With this aim, in this article, the financial time series is firstly modeled using generalized autoregressive conditional heteroscedasticity (GARCH) models, where the parameters of GARCH models can represent the dynamic feature of the volatility in each time series. Therefore, the following clustering is realized based on the GARCH model parameters, which can help reduce the dimensionality of the original time series at the same time. Then, to produce semantically sound clustering results, we granulate the parameters based on the axiomatic fuzzy set (AFS) theory and structure them into a collection of meaningful and semantically sound entities, i.e., AFS information granules. Furthermore, the hierarchical structure of AFS information granules is built to realize time series clustering under the framework of granular computing. In the proposed approach, the characteristics of financial time series is fully considered to proceed dimensionality reduction, and the semantic clustering results obtained for different numbers of clusters are guaranteed to be the most informative. In the experiments, an application for clustering the time series coming from Chinese Yuan exchange rates against international currencies is presented to demonstrate the performance of the proposed clustering method. The results of clustering of the proposed method are the same as those of the fuzzy C-means algorithm and the hierarchical clustering with ward linkage, where the clustering results produced by the AFS hierarchical clustering exhibit well-articulated semantics at each level of the hierarchy.

MAGDM-oriented dual hesitant fuzzy multigranulation probabilistic models based on MULTIMOORA

In real world, multi-attribute group decision making (MAGDM) is a complicated cognitive process that involves expression, fusion and analysis of multi-source uncertain information. Among diverse soft computing tools for addressing MAGDM, the ones from granular computing (GrC) frameworks perform excellently via efficient strategies for multi-source uncertain information. However, they usually lack convincing semantic interpretations for MAGDM due to extreme information fusion rules and instabilities of information analysis mechanisms. This work adopts a typical GrC framework named multigranulation probabilistic models to enrich semantic interpretations for GrC-based MAGDM approaches, and constructs MAGDM-oriented multigranulation probabilistic models with dual hesitant fuzzy (DHF) information in light of the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) method. After reviewing several basic knowledge, we first put forward four types of DHF multigranulation probabilistic models. Then, according to the MULTIMOORA method, a DHF MAGDM algorithm is designed via the proposed theoretical models in the context of person-job (P-J) fit. Finally, an illustrative case study for P-J fit is investigated, and corresponding validity tests and comparative analysis are conducted as well to demonstrate the rationality of the presented models.

Granulated deep learning and Z-numbers in motion detection and object recognition

The article deals with the problems of motion detection, object recognition, and scene description using deep learning in the framework of granular computing and Z-numbers. Since deep learning is computationally intensive, whereas granular computing, on the other hand, leads to computation gain, a judicious integration of their merits is made so as to make the learning mechanism computationally efficient. Further, it is shown how the concept of z-numbers can be used to quantify the abstraction of semantic information in interpreting a scene, where subjectivity is of major concern, through recognition of its constituting objects. The system, thus developed, involves recognition of both static objects in the background and moving objects in foreground separately. Rough set theoretic granular computing is adopted where rough lower and upper approximations are used in defining object and background models. During deep learning, instead of scanning the entire image pixel by pixel in the convolution layer, we scan only the representative pixel of each granule. This results in a significant gain in computation time. Arbitrary-shaped and sized granules, as expected, perform better than regular-shaped rectangular granules or fixed-sized granules. The method of tracking is able to deal efficiently with various challenging cases, e.g., tracking partially overlapped objects and suddenly appeared objects. Overall, the granulated system shows a balanced trade-off between speed and accuracy as compared to pixel level learning in tracking and recognition. The concept of using Z-numbers, in providing a granulated linguistic description of a scene, is unique. This gives a more natural interpretation of object recognition in terms of certainty toward scene understanding.

Measures of uncertainty for a distributed fully fuzzy information system

ABSTRACTAs an important model in the field of artificial intelligence, an information system is a database that stands for relationships between objects and attributes. A distributed fully fuzzy information system is an information system with distributed fully fuzzy data. This paper investigates measures of uncertainty for a distributed fully fuzzy information system. The fuzzy -equivalence relation, induced by a fully fuzzy information system by using Gaussian kernel method, is first obtained. Then, fuzzy information structures in a distributed fully fuzzy information system is introduced. Next, Dependency between fuzzy information structures is depicted from three aspects, information distance for calculating the difference between fuzzy information structures is proposed in the same distributed fully fuzzy information system. Moreover, properties of fuzzy information structures in a distributed fully fuzzy information system are given by means of the inclusion degree. Finally, granulation measure and entropy measure of a given distributed fully fuzzy information system is proposed by means of its fuzzy information structures. These results will be very helpful for establishing a framework of granular computing and understanding the essence of uncertainty in distributed fully fuzzy information systems.

