Derived operators on M-fuzzifying convex spaces

Characterizations of $L$-concavities and $L$-convexities via derived relations

“…(4) In abstract convex structures, algebraic property of convex hulls is an essential feature of convex structure which is different from many other mathematic structures such as topological structures, convergence structure and matroid. With the development of fuzzy extensions of convex theory, such property has been accordingly extended by many means [3,12,17,19,24]. Thus it could be worth to discuss presentations of algebraic property in L-convex enclosed relation space, L-convex derived enclosed relation space and L-convex derived hull space.…”

“…In the framework of L-fuzzy setting, Wu et al introduced L-topologies derived internal relations, L-topological derived enclosed relations and L-topological derived neighborhood relations in L-topological spaces [26,27]. Also, in the framework of M -fuzzifying settings, scholars introduced some derived operators in M -fuzzifying convex structures and M -fuzzifying matroids [3,17,29,39]. These derived operators have a common feature which takes an axiom to show the relation between a set and its adherent points.…”

L-concave derived internal relations and L-convex derived enclosed relations

“…(4) Algebraic property of convex hulls is an essential feature of convex structure which is different from other mathematic structures such as topological structures, convergence structure and matroid. With the development of fuzzy extensions of convex theory, such property has been accordingly extended by many means [1,11,17,19,32]. Thus it could be worth to discuss presentations of algebraic property in L-convex enclosed relation space, L-convex derived enclosed relation space and L-convex derived hull space.…”

“…Shi extended this concept into fuzzy setting by which he characterized fuzzy topologies [18]. Also, derived operator has been applied to Mfuzzifying matroid [34,40] and M-fuzzifying convex space [1,17]. In the viewpoint of convex relations, Liao et al introduced L-convex enclosed relations and L-concave internal relations by which they characterize L-convex spaces and L-concave spaces [6,31].…”

L-topological derived neighborhood relations and L-topological derived remotehood relations

“…In addition, they further introduced (L, M)-fuzzy topological-convex enclosed relation and characterized (L, M)-fuzzy topological-convex structure [29]. Chen and Shen introduced M-fuzzifying derived operator by which they characterize M-fuzzifying convex structure [2,17]. Xin and Zhong introduced M-fuzzifying derived operator by which they characterize M-fuzzifying matroid [31,40].…”