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As an important technology in artificial intelligence, Granular Computing has emerged as a new multi-disciplinary paradigm and received much attention in recent years. Information granules forming an abstract and efficient characterization of large volumes of numeric data have been considered as the fundamental constructs of Granular Computing. By generating centroids (prototypes) and partition matrix, fuzzy clustering is a commonly encountered way of information granulation. As a reverse process of granulation, degranulation involves data reconstruction completed on a basis of the granular representatives (decoding information granules into numeric data). Previous studies have shown that there is a relationship between the reconstruction error and the performance of the granulation process. Typically, the lower the degranulation error is, the better performance of granulation process becomes. However, the existing methods of degranulation usually cannot restore the original numeric data, which is one of the important reasons behind the occurrence of the reconstruction error. To enhance the quality of reconstruction (degranulation), in this study, we develop an augmented scheme through modifying the partition matrix. By proposing the augmented scheme, we elaborate on a novel collection of granulation-degranulation mechanisms. In the constructed approach, the prototypes can be expressed as the product of the dataset matrix and the partition matrix. Then, in the degranulation process, the reconstructed numeric data can be decomposed into the product of the partition matrix and the matrix of prototypes. By modifying the partition matrix, the new partition matrix is constructed through a series of matrix operations. We offer a thorough analysis of the developed scheme. The experimental results are in agreement with the underlying conceptual framework. The results obtained on both synthetic and publicly available datasets are reported to show the enhancement of the data reconstruction performance thanks to the proposed method. It is pointed out that by using the proposed approach in some cases the reconstruction errors can be reduced close to zero by using the proposed approach. [ABSTRACT FROM AUTHOR]

In the analytic hierarchy process (AHP), the reciprocal matrix is generated based on the pairwise comparisons completed among all the alternatives or attributes under consideration. To ensure reliability and validity of the decision solution, a certain modification of entries of the matrix is usually needed to improve the consistency of the reciprocal matrix. This study aims to present a consistency improvement method by admitting some level of information granularity in the evaluation process. This gives rise to a granular rather than numeric matrix of pairwise comparisons. First, with a given average level of information granularity, we present an optimal granularity model that is characterized by maximal consistency. One can maximize the consistency degree by invoking a process of allocation of information granularity across the corresponding modifications of the reciprocal matrix. Based on the optimal granularity model, an interactive consistency improvement process is presented with the involvement of the decision maker. Then, an adaptive differential evolution algorithm is applied to optimize entries of the modified reciprocal matrix. Detailed experiments along with a thorough comparative analysis are completed to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Rule-based fuzzy models play a dominant role in fuzzy modeling and come with extensive applications in the system modeling area. Due to the presence of system modeling error, it is impossible to construct a model that fits exactly the experimental evidence and, at the same time, exhibits high generalization capabilities. To alleviate these problems, in this study, we elaborate on a realization of granular outputs for rule-based fuzzy models with the aim of effectively quantifying the associated modeling errors. Through analyzing the characteristics of modeling errors, an error model is constructed to characterize deviations among the estimated outputs and the expected ones. The resulting granular model comes into play as an aggregation of the regression model and the error model. Information granularity plays a central role in the construction of granular outputs (intervals). The quality of the produced interval estimates is quantified in terms of the coverage and specificity criteria. The optimal allocation of information granularity is determined through a combined index involving these two criteria pertinent to the evaluation of interval outputs. A series of experimental studies is provided to demonstrate the effectiveness of the proposed approach and show its superiority over the traditional statistical-based method. [ABSTRACT FROM AUTHOR]

The analytic hierarchy process (AHP) is widely employed to guide the decision-maker to rank or evaluate the alternatives in decision activities. Its fuzzy set-based version, i.e., the fuzzy AHP, has also been widely studied and applied since its inception. The essential distinction between the AHP and fuzzy AHP comes from the diverse transformation methods between the linguistic and numeric judgments. In this article, we conduct a thorough comparative study between the AHP and fuzzy AHP methods in the framework of two linguistic models, i.e., the linguistic model based on the membership functions and two-tuple linguistic model. First, four AHP and three fuzzy AHP methods are revisited with the involvement of two linguistic models. Then, the comparison criteria are involved by calculating the cardinal or ordinal deviation between the original information and decision solutions, and the effects of the transitivity of the reciprocal matrix are also discussed in the comparative study. Finally, the detailed experiments along with a thorough comparative analysis are conducted based on the random and publicly available data to show the difference between the AHP and fuzzy AHP methods. [ABSTRACT FROM AUTHOR]

