Convex fuzzy mapping and operations of convex fuzzy mappings

Authors:
Cheng Zhang;Xue-Hai Yuan;E. Stanley Lee
Affiliations:
College of Information Engineering Dalian University, Dalian 116622, P.R. China;Department of Mathematics Liaoning Normal University, Dalian 116029, P.R. China;Department of Industrial & Manufacturing Systems Engineering Kansas State University, Manhattan, KS 66506, U.S.A.
Venue:
Computers & Mathematics with Applications
Year:
2006

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Abstract

Convex and concave fuzzy mappings are considered in this paper. Based on the seminal work of Nanda and Kar on the definition of convex fuzzy mapping, the operations of convex fuzzy mapping are established. Some of the important concepts such as positively homogeneous, infimal convolution, right scalar multiplication, and convex hull are introduced and the corresponding theorems are demonstrated by using the parametric representation of fuzzy numbers.