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On Ranking of Continuous Z‐Numbers with Generalized Centroids and Optimization Problems Based on Z ‐Numbers
Author(s) -
Qiu Dong,
Xing Yumei,
Dong Rongwen
Publication year - 2018
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21928
Subject(s) - centroid , convexity , mathematics , rank (graph theory) , ranking (information retrieval) , function (biology) , combinatorics , order (exchange) , mathematical optimization , continuous function (set theory) , optimization problem , discrete mathematics , computer science , artificial intelligence , geometry , finance , evolutionary biology , financial economics , economics , biology
In this paper, we introduce the addition and g‐difference of continuous Z ‐numbers at first. Then, we define a new partial order to rank the Z ‐numbers with generalized centroids. The g‐derivative of Z ‐number function based on g‐difference is proposed. It is well known that convexity plays a vital role in optimization problems; consequently, we present the convexity of Z ‐number function. Furthermore, we provide the optimality conditions for optimization problems based on Z ‐numbers. Finally, the validity of the discussion is illustrated by an example.