Intuitionistic Fuzzy Rough Set-Based Granular Structures and Attribute Subset Selection

Attribute subset selection is an important issue in data mining and information processing. However, most automatic methodologies consider only the relevance factor between samples while ignoring the diversity factor. This may not allow the utilization value of hidden information to be exploited. For this reason, we propose a hybrid model named intuitionistic fuzzy (IF) rough set to overcome this limitation. The model combines the technical advantages of rough set and IF set and can effectively consider the above-mentioned statistical factors. First, fuzzy information granules based on IF relations are defined and used to characterize the hierarchical structures of the lower and upper approximations of IF rough set within the framework of granular computing. Then, the computation of IF rough approximations and knowledge reduction in IF information systems are investigated. Third, based on the approximations of IF rough set, significance measures are developed to evaluate the approximation quality and classification ability of IF relations. Furthermore, a forward heuristic algorithm for finding one optimal reduct of IF information systems is developed using these measures. Finally, numerical experiments are conducted on public datasets to examine the effectiveness and efficiency of the proposed algorithm in terms of the number of selected attributes, computational time, and classification accuracy.

Group Decision Making Based on a Framework of Granular Computing for Multi-Criteria and Linguistic Contexts

The usage of linguistic information involves computing with words, a methodology assuming linguistic values as computational elements, in group decision-making environments. In recent times, a new methodology founded on a framework of granular computing has been employed to manage linguistic information. An advantage of this methodology is that the distribution and the semantics of the linguistic values, in place of being initially established, are defined by the optimization of a certain criterion. In this paper, different from the existing approaches, we present a novel approach build on the basis of a granular computing framework that is able to cope with group decision-making problems defined in multi-criteria contexts, that is, those in which different criteria are considered to evaluate the possible alternatives for solving the problem. In particular, it models group decision-making problems in a more realistic way by taking into account that each criterion has an importance weight and by considering that each decision maker has a different importance weight for each criterion. This approach makes operational the linguistic values by associating them with intervals via the optimization of an optimization criterion composed of two important aspects that must be taken into account in this kind of decision problems, that is, the consensus at the level of group of decision makers and the consistency at the level of individual decision makers.

Information Structures and Uncertainty Measures in an Incomplete Probabilistic Set-Valued Information System

An information system is a database that represents relationships between objects and attributes. A set-valued information system is the generalized model of a single-valued information system. A set-value information system that contains probability distributions and missing values is called an incomplete probability set-value information system (IPSIS). Uncertainty measure is an effective tool for evaluation. This paper explores information structures and uncertainty measures in an IPSIS. According to the Bhattacharyya distance, the distance between two objects in a given subsystem of an IPSIS is first proposed. Then, the tolerance relation on an object set, induced by a probability set-valued information system by using this distance, is obtained. Next, the information structure of this subsystem is introduced by a set vector. Moreover, the dependence between two information structures is studied by using the inclusion degree. Finally, as an application for information structures, measures of uncertainty for an IPSIS are investigated, and to evaluate the performance of the proposed measures, effectiveness analysis is given from the angle of statistics. These results will be helpful for establishing a framework of granular computing and understanding the essence of uncertainty in an IPSIS.

Relationships between knowledge bases and their uncertainty measures

A knowledge base is a basic concept in rough set theory. Uncertainty measures are critical evaluation tools in machine learning fields. This article investigates relationships between knowledge bases and their uncertainty measures. Firstly, dependence and independence between knowledge bases are proposed, and are characterized by the inclusion degree. Secondly, knowledge distance between knowledge bases is studied. Thirdly, invariant and inverse invariant characteristics of knowledge bases under homomorphisms based on data compression are obtained. Fourthly, measuring uncertainty of knowledge bases is investigated, and an example is provided to illustrate the fact that knowledge granulation, rough entropy, knowledge entropy, and knowledge distance are neither invariant nor inverse invariant under homomorphisms based on data compression. Finally, a numerical experiment is provided to show features of the proposed measures for uncertainty of knowledge bases, and effectiveness analysis is conducted from the two aspects of dispersion and correlation. These results will be helpful for the establishment of a framework of granular computing in knowledge bases.

Computing with words for student strategy evaluation in an examination

In the framework of Granular Computing (GC), Interval type 2 Fuzzy Sets (IT2 FSs) play a prominent role by facilitating a better representation of uncertain linguistic information. Perceptual Computing (Per C), a well known computing with words (CWW) approach, and its various applications have nicely exploited this advantage. This paper reports a novel Per C based approach for student strategy evaluation. Examinations are generally oriented to test the subject knowledge of students. The number of questions that they are able to solve accurately judges success rates of students in the examinations. However, we feel that not only the solutions of questions, but also the strategy adopted for finding those solutions are equally important. More marks should be awarded to a student, who solves a question with a better strategy compared to a student, whose strategy is relatively not that good. Furthermore, the students strategy can be taken as a measure of his or her learning outcome as perceived by a faculty member. This can help to identify students, whose learning outcomes are not good, and, thus, can be provided with any relevant help, for improvement. The main contribution of this paper is to illustrate the use of CWW for student strategy evaluation and present a comparison of the recommendations generated by different CWW approaches. CWW provides us with two major advantages. First, it generates a numeric score for the overall evaluation of strategy adopted by a student in the examination. This enables comparison and ranking of the students based on their performances. Second, a linguistic evaluation describing the student strategy is also obtained from the system. Both these numeric score and linguistic recommendation are together used to assess the quality of a students strategy. We found that Per-C generates unique recommendations in all cases and outperforms other CWW approaches.

