Fuzzy clustering with semantic interpretation

Liu, Xiaodong; Wang, Xianchang; Pedrycz, Witold

doi:10.1016/j.asoc.2014.09.037

Cited by 20 publications

(22 citation statements)

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“…It provides an effective tool to convert the information in observed data into the membership functions and logic operations of fuzzy concepts. The recent research literature on AFS studies and their applications [14][15][16][17]21,22,33,42] reveals that it has become a flexible and powerful framework for representing human knowledge and studying intelligent systems in real-world applications. The AFS theory is based on the AFS algebra-a kind of semantic methodology of fuzzy concepts, and AFS structure-a kind of mathematical description of data structures.…”

Section: Axiomatic Fuzzy Set (Afs) Theorymentioning

confidence: 99%

A hybrid decision support model using axiomatic fuzzy set theory in AHP and TOPSIS for multicriteria route selection

Singh

2018

Complex Intell. Syst.

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This paper presents a hybrid decision support model aimed to help the travelers in selecting best route among multiple alternatives. The proposed model consists of three parts: (i) analytic hierarchy process (AHP) to determine relative importance of route attributes, (ii) axiomatic fuzzy set (AFS) theory for description of alternative routes, and (iii) technique for order preference by similarity to ideal solution (TOPSIS)-based final selection. TOPSIS methodology is used to determine ranking order of alternative routes in multicriteria decision situations. In TOPSIS, the alternative routes are described using AFS theory to normalize the decision matrix for consistent rating of routes over attributes. The main advantage of the developed model is that it copes inconsistency caused by both, different types of fuzzy numbers and normalization methods. An illustrative example of route selection is presented to better understand the hybrid methodological process. A comparative analysis with an established multicriteria decision-making technique shows the effectiveness and validity of the hybrid model for route selection.

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Section: Axiomatic Fuzzy Set (Afs) Theorymentioning

confidence: 99%

A hybrid decision support model using axiomatic fuzzy set theory in AHP and TOPSIS for multicriteria route selection

Singh

2018

Complex Intell. Syst.

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“…Step 1: Select simple concept set A x M, for each sample x. (Variants; Liu & Ren, 2010;Liu et al, 2015;).…”

Section: Afs Clusteringmentioning

confidence: 99%

Knowledge discovery and semantic learning in the framework of axiomatic fuzzy set theory

Liu

Jia

Wang

et al. 2018

WIREs Data Min & Knowl

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Axiomatic fuzzy set (AFS) theory facilitates a way on how to transform data into fuzzy sets (membership functions) and implement their fuzzy logic operations, which provides a flexible and powerful tool for representing human knowledge and emulate human recognition process. In recent years, AFS theory has received increasing interest. In this survey, we report the current developments of theoretical research and practical advances in the AFS theory. We first review some notion and foundations of the theory with an illustrative example, then, we focus on the various extensions of AFS theory for knowledge discovery, including clustering, classification, rough sets, formal concept analysis, and other learning tasks. Due to its unique characteristics of semantic representation, AFS theory has been applied in multiple domains, such as business intelligence, computer vision, financial analysis, and clinical data analysis. This survey provides a comprehensive view of these advances in AFS theory and its potential perspectives. This article is categorized under: Technologies > Computational Intelligence

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“…AFS theory based clustering has been attempted in [24][25][26]. Instead of using the popular Euclidean metric, AFS clustering approaches capture the underlying data structure through fuzzy membership function, and the distances between samples are represented by membership degree.…”

Section: Related Workmentioning

confidence: 99%

“…Therefore, a re-clustering process is needed for the original AFS clustering [26] (e.g., to pick up samples which are not clustered in the previous clustering process). The above processes are nontrivial and time-consuming.…”

Section: Related Workmentioning

confidence: 99%

“…The proposed method AFSSC method and the widely used NJW spectral clustering (SC) [12], self-tuning spectral clustering (STSC) [13], and AFS clustering (AFS) [26] methods are applied on the same data sets from UCI, USPS handwritten digits, as well as CMU-PIE and Yale face image sets. In the experiment, for SC, the value of s is obtained by searching and the one which gives the best result is picked, as suggested in [12].…”

Section: Experimental Settingsmentioning

confidence: 99%

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