Publications

We explore switching techniques between q-fractional fuzzy sets (qFr sets) and various other classes of fuzzy sets to establish connections and provide a comprehensive framework. In particular, we examine the relationships between qFr sets and interval-valued fuzzy sets (IVFS), type 2 fuzzy sets(T2FS), intuitionistic fuzzy sets(IFS), Pythagorean fuzzy sets(PFS), q-rung orthopair fuzzy sets (q-ROFS), and linear diophantine fuzzy sets(LDFS). By examining these interconnections, we aim to understand better qFr sets and their applications in a wide range of fuzzy systems. It is possible to convert qFr sets into other fuzzy set models using the derived switching techniques, facilitating the utilization of existing methods and algorithms. The versatility of qFr sets, combined with the bridging techniques presented, holds promise for addressing complex problems in decision-making, pattern recognition, and other applications where uncertainty and imprecision play significant roles. Through case studies and practical applications, we illustrate the effectiveness and usefulness of the proposed switching techniques, showcasing their potential impact on real-world scenarios.

Efficient and robust data clustering remains a challenging task in data analysis. Recent efforts have explored the integration of granular-ball (GB) computing with clustering algorithms to address this challenge, yielding promising results. However, existing methods for generating GBs often rely on single indicators to measure GB quality and employ threshold-based or greedy strategies, potentially leading to GBs that do not accurately capture the underlying data distribution. To address these limitations, this article leverages the principle of justifiable granularity (POJG) to measure the quality of a GB for clustering tasks and introduces a novel GB generation method, termed GB-POJG. Specifically, a comprehensive metric integrating the coverage and specificity of a GB is introduced to assess GB quality. Utilizing this quality metric, GB-POJG incorporates a strategy of maximizing overall quality and an anomaly detection method to determine the generated GBs and identify abnormal GBs, respectively. Compared to previous GB generation methods, GB-POJG maximizes the overall quality of generated GBs while ensuring alignment with the data distribution, thereby enhancing the rationality of the generated GBs. Experimental results obtained from both synthetic and publicly available datasets underscore the effectiveness of GB-POJG, showcasing improvements in clustering accuracy and normalized mutual information. All codes have been released at https://zenodo.org/records/13643332.

The study introduces a concept of mappings realized in presence of information granules and offers a design framework supporting the formation of such mappings. Information granules are conceptually meaningful entities formed on a basis of a large number of experimental input–output numeric data available for the construction of the model. We develop a conceptually and algorithmically sound way of forming information granules. Considering the directional nature of the mapping to be formed, this directionality aspect needs to be taken into account when developing information granules. The property of directionality implies that while the information granules in the input space could be constructed with a great deal of flexibility, the information granules formed in the output space have to inherently relate to those built in the input space. The input space is granulated by running a clustering algorithm; for illustrative purposes, the focus here is on fuzzy clustering realized with the aid of the fuzzy C-means algorithm. The information granules in the output space are constructed with the aid of the principle of justifiable granularity (being one of the underlying fundamental conceptual pursuits of Granular Computing). The construct exhibits two important features. First, the constructed information granules are formed in the presence of information granules already constructed in the input space (and this realization is reflective of the direction of the mapping from the input to the output space). Second, the principle of justifiable granularity does not confine the realization of information granules to a single formalism such as fuzzy sets but helps form the granules expressed any required formalism of information granulation. The quality of the granular mapping (viz. the mapping realized for the information granules formed in the input and output spaces) is expressed in terms of the coverage criterion (articulating how well the experimental data are “covered” by information granules produced by the granular mapping for any input experimental data). Some parametric studies are reported by quantifying the performance of the granular mapping (expressed in terms of the coverage and specificity criteria) versus the values of a certain parameters utilized in the construction of output information granules through the principle of justifiable granularity. The plots of coverage–specificity dependency help determine a knee point and reach a sound compromise between these two conflicting requirements imposed on the quality of the granular mapping. Furthermore, quantified is the quality of the mapping with regard to the number of information granules (implying a certain granularity of the mapping). A series of experiments is reported as well.

ion as a key to knowledge processing (acquisition, integration, reuse...) Granular Computing: diversity of formal environments Set theory, interval analysis Fuzzy sets Rough sets Probabilistic granules

The paradigm of fuzzy modelling entails development of relationships (dependencies) between the linguistic entities defined for system's variables. The key feature of the fuzzy models pertains to their significant flexibility so they could easily be modified to comply with the principle of incompatibility. Considering the existing panoply of fuzzy models one can easily conclude that most of them are embraced under an umbrella of a single conceptual structure. From a functional point of view this structure is perceived as a combination of the two conceptual interfaces and a single processing block aimed at developing calculus of the linguistic labels. The interfaces produce all the links that are necessary to combine the physical (numerical) level of the real-world system with that of a conceptual character realized within the fuzzy model and articulated at the level of the linguistic entities. The presentation will address the main methodological aspects concerning these functional components with a particular emphasis placed on the associated design principles. The main issues dominating the design of the interfaces pertain to the implemented level of information granularity, optimality of linguistic labels, and linguistic-to-numerical transformations. The processing level of the fuzzy modelling will be considered through the use of fuzzy neural networks. These distributed computing structures are highly heterogeneous as they are constructed with the aid of several distinct types of logic-oriented neurons. The advantages of the fuzzy neural networks such as an implicit scheme of knowledge encapsulation that is carried out there will be discussed in detail.

Summary form only given. Information granules and their computing, which give rise to the framework of Granular Computing, deliver interesting opportunities to endow processing with an important facet of human-centricity. This facet directly implies that the underlying processing supports non-numeric data inherently associated with the variable perception of humans and generates results being seamlessly comprehended by users. Given that systems, which are quite commonly become distributed and hierarchical, managing granular information in hierarchical and distributed architectures is of growing interest, especially when invoking mechanisms of knowledge generation and knowledge sharing. The outstanding feature of human centricity of Granular Computing along with essential fuzzy set-based constructs constitutes the crux of our study. We elaborate on some new directions of knowledge elicitation and quantification realized in the setting of fuzzy sets. With this regard, we concentrate on an idea of knowledge-based clustering, which aims at the seamless realization of the data-expertise design of information granules. It is also emphasized that collaboration and reconciliation of locally available knowledge give rise to the concept of higher type information granules. The other interesting directions enhancing human centricity of computing with fuzzy sets, deals with non-numeric, semi-qualitative characterization of information granules (fuzzy sets) as well as inherent evolving capabilities of associated human-centric systems. We discuss a suite of algorithms facilitating a qualitative assessment of fuzzy sets, formulate a series of associated optimization tasks guided by well-formulated performance indexes, and discuss the underlying essence of the resulting solutions.