In the real world, phenomena are often observed and recorded by multiple organizations which results in multiple sources of data. When dealing with such data, the centralized modeling approach aims to achieve collaborative modeling by fusing multiple sources of data into a single data set, which may pose challenges to data privacy. Unlike centralized modeling, the distributed modeling approach can effectively solve the privacy issue. However, modeling approaches based on this idea still suffer from either low prediction accuracy or high communication costs. In this study, we propose a collaborative modeling strategy for multi-source data based on fuzzy rule-based models (FRBMs) to balance the needs of both model prediction accuracy and efficiency. First , we adopt the concept and algorithm of collaborative fuzzy clustering (CFC) to improve prediction accuracy and reduce communication costs by improving the CFC algorithm. Then , we construct a granular FRBM for multi-source data based on the principle of justifiable granularity (PJG) by integrating local models into a more robust and perfect global model. Finally , we improve the performance evaluation index of the existing granular FRBM and propose two model optimization schemes to further improve the performance of the model. We conduct experiments on both synthetic and publicly available data sets to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Forest fires are an abrupt and highly destructive meteorological disaster that can occur in all regions of the world, resulting in significant ecological, economic and social losses. Moreover, the causes of forest fire disasters are usually complex, involving several uncertain factors such as temperature, relative humidity, wind speed and rainfall. All of those pose the greatest challenge to the study of forest fire management (FRM). In order to efficiently explore FRM via valid intelligent decision-making techniques, a novel model of regret theory (RT)-based multi-granularity (MG) three-way decisions (TWD) in incomplete T-spherical fuzzy (T-SF) environments has been constructed, where incomplete T-spherical fuzzy sets (T-SFSs) have been employed to describe diverse types of uncertain information in FRM, and RT-based MG TWD is conducive to analyzing multi-source T-SF information via reducing decision risks and modeling bounded rationality owned by decision-makers (DMs). Specifically, the concept of MG T-SF incomplete information systems (IISs) has been first constructed for information depictions of FRM. Then, MG T-SF IISs have been processed via the presented T-SF similarity principles for developing adjustable MG T-SF probabilistic rough sets (PRSs). Afterwards, an RT-based MG TWD approach has been built with the support of adjustable MG T-SF PRSs. Finally, a real-world FRM case analysis has been performed by using the built RT-based MG TWD approach, and extensive comparative and experimental analyses have been performed to validate the practicability of the presented methodology. To sum up, the presented methodology has simultaneously incorporated MG T-SF IISs, MG TWD and RT to model various uncertainties, valid information fusion processes and bounded rationality for FRM, which serves as a valid intelligent decision-making technique in processing incomplete and imprecise multi-source information with plentiful decision risks and regret emotions. • Multi-granularity T-spherical fuzzy incomplete information systems are built. • An adjustable multi-granularity T-spherical fuzzy probabilistic model is presented. • A completion method for T-spherical fuzzy incomplete information is proposed. • The validity and superiority of the regret-theory-based TWD method are verified. [ABSTRACT FROM AUTHOR]

Fuzzy rule-based models have been widely used due to their interpretability and effectiveness. However, they still encounter challenges when dealing with multivariable and large-scale data. In this study, we first propose a novel approach to establish a selective sampling and mapping data reduction method. The method focuses on reducing data variables while decreasing the number of samples, and an appropriate scaling size can be chosen for different situations. Then, a multivariable data-driven fuzzy rule-based model is developed based on the processed data. Moreover, the data projection approach using the distance metric helps to preserve the structural characteristics of the original data. The results are visually presented to facilitate an interpretable description of the subsequent rule-based modeling. Furthermore, due to the inevitable inaccuracy in the projection process of numeric modeling, we introduce the allocation of information granularity to extend the model to a granular form at a more abstract level. Experimental studies on both synthetic and publicly available datasets demonstrate that the proposed method has superior effectiveness and efficiency compared to the existing state-of-the-art regression algorithms. • We propose a novel selective sampling and mapping data reduction (SSMDR) method to exploit the data structure relationship. • We exploit the advantages of the SSMDR method to handle multivariable data-driven fuzzy modeling problems. • We extend the numerical fuzzy rule-based model to a higher-level granular model that can handle potential information loss. • We develop a comprehensive visual interpretable framework to achieve interpretable analysis in terms of three aspects: visualization structure, interpretable reasoning process, and granular structure. [ABSTRACT FROM AUTHOR]

In the elicitation of decision makers' fuzzy and uncertain assessments, linguistic terms are natural and efficient as the preference modeling tools. Although the linguistic variables are available, they would not be operational without any detailed quantification. Motivated by the flexibility of information granularity, this paper develops information granules to represent linguistic terms in the form of intervals and interval type-2 fuzzy sets (IT2FSs) in best worst method (BWM). The development is aimed at minimizing inconsistency in the decision making (DM) process to ensure the rationality of the assessments provided by decision makers. Furthermore, the input and output based consistencies of BWM are considered. The granulation of entries of pairwise comparison vectors are the foundation of BWM to formulate an optimization problem where particle swarm optimization (PSO) algorithm serves as the optimization framework. Both individual and group decision making (GDM) scenarios are taken into consideration. For the GDM process, a performance index for measuring the group consensus is also proposed. Several examples and validity analysis are covered to illustrate the major ideas of this study. Finally, as a case study, a recommendation of the sequence of visiting tourist attractions in Wuhan and the corresponding comparative analysis are represented. • A granular computing-based method in BWM framework is proposed. • Construction of granular linguistic information to represent preference information of DMs is given. • A novel Euclidean distance function to measure the agreement among the group is proposed. • A case study of scenic spots recommendation in Wuhan with online reviews is exhibited. [ABSTRACT FROM AUTHOR]