Nearness approximation space based on axiomatic fuzzy sets

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

“…During the past decade, AFS theory has been developed forming the following important methodologies: AFS clustering (Liu, Wang, et al, ; Liu & Ren, ; Liu et al, ; Q. Li et al, ; Ren et al, ), AFS classification (Liu et al, ; Liu & Liu, ; Liu & Pedrycz, ; Ren et al, ), AFS rough set (Ebonzo & Liu, ; Liu et al, ; L. Wang, Ren, et al, ; L. Wang, et al, ), AFS formal concept analysis (L. Wang & Liu, ; L. Wang et al, ; L. Wang & Liu, ), and AFS pseudometric topology (Ding et al, ). This section discusses the above important researches of AFS methodology on knowledge discovery and semantic representation, from which we can see that AFS theory has a great potential to formalize human concepts and their semantic logic operations.…”

“…The AFS clustering algorithm is summarized in Algorithm 1 (Liu, Wang, et al, ), which is the basic AFS clustering procedure. Various developments and variants of Algorithm 1 have been reported in the studies of Ding et al (), Ren et al (), Liu and Ren (), Liu et al (), Q. Li et al (), L. Wang, Ren, and Liu (), L. Wang, et al (), and Liu and Pedrycz (). Example is used to illustrate the procedure of AFS clustering algorithm and related developments.…”

“…Choosing different threshold α , the descriptions of the clusters may be different, which is discussed in the studies by Liu et al (), Liu and Pedrycz (), and Ren et al (). In contrast with the above method, the near set on the basis of AFS theory also can be used to obtain the descriptions of clusters (L. Wang, Ren, et al, ; L. Wang, et al, ).…”

“…The connection between AFS fuzzy logic system and Zadeh algebra is established in the work of Kukkurainen (). From data mining and knowledge discovery methodology point of view, AFS theory has been extended for many learning tasks including AFS clustering (Liu, Wang, & Chai, ; Ding, Liu, & Chen, ; Ren, Song, & Liu, ; Liu & Ren, ; Liu, Wang, & Pedrycz, ; Q. Li, Ren, Li, & Liu, ; Y. Wang, Duan, Liu, Wang, & Li, ), AFS classification (Duan et al, ; Liu, Feng, & Pedrycz, ; Liu & Liu, ; Liu & Pedrycz, ; Ren, Liu, & Cao, ), AFS rough set (Liu, Pedrycz, Chai, & Song, ; Ebonzo & Liu, ; L. Wang, Ren, & Liu, ; L. Wang, Liu, & Qiu, ), AFS formal concept analysis (FCA; L. Wang & Liu, ; L. Wang, Liu, & Cao, ; L. Wang & Liu, ), and AFS pseudometric topology (Ding et al, ). During the past decade, we have witnessed a variety of applications of AFS theory in many fields, such as computer vision (Q. Li, Ren, Li, & Liu, ; Ren, Li, Liu, & Li, ; Sarkhel, Das, Saha, & Nasipuri, ; Z. Li, Zhang, Duan, Wang, & Shi, ; Z. Li et al, ), financial data analysis (Liu & Liu, ; W. Wang & Liu, ; Tao, Liu, & Chen, ; Tian, Liu, & Wang, ; Guo, Pedrycz, & Liu, ), business intelligence (Bi, Cai, Liu, & Li, ; Xu, Liu, & Chen, ; Y. Li, Liu, & Chen, , , ; Tao, Chen, Liu, & Wang, ; Ebonzo & Liu, ; Y. Wang, Ma, Lao, & Wang, ; Y. Wang, Ma, Xu, Wang, & Liu, ; Ebonzo, Lu, & Liu, ), and clinical data analysis (Silva, Vieira, & Sousa, ).…”

“…Li, Ren, Li, & Liu, 2016b;, AFS classification (Duan et al, 2018;Liu, Feng, & Pedrycz, 2013;Liu & Pedrycz, 2007;Ren, Liu, & Cao, 2011), AFS rough set (Liu, Pedrycz, Chai, & Song, 2009;Ebonzo & Liu, 2011;L. Wang, Ren, & Liu, 2012;L. Wang, Liu, & Qiu, 2012), AFS formal concept analysis (FCA; L. Wang & Liu, 2008;L.…”