### Information measures of interval valued Pythagorean fuzzy sets and their applications

SUN Qian-qian, LI Xiao-nan*

1. School of Mathematics and Statistics, Xidian University, Xian 710071, Shaanxi, China
• Online:2019-09-20 Published:2019-07-30

Abstract: Entropy, distance and similarity are important information measurement tools in fuzzy sets and their generalization theories. The information metrics research based on interval valued Pythagorean fuzzy sets mostly involves the distance formula of interval valued Pythagorean fuzzy numbers, and rarely involves metrics of ambiguity and similarity. In view of this situation, firstly, the axiomatization definition of entropy, distance and similarity of interval valued Pythagorean fuzzy sets is first proposed. Then study the relationship between entropy, distance and similarity. Finally, the entropy and similarity of the interval valued Pythagorean fuzzy set are applied to the field of pattern recognition. Comparative analysis shows the flexibility and effectiveness of the proposed measures.

CLC Number:

• O159
 [1] ZADEH L A. Fuzzy sets[J]. Information Control, 1965, 8(3):338-365.[2] ATANASSOV K T. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1896, 20(1):87-96.[3] ATANASSOV K T. Intuitionistic fuzzy sets: theory and applications[M]. Heidelberg: Physica-Verlag, 1999.[4] XU Zeshui. Intuitionistic fuzzy aggregation operators[J]. IEEE Transactions on Fuzzy Systems, 2007, 15(6):1179-1187.[5] 徐泽水. 直觉模糊信息集成理论及应用[M]. 北京: 科学出版社,2008. XU Zeshui. Intuitionistic fuzzy information aggregation[M]. Beijing: Science Press, 2008.[6] ATANASSOV K T. On intuitionistic fuzzy sets theory[M]. Berlin: Springer, 2012.[7] 雷英杰. 直觉模糊集理论及应用[M]. 北京: 科学出版社,2014. LEI Yingjie. Intuitionistic fuzzy set theory and its application[M]. Beijing: Science Press, 2014.[8] LI Xiaonan, YI Huangjian. Intuitionistic fuzzy matroids[J]. Journal of Intelligent & Fuzzy Systems, 2017, 33(6):3653-3663.[9] JAMKHANEH E B, GARG H. Some new operations over the generalized intuitionistic fuzzy sets and their application to decision-making process[J]. Granular Computing, 2018, 3(2):111-122.[10] YAGER R R. Pythagorean fuzzy subsets[C] // 2013 Joint IFSA World Congress and NAFIPS Annual Meeting(IFSA/NAFIPS). Edmonton, Canada: IEEE, 2013: 57-61.[11] YAGER R R. Pythagorean membership grades in multicriteria decision making[J]. IEEE Transactions on Fuzzy Systems, 2014, 22(5):958-965.[12] 刘卫锋,何霞. 毕达哥拉斯犹豫模糊集[J]. 模糊系统与数学,2016,30(4):108-113. LIU Weifeng, HE Xia. Pythagorean hesitant fuzzy set[J]. Fuzzy System and Mathematics, 2016, 30(4):108-113.[13] 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):225-229. PENG Xindong, YANG Yong, SONG Juanping, et al. Pythagorean fuzzy soft set and its application[J]. Computer Engineering, 2015, 41(7):225-229.[14] ZHANG Xiaolu, XU Zeshui. Extension of TOPSIS to multiple critiple criteria decision making with pythagorean fuzzy sets[J]. International Journal of Intelligent Systems, 2014, 29(12):1061-1078.[15] 何霞,杜迎雪,刘卫锋. 毕达哥拉斯模糊幂平均算子[J]. 模糊系统与数学,2016,30(6):117-126. HE Xia, DU Yingxue, LIU Weifeng. Pythagorean fuzzy power average operators[J]. Fuzzy System and Mathematics, 2016, 30(6):117-126.[16] ZHANG Xiaolu. A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision[J]. International Journal of Intelligent Systems, 2016, 31(6):593-611.[17] WEI Guiwu. Pythagorean fuzzy interaction aggregation operators and their applications to multiple attribute decision making[J]. Journal of Intelligent & Fuzzy Systems, 2017, 33(4):2119-2132.[18] 刘卫锋,杜迎雪,常娟. 毕达哥拉斯模糊交叉影响集成算子及其决策应用[J]. 控制与决策,2017,32(6):1034-1040. LIU Weifeng, DU Yingxue, CHANG Juan. Pythagorean fuzzy interaction aggregation operators and applications in decision making[J]. Control and Decision, 2017, 32(6):1034-1040.[19] WEI Guiwu, LU Mao. Pythagorean fuzzy power aggregation operators in multiple attribute decision making[J]. International Journal of Intelligent Systems, 2018, 33(1):169-186.[20] 丁恒,李延来. 基于毕达哥拉斯模糊幂加权平均算子的多属性群决策方法[J]. 计算机工程与应用,2018,54(5):1-6. DING Heng, LI Yanlai. Multiple attribute group decision making method based on Pythagorean fuzzy power weighted average operator[J]. Computer Engineering and Applications, 2018, 54(5):1-6.[21] PENG Xindong, YANG Yong. Fundamental properties of interval-valued Pythagorean fuzzy aggregation operator[J]. International Journal of Intelligent Systems, 2016, 31(5):444-487.[22] WEI Guiwu, LU Mao. Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making[J]. International Journal of Intelligent Systems, 2016, 33(5):1043-1070.[23] DU Yuqin, HOU Fujun, ZAFAR W, et al. A novel method for multiattribute decision making with interval-valued Pythagorean fuzzy linguistic information[J]. International Journal of Intelligent Systems, 2017, 32(10):1085-1112.[24] ZADEH A. Fuzzy sets and systems[C] // Proceedings of the Symposium on Systems Theory. New York: Polytechnic Institute of Brooklyn, 1965: 29-37.[25] ZHANG Qiansheng, JIANG Shengyi, JIA Baoguo, et al. Some information measures for interval-valued intuitionistic fuzzy sets[J]. International Journal of Information Sciences, 2010, 180(24):5130-5145.[26] PENG Xindong, YUAN Huiyong, YANG Yong. Pythagorean fuzzy information measures and their applications[J]. International Journal of Intelligent Systems, 2017, 32(10):991-1029.[27] RAHMAN K, ABDULLAH S, ALI A. Some induced aggregation operators based on interval-valued Pythagorean fuzzy numbers[J]. Granular Computing, 2019, 4(1):53-62.[28] LIU Yi, QIN Ya, HAN Yun. Multiple criteria decision making with probabilities in interval-valued Pythagorean fuzzy setting[J]. International Journal of Fuzzy System, 2018, 20(2):558-571.[29] WEI Guiwu, WEI Yu. Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications[J]. International Journal of Intelligent Systems, 2018, 33(2):1-18.[30] GARG H. New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making[J]. International Journal of Intelligent Systems, 2018, 33(3):653-683.
 [1] Zhen-peng LIU,Wen-sheng WANG,Yu-peng HE,Jing-wei SUN,Bin ZHANG. A deployment strategy for fault recovery of SDN control nodes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(5): 21-27. [2] An-min ZHOU,Lei HU,Lu-ping LIU,Peng JIA,Liang LIU. Malicious Office document detection technology based on entropy time series [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(5): 1-7. [3] GONG Shuang-shuang, CHEN Yu-feng, XU Jin-an, ZHANG Yu-jie. Extraction of Chinese multiword expressions based on Web text [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(9): 40-48. [4] XU Wei-cheng, LI Xin-peng. Generalized Cav(u)theorem for repeated games with incomplete information on one side [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 42-45. [5] LI Guo-cheng, WANG Ji-xia. Calibrating option pricing models with cross entropy bat algorithm [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 80-89. [6] 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. [7] HUANG Dong, XU Bo, XU Kan, LIN Hong-fei, YANG Zhi-hao. Short text clustering based on word embeddings and EMD [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 66-72. [8] ZHANG Cong, PEI Jia-huan, HUANG Kai-yu, HUANG De-gen, YIN Zhang-zhi. Semantic graph optimization algorithm based chinesemicroblog opinion summarization [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 59-65. [9] YU Wen-jing, BI Dong-xu, YAN Xue-feng. The inpainting of affine similarity damaged image based on structure automatic match [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(3): 32-37. [10] ZHU Xiao-ying, PANG Shi-you. On the maximal eccentric distance sum of tree with given domination number [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 30-36. [11] ZHANG Xiao-dong, DONG Wei-guang, TANG Min-an, GUO Jun-feng, LIANG Jin-ping. gOMP reconstruction algorithm based on generalized Jaccard coefficient for compressed sensing [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 23-28. [12] HUANG Shu-qin, XU Yong, WANG Ping-shui. User similarity calculation method based on probabilistic matrix factorization and its recommendation application [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 37-43. [13] . An approach of detecting LDoS attacks based on the euclidean distance of available bandwidth in cloud computing [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(9): 92-100. [14] ZHAI Peng, LI Deng-dao. The fuzzy clustering algorithm based on inclusion index of Gausian membership function [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 102-105. [15] ZHAO Bin, HE Jing-sha, ZHANG Yi-xuan. The method of determining decision attribute weight based on information entropy and membership [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(3): 86-90.
Viewed
Full text

