JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (10): 72-81.doi: 10.6040/j.issn.1671-9352.0.2017.631

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Preinvexity of n-dimensional fuzzy number-valued functions

GONG Zeng-tai, GAO Han   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2017-12-11 Online:2018-10-20 Published:2018-10-09

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Abstract: By means of the partial order relation in n-dimensional fuzzy number space, some preinvexity of n-dimensional fuzzy number-valued functions are defined, including preinvexity, weakly preinvexity, strictly preinvexity, weakly strictly preinvexity, prequasiinvexity, weakly prequasiinvexity, strictly prequasiinvexity, weakly strictly prequasiinvexity, and so on. In addition, their interrelation of the preinvexity of n-dimensional fuzzy number-valued functions are discussed, and some examples are given to illustrate the interrelation of the preinvexity.

Key words: invex sets, preinvexity fuzzy number-valued functions, n-dimensional fuzzy number space

CLC Number: 

  • O175.8
[1] NANDA S, KAR K. Convex fuzzy mappings[J]. Fuzzy Sets Systems, 1992, 48(1):129-132.
[2] FURUKAWA N. Convexity and local Lipschitz continuity of fuzzy-valued mappings[J]. Fuzzy Sets Systems, 1998, 93(1):113-119.
[3] SYAU Y R. On convex and concave fuzzy mappings[J]. Fuzzy Sets Systems, 1999, 103(1):163-168.
[4] SYAU Y R. Some properties of convex fuzzy mappings[J]. Journal of Fuzzy Mathematics, 1999, 7(1):151-160.
[5] GOETSCHEL R, VOXMAN JR W. Elementary fuzzy calculus[J]. Fuzzy Sets Systems, 1986, 18(1):31-43.
[6] YANG Xinmin, TEO K L, YANG Xiaoqi. A characterization of convex function[J]. Applied Mathematics Letters, 2000, 13(1):27-30.
[7] YAN Hong, XU Jiuping. A class of convex fuzzy mappings[J]. Fuzzy Sets and Systems, 2002, 129(1):47-56.
[8] ZHANG Cheng, YUAN Xuehai, LEE E S. Convex fuzzy mapping and operations of convex fuzzy mappings[J]. Computers and Mathematics with Applications, 2006, 51(1):143-152.
[9] PANIGRAHI M, PANDA G, NANDA S. Convex fuzzy mapping with differentiability and its application in fuzzy optimization[J]. European Journal of Operational Research, 2008, 185(1):47-62.
[10] LI Jueyou, NOOR M A. On properties of convex fuzzy mappings[J]. Fuzzy Sets and Systems, 2013, 219(2):113-125.
[11] NOOR M A. Fuzzy preinvex functions[J]. Fuzzy Sets and Systems, 1994, 64(1):95-104.
[12] SYAU Y R. Preinvex fuzzy mappings[J]. Computers and Mathematics with Applications, 1999, 37(3):31-39.
[13] GONG Zengtai, HAI Shexiang. Convexity of n-dimensional fuzzy number-valued functions and its applications[J]. Fuzzy Sets and Systems, 2016, 295:19-36.
[14] HAI Shexiang, GONG Zengtai, LI Hongxia. Generalized differentiability for n-dimensional fuzzy number-valued functions and fuzzy optimization[J]. Information Sciences, 2016, 374:151-163.
[15] 吴从炘, 马明. 模糊分析学基础[M]. 北京: 国防工业出版社, 1991. WU Congxin, MA Ming. Fuzzy analytical fundamation[M]. Beijing: Defense Industry Press, 1991.
[16] 杨新民, 戎卫东. 广义凸性及其应用[M]. 北京: 科学出版社, 2015. YANG Xinmin, RONG Weidong. Generalized convexity and application[M]. Beijing: Science Press, 2015.
[17] MOHAN S R, NEOGY S K. On invex sets and preinvex functions[J]. Journal of Mathematical Analysis and Applications, 1995, 189:901-908.
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