Abstract
AbstractIn this study, we offer a general view at the area of fuzzy modeling and elaborate on a new direction of system modeling by introducing a concept of granular models. Those models constitute a generalization of existing fuzzy models and, in contrast to existing models, generate results in the form of information granules (such as intervals, fuzzy sets, rough sets and others). We present a rationale and some key motivating arguments behind the emergence of granular models and discuss their underlying design process. Central to the development of granular models are granular spaces, namely a granular space of parameters of the models and a granular input space. The development of the granular model is completed through an optimal allocation of information granularity, which optimizes criteria of coverage and specificity of granular information. The emergence of granular models of type-2 and type-n, in general, is discussed along with an elaboration on their formation. It is shown that achieving a sou...
Highlights
Fuzzy models and fuzzy modeling are one of the most visible applied manifestations of fuzzy sets
While there are a number of ways to define fuzzy models and the environment of fuzzy modeling, in general, the following somewhat generic definition could be offered
Fuzzy models can be regarded as models whose architecture dwells upon the constructs of fuzzy sets, their functioning adheres to the fundamental ways of processing of fuzzy sets and their development is supported by the design methodology pertinent to fuzzy sets
Summary
Fuzzy models and fuzzy modeling are one of the most visible applied manifestations of fuzzy sets. At the same time fuzzy modeling is impacted by the developments occurring in other areas including optimization. Fuzzy models offered a new way of thinking about system modeling bringing interesting and innovative facets to the area of system modeling. We venture into the future directions of fuzzy models and a way in which further developments can be envisioned. We start by casting the pursuits of fuzzy models, their design agenda in a certain historical context and identifying the key phases of the evolution of the overall area of fuzzy modeling. This helps us visualize the evolution of the area of fuzzy modeling. Understanding of different roles of fuzzy sets, especially in the formation of fuzzy sets either to describe system variables or being used at the structural level of capturing the dependencies among inputs and outputs in a certain relational format, refer to Figure 1
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