Fuzzy Interpolation with Extensional Fuzzy Numbers

The article develops further directions stemming from the arithmetic of extensional fuzzy numbers. It presents the existing knowledge of the relationship between the arithmetic and the proposed orderings of extensional fuzzy numbers—so-called S-orderings—and investigates distinct properties of such orderings. The desirable investigation of the S-orderings of extensional fuzzy numbers is directly used in the concept of S-function—a natural extension of the notion of a function that, in its arguments as well as results, uses extensional fuzzy numbers. One of the immediate subsequent applications is fuzzy interpolation. The article provides readers with the basic fuzzy interpolation method, investigation of its properties and an illustrative experimental example on real data. The goal of the paper is, however, much deeper than presenting a single fuzzy interpolation method. It determines direction to a wide variety of fuzzy interpolation as well as other analytical methods stemming from the concept of S-function and from the arithmetic of extensional fuzzy numbers in general.

A Bidirectional Reasoning Based on Fuzzy Interpolation

In order to deal with both the “curse of dimensionality” and the “sparse rule base” simultaneously, an initial idea of hierarchical bidirectional fuzzy interpolation is presented in this article, combining hierarchical fuzzy systems and forward/backward fuzzy rule interpolation. In particular, backward fuzzy interpolation can be employed to allow interpolation to be carried out when certain antecedents of observation variables are absent, whereas conventional methods do not work. Hierarchical bidirectional fuzzy interpolation is applicable to situations where a multiple multi-antecedent rules system needs to be reconstructed to a multi-layer fuzzy system and any sub-layer rule base is sparse. The implementation of this approach is based on fuzzy rule interpolative reasoning that utilities scale and move transformation. An illustrative example and application scenario are provided to demonstrate the efficacy of this proposed approach.

A Novel Approach With Dynamic Fuzzy Inference for Big Data Classification Problems

Currently, big data and its applications have become emergent topics. To deal with the uncertainty in data sets, fuzzy system-based models were explored and stand out for many applications. However, when a given observation has no overlap with antecedent values, no rule can be invoked, or even the invoked rules with missing values in classical fuzzy inference can also appear in big data environment, and therefore, no consequence can be derived. Fortunately, fuzzy rule interpolation techniques can support inference in such cases. Combining traditional fuzzy reasoning technique and fuzzy interpolation method may promote the accuracy of inference conclusion. Therefore, in this chapter, an initial investigation into the framework of MapReduce with dynamic fuzzy inference/interpolation for big data applications (BigData-DFRI) is reported. The results of an experimental investigation of this method are represented, demonstrating the potential and efficacy of the proposed approach.

A New MapReduce Approach with Dynamic Fuzzy Inference for Big Data Classification Problems

Currently, big data and its applications have become one of the emergent topics. In practice, MapReduce framework and its different extensions are the most popular approaches for big data. Fuzzy system based models stand out for many applications. However, when a given observation has no overlap with antecedent values, no rule can be invoked in classical fuzzy inference can also appear in big data environment, and therefore no consequence can be derived. Fortunately, fuzzy rule interpolation techniques can support inference in such cases. Combining traditional fuzzy reasoning technique and fuzzy interpolation method may promote the accuracy of inference conclusion. Therefore, in this article, an initial investigation into the framework of MapReduce with dynamic fuzzy inference/interpolation for big data applications (BigData-DFRI) is reported. The results of an experimental investigation of this method are represented, demonstrating the potential and efficacy of the proposed approach.