Titlebook: An Introduction to Computing with Fuzzy Sets; Analysis, Design, an Witold Pedrycz Book 2021 The Editor(s) (if applicable) and The Author(s)

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Die Facetten der Software-Krise, condensed view at the data. From this perspective, clustering can be sought as a conceptually sound and algorithmically appealing vehicle to construct fuzzy sets, viz. determine their membership grades (functions). Because the clustering process revolves about available data, we refer to this meth

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Fuzzy Relations and Relational Computing,riables, components, modules, etc. Fuzzy relations generalize the concept of relations in the same manner as fuzzy sets generalize the fundamental idea of sets [., ., .]. Fuzzy relations are highly instrumental in problems of information retrieval, pattern classification, control and decision-making

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Fuzzy Set Transformation and Fuzzy Arithmetic,on principle is discussed in detail. Two key ways of mapping fuzzy sets are discussed: the one based on the representation theorem (which directly links to the mapping realized in interval analysis) and another one based on the use of the extension principle). The detailed formulas are developed for

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Higher Type, Higher Order Fuzzy Sets and Hybrid Fuzzy Sets,rder. In general, when talking about information granules of higher type, say type-2, we mean information granules whose elements are characterized by membership grades, which themselves are information granules (instead of being plain numeric values). For instance, in type-2 fuzzy sets, membership

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Fuzzy Clustering,f the generic tools of data analytics aimed at revealing a structure in data and are regarded as a essential prerequisite for a slew of detailed algorithms (Anderberg in Cluster analysis for applications. Academic Press, New York, 1973 [.]). There are numerous applications of clustering (Bezerra et

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The Principle of Justifiable Granularity, data (data-driven constructs). Both of them, in spite of compelling arguments, exhibit some limitations and weaknesses. The approach discussed here and referred to as a principle of justifiable granularity, can be regarded as the one that exploits the available experimental data while augmenting th