Study of fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) was proposed and analyzed. Unlike fuzzy set, IFSs contain uncertainty named hesitance, which is contained in fuzzy membership function ...Study of fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) was proposed and analyzed. Unlike fuzzy set, IFSs contain uncertainty named hesitance, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of many entropy definitions. By considering different fuzzy entropy definitions, fuzzy entropy on IFSs is designed and discussed. Similarity measure was also presented and its usefulness was verified to evaluate degree of similarity.展开更多
Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric(p. q. metric) p: L^x xL^x -[0,∞] where L is acompletely distributive latt...Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric(p. q. metric) p: L^x xL^x -[0,∞] where L is acompletely distributive lattice, and the associated family of neighborhood mappings {Dr |r>O}. Thefuzzy metric space in Erceg's sense is denoted by (L^x, p, Dr) since there exists a one to one correspondence between fuzzy p. q. metrics and associatcd families of neighborhood mapping, a family{Dr|r>0}satisfying certain conditions is also callcd a (standard) fuzzy p. q metric. In [2] Liang defimed apointwise fuzzy p. q. metric d: P(L^x)×P(L^x)-[0, ∞) and applicd it to the construction of theproduct fuzzy metric. In this paper, we give axiomatic definitions of molcculewise and展开更多
基金Project(ER120001) supported by Development of Application Technology BioNano Super Composites, Korea
文摘Study of fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) was proposed and analyzed. Unlike fuzzy set, IFSs contain uncertainty named hesitance, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of many entropy definitions. By considering different fuzzy entropy definitions, fuzzy entropy on IFSs is designed and discussed. Similarity measure was also presented and its usefulness was verified to evaluate degree of similarity.
文摘Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric(p. q. metric) p: L^x xL^x -[0,∞] where L is acompletely distributive lattice, and the associated family of neighborhood mappings {Dr |r>O}. Thefuzzy metric space in Erceg's sense is denoted by (L^x, p, Dr) since there exists a one to one correspondence between fuzzy p. q. metrics and associatcd families of neighborhood mapping, a family{Dr|r>0}satisfying certain conditions is also callcd a (standard) fuzzy p. q metric. In [2] Liang defimed apointwise fuzzy p. q. metric d: P(L^x)×P(L^x)-[0, ∞) and applicd it to the construction of theproduct fuzzy metric. In this paper, we give axiomatic definitions of molcculewise and
