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Title Generalized convexities related to aggregation operators of fuzzy sets Author info Susana Díaz ... [et al.] Author Díaz Susana (5%)
Co-authors Induráin Esteban (5%)
Janiš Vladimír 1963- (80%) UMBFP10 - Katedra matematiky
Llinares Juan Vicente (5%)
Montes Susana (5%)
Source document Kybernetika. Roč. 53, č. 3 (2017), s. 383-393. - Praha : Akademie věd České republiky, 2017 Keywords fuzzy množiny - fuzzy sets konvexnosť - convexity aggregation functions Language English Country Czech Republic systematics 51 Annotation We analyze the existence of fuzzy sets of a universe that are convex with respect to cer- tain particular classes of fusion operators that merge two fuzzy sets. In addition, we study aggregation operators that preserve various classes of generalized convexity on fuzzy sets. We focus our study on fuzzy subsets of the real line, so that given a mapping F : [0, 1] × [0,1] → [0,1], a fuzzy subset, say X, of the real line is said to be F-convex if for any x,y,z ∈ R such that x ≤ y ≤ z, it holds that μX(y) ≥ F(μX(x),μX(z)), where μX : R → [0,1] stands here for the membership function that defines the fuzzy set X. We study the existence of such sets paying attention to different classes of aggregation operators (that is, the corresponding functions F , as above), and preserving F -convexity under aggregation of fuzzy sets. Among those typical classes, triangular norms T will be analyzed, giving rise to the concept of norm convexity or T-convexity, as a particular case of F-convexity. Other different kinds of generalized convexities will also be discussed as a by-product Public work category ADC No. of Archival Copy 40454 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Title Aggregation of convex intuitionistic fuzzy sets Author info Suzana Diaz ... [et al.] Author Diaz Suzana (10%)
Co-authors Induráin Esteban (10%)
Janiš Vladimír 1963- (70%) UMBFP10 - Katedra matematiky
Montes Susana (10%)
Source document Information sciences. Vol. 308, (2015), pp. 61-71. - New York : Elsevier Science Ltd., 2015 Keywords fuzzy množiny - fuzzy sets intuitionistic fuzzy sets konvexnosť - convexity aggregation functions Language English Country United States of America systematics 51 Annotation Aggregation of intuitionistic fuzzy sets is studied from the point of view of preserving vari- ous kinds of convexity. We focus on aggregation functions for intuitionistic fuzzy sets. These functions correspond to simultaneous separate aggregations of the membership as well as of the nonmembership indicators. It is performed by means of the so-called repre- sentable functions. Sufficient and necessary conditions are analyzed in order to guarantee that the composition of two intuitionistic fuzzy sets preserves convexity Public work category ADC No. of Archival Copy 33029 Repercussion category WU, Xiu-Yun - BAI, Shi-Zhong. On M-fuzzifying JHC convex structures and M-fuzzifying Peano interval spaces. In Journal of intelligent & fuzzy systems. ISSN 1064-1246, 2016, vol. 30, no. 4, pp. 2447-2458.
SONG, Yafei - WANG, Xiaodan - WU, Wenhua - LEI, Lei - QUAN, Wen. Uncertainty measure for Atanassov’s intuitionistic fuzzy sets. In Applied intelligence. ISSN 0924-669X, 2017, vol. 46, no. 4, pp. 757-774.
WU, Xiu Yun - LI, Er Qiang - BAI, Shi Zhong. Geometric properties of M-fuzzifying convex structures. In Journal of intelligent and fuzzy systems. ISSN 1064-1246, 2017, vol. 32, no. 6, pp. 4273-4284.
RASHID, Tabasam - BEG, Ismat. Convex hesitant fuzzy sets. In Journal of intelligent and fuzzy systems. ISSN 1064-1246, 2016, vol. 30, no. 5, pp. 2791-2796.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika unrecognised