JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (9): 43-53.doi: 10.6040/j.issn.1671-9352.0.2019.038

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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

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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.

Key words: interval valued Pythagorean fuzzy set, entropy, distance, similarity, pattern recognition

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.
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