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

Previous Articles     Next Articles

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

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.
[1] WANG Su-yun, LI Yong-jun. Solvability of nonlinear second-order boundary value problems with nonlinearities which cross the resonance points [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 53-56.
[2] . Existence of positive solutions for a class of nonlinear second-order Dirichlet problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 64-69.
[3] YE Fu-mei. Existence results of a resonance problem with derivative terms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 25-31.
[4] ZHANG Shen-gui. Multiple solutions of Navier boundary value problem for fourth-order elliptic equation with variable exponents [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 32-37.
[5] ZHANG Di, LIU Wen-bin. Existence of solutions for p(t)-Laplacian fractional infinite-point boundary value problems at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 72-80.
[6] . Periodic solutions for second order singular damped differential equations with a weak singularity [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 84-88.
[7] YAN Dong-liang. Positive solutions of a second order periodic problems with derivative terms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(9): 69-75.
[8] GONG Zeng-tai, KOU Xu-yang. Representation of Choquet integral of the set-valued functions with respect to fuzzy measures and the characteristic of its primitive [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 1-9.
[9] LI Tao-tao. Existence of radial positive solutions of second-order semi-positone elliptic differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 48-55.
[10] ZHANG Sha, JIA Mei, LI Yan, LI Xiao-chen. Existence and uniqueness of solutions for three point boundary value problems of impulsive fractional differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 66-72.
[11] . Uniqueness of solution for singular boundary value problems of fourth-order differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 73-76.
[12] GUO Li-jun. Existence of positive solutions for a third-order three-point boundary value problem of nonlinear differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 47-53.
[13] ZHU Wen-wen. Existence and multiplicity of positive solutions of first order periodic boundary value problems with parameter [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 36-41.
[14] LI Xiao-yan, XU Man. Existence and multiplicity of nontrivial solutions of Dirichlet problems for second-order impulsive differential equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 29-35.
[15] ZHANG Shen-gui. Multiplicity of solutions for Kirchhoff type equation involving the p(x)-biharnonic operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 48-53.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!