Abstract

Cited

Shared
Discussed
 [1] YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78 -82 . [2] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 . [3] DONG Li-hong1,2, GUO Shuang-jian1. The fundamental theorem for weak Hopf module in  Yetter-Drinfeld module categories[J]. J4, 2013, 48(2): 20 -22 . [4] LI Jiao. Existence and uniqueness results for Caputo fractional differential  equations with initial value conditions[J]. J4, 2013, 48(4): 60 -64 . [5] XIE Tao, ZUO Ke-zheng. [J]. J4, 2013, 48(4): 95 -103 . [6] WANG Yi ,LIU Ai-lian . Cobweb models on time scales[J]. J4, 2007, 42(7): 41 -44 . [7] CHENG Li-qing1,2, SHI Qiao-lian2. A new hybrid conjugate gradient method[J]. J4, 2010, 45(6): 81 -85 . [8] SHI Yan-hua1, SHI Dong-yang2*. The quasi-Wilson nonconforming finite element approximation to  pseudo-hyperbolic equations[J]. J4, 2013, 48(4): 77 -84 . [9] REN Hui-xue,YANG Yan-zhao,LIN Ji-mao,QI Yin-shan,ZHANG Ye-qing . Synthesis and characterization of 5-bromo-3-sec-butyl-6-methyluracil[J]. J4, 2007, 42(7): 9 -12 . [10] ZHAO Tong-xin1, LIU Lin-de1*, ZHANG Li1, PAN Cheng-chen2, JIA Xing-jun1. Pollinators and pollen polymorphism of  Wisteria sinensis (Sims) Sweet[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 1 -5 .