In this paper, we study covering-based multigranulation decision-theoretic rough sets in a multi-covering space. From viewpoints of granule, we propose the notions of covering-based mean multigranulation decision-theoretic rough sets, covering-based optimistic multigranulation decision-theoretic ro ugh sets and covering-based pessimistic multigranulation decision-theoretic rough sets, realized, on the basis of Bayesian decision procedure. We first investigate some basic properties of those models. Then, we investigate the relationships between the proposed covering-based multigranulation decision-theoretic rough set models and other related rough set models. Thirdly, we elaborate on the interrelationships among the proposed models. Finally, an example is employed to illustrate the application of the proposed models.
Multi-view learning becomes increasingly attractive and promising because multimodal or multi-view data are commonly encountered in real-world applications. In this study, we develop a novel multi-view Takagi–Sugeno–Kang (TSK) fuzzy system framework to handle classification problems for such data. We propose an anchor and graph subspace clustering strategy to discover and represent the actual latent data distribution for each view separately. In this way, the discriminate anchors (landmarks) are learned to capture the main structure of the multi-view data. This strategy also provides a computationally efficient clustering algorithm with respect to the number of instances. These resulting anchors are formed as the prototypes of information granules (IGs) for fuzzy modeling. Then we construct an information-granule-based multi-view TSK fuzzy classification model inherited from the natural interpretability of fuzzy rule-based systems. Concretely, the relationship between the multi-view input and label output spaces is depicted by IGs-oriented fuzzy rules. The experimental studies involve various commonly used benchmark datasets, which indicate that our proposed method achieves comparable or better performance compared to the state-of-the-art algorithms.
In artificial intelligence systems, a question on how to express the uncertainty in knowledge remains an open issue. The negation scheme provides a new perspective to solve this issue. In this paper, we study quantum decisions from the negation perspective. Specifically, complex evidence theory (CET) is considered to be effective to express and handle uncertain information in a complex plane. Therefore, we first express CET in the quantum framework of Hilbert space. On this basis, a generalized negation method is proposed for quantum basic belief assignment (QBBA), called QBBA negation. In addition, a QBBA entropy is revisited to study the QBBA negation process to reveal the variation tendency of negation iteration. Meanwhile, the properties of the QBBA negation function are analyzed and discussed along with special cases. Then, several multisource quantum information fusion (MSQIF) algorithms are designed to support decision making. Finally, these MSQIF algorithms are applied in pattern classification to demonstrate their effectiveness. This is the first work to design MSQIF algorithms to support quantum decision making from a new perspective of "negation", which provides promising solutions to knowledge representation, uncertainty measure, and fusion of quantum information.
Behavioral decision making is an area of multidisciplinary research attracting growing interest of scientists and practitioners, economists, and business people. A wide spectrum of successful theories is present now, including Prospect theory, multiple priors models, studies on altruism, trust and fairness. However, these theories are developed for precise and complete information, whereas real information concerning a decision maker's (DM) behavior and environment is imperfect, qualitative, and, as a result, often described in natural language (NL). We suggest an approach based on modeling a DM's behavior by a set of states. Each state represents a certain principal behavior. In our approach, states of nature and DM's states constitute a single space of combined states. For formalizing relevant information described in NL, we use fuzzy set theory. The utility model is based on Choquet-like integration over combined states. The investigations show that Expected Utility, Choquet Expected Utility and Cumulative Prospect Theory are special cases of the suggested approach. We apply the suggested approach to solving a benchmark and a real-life decision problem. The obtained results show validity of the suggested approach.
In this study, we augment the highly impressive record of developments of fuzzy models by bringing the ideas of evolvable and knowledge-consistent fuzzy modeling. More often than in the past, we are exposed to highly distributed data reflecting some temporal or spatial variability of the problem. Owing to some non-technical reasons (e.g., data privacy and security) or existing technical constraints, the models built locally cannot take advantage of the data available elsewhere. Instead one could be provided with some more abstract entities such as information granules that are reflective of the knowledge conveyed by some other models which could be effectively shared. The two main categories of design schemes discussed here demonstrate the effect of achieving knowledge consistency which augments the existing paradigm of fuzzy modeling. In the first one, we are concerned with sharing temporal knowledge where the models are formed for temporal data available in successive time slices pertinent to the problem at hand and the available temporal knowledge (captured in terms of the structure and parameters of the models) whose usage incorporates the factor of time. In this sense, the resulting fuzzy models become highly evolvable modeling architectures. The spatial nature of knowledge is associated with fuzzy models which are constructed on a basis of data pertinent to some local regions (such as sections of wireless sensor networks, sales regions, etc.). While the introduced conceptual developments are of substantial level of generality, the study will focus on a family of rule-based fuzzy models to illustrate the ensuing algorithmic aspects of the fundamental concepts.
A heterogeneous neural network consisting of logic neurons and realizing mappings in [0, 1] hypercubes is presented. The two kinds of neurons studied are utilized to perform matching functions (equality or reference neurons) and aggregation operations (aggregation neurons). All computations are driven by logic operations widely used in fuzzy set theory. The network is heterogeneous in its nature and includes two types of neurons organized into a structure detecting individual regions of patterns (using reference neurons) and combining them to yield a final classification decision.
Given a widespread interest in rough sets as being applied to various tasks of data analysis, it is not surprising at all that we have witnessed a wave of further generalizations and algorithmic enhancements of this original concept. In this study, we investigate an idea of rough fuzzy random sets. This construct provides us with a certain generalization of rough sets by introducing the concept of inclusion degree. The underlying objective behind this development is to address the problems which involve co-existing factors of fuzziness and randomness thus giving rise to a notion of the fuzzy random approximation space based on inclusion degree. Some essential properties of rough approximation operators of such rough fuzzy random sets are discussed. Further theoretical foundations for the formation of rules constructed on a basis of available decision tables are offered as well.
This study introduces a new concept of shadowed sets that can be regarded as a certain operational framework simplifying processing carried out with the aid of fuzzy sets and enhancing interpretation of results obtained therein. Some conceptual links between this idea and some others known in the literature are established. In particular, it is demonstrated how fuzzy sets can induce shadowed sets. Subsequently, shadowed sets reveal interesting conceptual and algorithmic relationships existing between rough sets and fuzzy sets. Detailed computational aspects of shadowed sets are discussed. Several illustrative examples are provided.