Knowledge structures in a tolerance knowledge base and their uncertainty measures

Rough set theory is a useful tool for dealing with imprecise knowledge. Its important notion is a knowledge base. In a knowledge base, one can approximately describe the target notion in terms of existing knowledge structures. A tolerance knowledge base is the generalization of knowledge bases. This paper investigates knowledge structures in a tolerance knowledge base and their uncertainty measures. Knowledge structures in a tolerance knowledge base are first depicted by means of set vectors. Then, dependence and independence between knowledge structures are described by using inclusion degree. Next, mapping and lattice characterizations of knowledge structures are given. Finally, measuring uncertainty of knowledge structures in a tolerance knowledge base is studied, two numerical experiments on the congressional voting records data set that comes from UCI Repository of machine learning databases are conducted, and based on these numerical experiments, effectiveness analysis from the angle of statistics is given to evaluate the performance of the proposed measures. These results will be helpful for establishing a framework of granular computing in knowledge bases.

Information structures in a lattice-valued information system

An information system as a database that represents relationships between objects and attributes is an important mathematical model in the field of artificial intelligence. A lattice-valued information system is the generalization of an information system. Its information structures are mathematical structures of the families of information granules granulated from its data sets. This paper explores information structures in a lattice-valued information system. The concept of information structures in a lattice-valued information system is first introduced by set vectors. Then, dependence, partial dependence, and independence between two information structures are proposed. Next, information distance between two information structures is studied. Moreover, properties of information structures are given. Finally, group, lattice, and mapping characterizations of information structures are obtained. These results will be helpful for building a framework of granular computing in lattice-valued information systems.

Granular Computing Models and Methods Based on the Spatial Granulation

Automatic data processing and extraction of rules from large datasets has gained considerable interest during the last years. Several approaches have been proposed, mainly based both statistical and fuzzy sets approaches. In this paper, we propose a new view to the approaches to represent the large datasets and to find rules in one. That makes use of so-called Information Granulation and Computing with Words methods. The basic Ideas and principles of Granular Computing have been studied explicitly or implicitly in many fields in isolation. With the recently renewed and fast growing interest, it is time to extract the commonality from a diversity of fields and to study systematically and formally the domain independent principles of Granular Computing in a unified model. A framework of granular computing can be improved by applying the inherited principles of Space Granulation and Computing with Shapes. In this paper, we examine a framework from new perspectives of granular computing, based on Space Granulation and Computing with Shapes for the granulated data processing and problem solving.

An overview on the roles of fuzzy set techniques in big data processing: Trends, challenges and opportunities

In the era of big data, we are facing with an immense volume and high velocity of data with complex structures. Data can be produced by online and offline transactions, social networks, sensors and through our daily life activities. A proper processing of big data can result in informative, intelligent and relevant decision making completed in various areas, such as medical and healthcare, business, management and government. To handle big data more efficiently, new research paradigm has been engaged but the ways of thinking about big data call for further long-term innovative pursuits. Fuzzy sets have been employed for big data processing due to their abilities to represent and quantify aspects of uncertainty. Several innovative approaches within the framework of Granular Computing have been proposed. To summarize the current contributions and present an outlook of further developments, this overview addresses three aspects: (1) We review the recent studies from two distinct views. The first point of view focuses on what types of fuzzy set techniques have been adopted. It identifies clear trends as to the usage of fuzzy sets in big data processing. Another viewpoint focuses on the explanation of the benefits of fuzzy sets in big data problems. We analyze when and why fuzzy sets work in these problems. (2) We present a critical review of the existing problems and discuss the current challenges of big data, which could be potentially and partially solved in the framework of fuzzy sets. (3) Based on some principles, we infer the possible trends of using fuzzy sets in big data processing. We stress that some more sophisticated augmentations of fuzzy sets and their integrations with other tools could offer a novel promising processing environment.

Properties of a Granular Computing Framework for Mining Relational Data

This work investigates properties of a framework for mining relational data. The framework is constructed based on granular computing theory and is equipped with a method for deriving information granules from relational data. Such granules are the basis for discovering knowledge of a different type. It is shown in the paper that thanks to the properties one can improve the performance of tasks such as relational objects representation, search space limitation, and relational patterns generation.