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This paper provides a new generalization of fuzzy finite state machines,\nfuzzy transformation semigroups and their relationship. Consider a cubic\nstructure, we introduce cubic finite state machines, cubic transformation\nsemigroups, cubic successor, cubic exchange properties cubic subsystems,\ncubic submachines, cubic q-twins, cubic retrievable and study fundamental\nproperties of them. We provide relationship between cubic $q$-twins and a\ncubic $q$-related. We provide a characterization of a cubic retrievable. We\ndefine cfsm homomorphism and investigated related properties. We show that\nthe composition of strong cfsm homomorphism is also strong. We also define\ncubic transformation semigroup and it related properties. We define cts\nhomomorphism and its properties.
The concept of Semantic Web has introduced an important form of knowledge representation - ontology. As a hierarchical structure of concepts together with their definitions ontology provides means for expressing semantics of data. The ability to build rules with ontology concepts and to perform reasoning increases its attractiveness even further. This paper proposes a framework for expressing fuzzy temporal information using ontology. The framework is built based on ontology suitable for expressing facts and building rules that include fuzzy and temporal terms. This proposed fuzzy temporal ontology can be imported to any domain ontology and used a knowledge base in variety of applications. The paper includes description of build-in predicates needed for constructing fuzzy temporal rules. Simple examples of application of the predicates are presented.
In time-series forecasting, it is an important task to make an accurate and interpretable long-term prediction. In this article, we present a novel approach developed from the perspective of granular computing (GrC) to realize the long-term prediction of time series. The proposed method first employs a sliding window strategy to smooth on the raw time series. Subsequently, the smoothed time series is transformed into the corresponding granular time series that is depicted by evolving shape with the aid of the clustering algorithm based on the dynamic time warping (DTW) distance. Finally, a Takagi–Sugeno (TS) architecture-like granular model (GrM) is formed by deriving the relations implying in the granular time series and offers the granular output in the numeric vector format. The GrM adopts the pattern-to-pattern inference mechanism to realize the long-term prediction of time series at the vector level. Experiments on several datasets demonstrate that the proposed method not only has the ability to circumvent the cumulative error but also makes the resulting GrM equip better interpretability.