TY - JOUR
T1 - A note on generalized convexity for fuzzy mappings through a linear ordering
AU - Chalco-Cano, Y.
AU - Rufián-Lizana, A.
AU - Román-Flores, H.
AU - Osuna-Gómez, R.
PY - 2013/11/16
Y1 - 2013/11/16
N2 - In this paper, we study generalized convexity for fuzzy mappings that are defined through a linear ordering on the space of fuzzy intervals. On top of the concepts of convexity, preinvexity and prequasiinvexity, which have been introduced previously by other authors, we now introduce the concept of invex fuzzy mappings. For this purpose, we first consider the notion of strongly generalized differentiability for fuzzy mappings and we establish new properties thereof. Then, we introduce the ith strongly generalized partial derivative of a fuzzy function. After that, we present new characterizations for convex and invex fuzzy mappings. Finally, we study local-global minimum properties for convex and invex fuzzy mappings.
AB - In this paper, we study generalized convexity for fuzzy mappings that are defined through a linear ordering on the space of fuzzy intervals. On top of the concepts of convexity, preinvexity and prequasiinvexity, which have been introduced previously by other authors, we now introduce the concept of invex fuzzy mappings. For this purpose, we first consider the notion of strongly generalized differentiability for fuzzy mappings and we establish new properties thereof. Then, we introduce the ith strongly generalized partial derivative of a fuzzy function. After that, we present new characterizations for convex and invex fuzzy mappings. Finally, we study local-global minimum properties for convex and invex fuzzy mappings.
KW - Differentiable fuzzy mappings
KW - Fuzzy generalized convexity
KW - Fuzzy optimization
UR - https://www.scopus.com/pages/publications/84885666779
U2 - 10.1016/j.fss.2013.07.001
DO - 10.1016/j.fss.2013.07.001
M3 - Article
AN - SCOPUS:84885666779
SN - 0165-0114
VL - 231
SP - 70
EP - 83
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
ER -