JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (1): 33-40.doi: 10.6040/j.issn.1671-9352.4.2019.121

Previous Articles     Next Articles

Algebraic structures of generalized Pythagorean fuzzy soft set

ZHANG Hai-dong1,2*, Jia-hua Duojie2, HE Yan-ping3   

  1. Northwest Minzu University 1. Key Laboratory of Chinas Ethnic Languages and Information Technology of Ministry of Education;
    2. School of Mathematics and Computer Science;
    3. School of Electrical Engineering, Lanzhou 730030, Gansu, China
  • Published:2020-01-10

Abstract: The Pythagorean fuzzy soft set theory is generalized and the concept of the generalized Pythagorean fuzzy soft set is introduced. In order to establish the theoretical basis for the generalized Pythagorean fuzzy soft set, we define some operation operators of the model, and discuss its lattice structures. First, three lattice structures of the generalized Pythagorean fuzzy soft set are constructed. Then it is also proved that the three lattice structures are soft algebraic structures. Finally, we explore three complemented distributive lattices which are also called Boolean lattices.

Key words: generalized Pythagorean fuzzy soft set, operator, soft algebra, Boolean lattice

CLC Number: 

  • O153.1
[1] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.
[2] ATANASSOV K. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20(1):87-96.
[3] TURKSEN I B. Interval valued fuzzy sets based on normal forms[J]. Fuzzy Sets and Systems, 1986, 20(2):191-210.
[4] MOLODTSOV D A. Soft set theory-first results[J]. Computers and Mathematics with Applications, 1999, 37(4):19-31.
[5] MAJI P K, BISWAS R, ROY A R. Soft set theory[J]. Computers and Mathematics with Applications, 2003, 45:555-562.
[6] ALI M I, FENG F, LIU X Y,et al. On some new operations in soft set theory[J]. Computers and Mathematics with Applications, 2009, 57:1547-1553.
[7] QIN Keyun, HONG Zhiyong. On soft equality[J]. Journal of Computational and Applied Mathematics, 2010, 234:1347-1355.
[8] BABITHA K V, SUNIL J J. Transitive closures and orderings on soft sets[J]. Computers and Mathematics with Applications, 2011, 62:2235-2239.
[9] JUN Y B. Soft BCK/BCI-algebras[J]. Computers and Mathematics with Applications, 2008, 56(5):1408-1413.
[10] MAJI P K, BISWAS R, ROY A R. Fuzzy soft set[J]. Journal of Fuzzy Mathematics, 2001, 9(3):589-602.
[11] MAJUMDAR P, SAMANTA S K. Generalized fuzzy soft sets[J]. Computers and Mathematics with Applications, 2010, 59(4):1425-1432.
[12] MAJI P K, BISWAS R, ROY A R. Intuitionistic fuzzy soft set[J]. Journal of Fuzzy Mathematics, 2001, 9(3):677-692.
[13] GARG H, ARORA R. Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making[J]. Applied Intelligence, 2018, 48(2):343-356.
[14] YANG X B, LIN T Y, YANG J Y, et al. Combination of interval-valued fuzzy set and soft set[J]. Computers and Mathematics with Applications, 2009, 58(3):521-527.
[15] ZHANG Haidong, XIONG Lianglin, MA Weiyuan. On interval-valued hesitant fuzzy soft sets[J]. Mathematical Problems in Engineering, 2015, 2015(3):1-17.
[16] ZHANG Haidong, SHU Lan. Dual hesitant fuzzy soft set and its properties[J]. Fuzzy Systems & Operations Research and Management, 2016, 367:171-182.
[17] JIANG Yuncheng, LIU Hai, TANG Yong, et al. Semantic decision making using ontology-based soft sets[J]. Mathematical and Computer Modelling, 2011, 53:1140-1149.
[18] HU Junhua, PAN Li, YANG Yan, et al. A group medical diagnosis model based on intuitionistic fuzzy soft sets[J]. Applied Soft Computing Journal, 2019, 77:453-466.
[19] QIN Keyun, ZHAO Hua. Lattice structures of fuzzy soft set[J]. Lecture Notes in Computer Science, 2010, 6215:126-133.
[20] 郭智莲, 杨海龙. 区间值模糊软集的格结构[J]. 计算机工程与应用, 2011, 47(33):7-9. GUO Zhilian, YANG Hailong. Lattice structures of interval-valued fuzzy soft sets[J]. Computer Engineering and Applications, 2011, 47(33):7-9.
[21] 周小强, 李庆国. 广义直觉模糊软集的格结构[J]. 湖南大学学报(自然科学版), 2014, 41(3):113-116. ZHOU Xiaoqiang, LI Qingguo. Lattice structure of generalized intuitionistic fuzzy soft sets[J]. Journal of Hunan University(Natural Science), 2014, 41(3):113-116.
[22] YAGER R R. Pythagorean membership grades in multi-criteria decision making[J]. IEEE Transaction on Fuzzy Systems, 2014, 22(4):958-965.
[23] 彭新东,杨勇,宋娟萍,等.毕达哥拉斯模糊软集及其应用[J].计算机工程,2015,41(7):224-229. PENG Xindong, YANG Yong, SONG Juanping, et al. Pythagorean fuzzy soft set and its application[J]. Computer Engineering, 2015, 41(7):224-229.
[24] JIA-HUA Duojie, ZHANG Haidong, HE Yanping. Possibility Pythagorean fuzzy soft set and its application[J]. Journal of Intelligent & Fuzzy Systems, 2019, 36(1):413-421.
[25] ZHANG Xiaolu, XU Zeshui. Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets[J]. International Journal of Intelligent Systems, 2014, 29(12):1061-1078.
