Geodesic
The study on semicopula based implications
Kybernetika, Tome 56 (2020) no. 4, pp. 662-694
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Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula is a special family semicopula and the priori fuzzy implication is a ($U,N$)-implication. Moreover, the case that the semicopula based implication is 2-increasing (directionally decreasing, respectively) is also considered.
Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula is a special family semicopula and the priori fuzzy implication is a ($U,N$)-implication. Moreover, the case that the semicopula based implication is 2-increasing (directionally decreasing, respectively) is also considered.
DOI : 10.14736/kyb-2020-4-0662
Classification : 03B52, 03E72
Keywords: fuzzy implications; semicopula based implications; ($U, N$)-implications; semicopula; 2-increasing 
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Peng, Zuming. The study on semicopula based implications. Kybernetika, Tome 56 (2020) no. 4, pp. 662-694. doi: 10.14736/kyb-2020-4-0662

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