[26] 张振琳. 离散数学[M]. 沈阳: 辽宁科学技术出版社, 2012: 112-118. ZHANG Zhenlin. Discrete mathematics [M]. Shenyang: Liaoning Science and Technology Press, 2012: 112-118.
[1] ZHANG Wei, FU Yan-ling. On decompositions of continuous generalized frames in Hilbert spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 76-80.
[2] DAI Lei, HUANG Xiao-jing, GUO Qi. Property(ω1)and the single-valued extension property [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 55-61.
[3] TAO Shuang-ping, YANG Yu-he. Weighted estimates of fractional maximal operator and its commutator on weighted λ-central Morrey spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 68-75.
[4] ZHANG Qian, LI Xuan, LI Xin, ZHENG Hui-hui, LI Lin-han, ZHANG Liang-yun. The construct of Rota-Baxter algebra on the Sweedler 4-dimensional Hopf algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 47-52.
[5] WANG Tao. Study on the approximation properties of Gauss-Weierstrass operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 96-98.
[6] FANG Xiao-zhen, SUN Ai-wen, WANG Min, SHU Li-sheng. Boundedness of generalized multilinear operators on variable exponent spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(4): 6-16.
[7] ZHANG Shen-gui. Applications of variational method to impulsive differential systems with variable exponent [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(4): 22-28.
[8] HAN Qi, YIN Shi-de, CHEN Zhi-he. Related properties of rotation operator in quantum computing [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 121-126.
[9] XIONG Xing-guo, LU Ling-xia. MV-algebra valued metric-based fuzzy rough sets [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 81-89.
[10] . Representation of the number operator in continuous-time Guichardet-Fock space [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(11): 108-114.
[11] JI Jie. Eigenvalues asymptotic formula and trace formula for a class of impulsive Sturm-Liouville operators [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(10): 49-56.
[12] SONG Jun-qiu, JIA Mei, LIU Xi-ping, LI Lin. Existence of positive solutions for fractional nonhomogeneous boundary value problem with p-Laplacian [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(10): 57-66.
[13] TAO Shuang-ping, GAO Rong. Estimates of multilinear fractional integrals and maximal operators on weighted Morrey spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 30-37.
[14] XIN Yin-ping, TAO Shuang-ping. Boundedness of Marcinkiewicz integrals operators with variable kernels on Herz-type Hardy spaces with variable exponent [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 38-43.
[15] . Representative forms of commutative BR0-algebras on a set by implication operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 86-94.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] CHEN Hong-yu1, ZHANG Li2. The linear 2-arboricity of planar graphs without 5-, 6-cycles with chord[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(06): 26 -30 .
[2] YE Xiao-ming, CHEN Xing-shu, YANG Li, WANG Wen-xian, ZHU Yi, SHAO Guo-lin, LIANG Gang. Anomaly detection model of host group based on graph-evolution events[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(9): 1 -11 .
[3] Zhao-xia WU,Jia-qi WANG. Wireless single spectrum secure auction algorithm[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(11): 51 -55 .
[4] WAN Peng-fei, GAO Xing-bao. Novel artificial bee colony algorithm based on objective space decomposition for solving multi-objective optimization problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(11): 56 -66 .
[5] WANG Xin, ZUO Wan-li, ZHU Feng-tong, WANG Ying. Important-node-based community detection algorithm[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(11): 67 -77 .
[6] WANG Ai-lan, SONG Wei-tao, ZHAO Xiu-feng. Properties of the expansion factor over quotient ring[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(11): 78 -84 .
[7] KONG Xiang-jun, WANG Pei. Good congruences associated with multiplicative quasi-adequate transversals[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 1 -3 .
[8] CHEN Hong-ling, WANG Hui-juan, GAO Hong-wei. Linear arboricity of graphs embedded in a surface of non-negative Euler characteristic[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 17 -22 .
[9] Yi-ran LI,Rong-hua ZHANG,Ze-dong LI,Yong NIU,Yong-tao ZHANG. Influence of stand structure of Acer truncatum forest on rainfall redistribution based on modified Gash model[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(1): 26 -35 .
[10] Ying ZHANG,Xue-song MA,Ru-yan JING,Feng-yun MA,Jian-yao GUO,Yan-ping WANG,Hua-tian WANG. Effects of successive-planting poplar plantation on soil microbial community[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(1): 36 -46 .