Interval-Valued Pythagorean Fuzzy Power Geometric-Geometric Heronian Mean Operators and Their Application in Multiple Attribute Group Decision Making

doi:10.12005/orms.2021.0387

Operations Research and Management Science ›› 2021, Vol. 30 ›› Issue (12): 78-83.DOI: 10.12005/orms.2021.0387

• heory Analysis and Methodology Study • Previous Articles Next Articles

Interval-Valued Pythagorean Fuzzy Power Geometric-Geometric Heronian Mean Operators and Their Application in Multiple Attribute Group Decision Making

LI Jin-jun¹, TI Ting-ting², BAO Yu-e², CHEN Ming-hao¹

1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
2. College of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao 028043, China

Received:2019-06-06 Online:2021-12-25

区间毕达哥拉斯模糊幂几何-几何Heronian平均算子及其在多属性群决策中的应用

李进军¹, 李婷婷², 包玉娥², 陈明浩¹

1.大连理工大学数学科学学院,辽宁大连 116024;
2.内蒙古民族大学数理学院,内蒙古通辽 028043

通讯作者: 陈明浩(1964-),男,朝鲜族,黑龙江哈尔滨人,教授, 博士生导师,从事不确定动力系统、模糊优化、组合优化等方面的研究。
作者简介:李进军(1992-),男,云南大理人,博士研究生,从事决策分析、信息融合等方面的研究;
基金资助:
国家自然科学基金面上项目(11771111);国家自然科学基金资助项目(61663037)

Abstract

Abstract: In this paper, the power geometric (PG) operator and the geometric Heronian mean (GHM) operator are combined based on interval-valued Pythagorean fuzzy environment, and the interval-valued Pythagorean fuzzy power geometric-geometric Heronian mean (IVPFPG-GHM) operator and interval-valued Pythagorean fuzzy weighted power geometric-geometric Heronian mean (IVPFWPG-GHM) operator are proposed. In the process of fuzzy information aggregation, the novel operators not only reflect the correlation between attributes, but also avoid the interference caused by experts' singular value (too large or too small). In addition, some basic properties of new operators are also studied. Finally, multiple attribute group decision making (MAGDM) method based on IVPFWPG-GHM operator is presented, and a practical example is given to illustrate its feasibility and rationality.

Key words: interval-valued pythagorean fuzzy number, power geometric operator, geometric heronian mean operator, interval-valued pythagorean fuzzy power geometric-geometric heronian mean operator, multiple attribute group decision making

摘要： 本文在区间毕达哥拉斯模糊环境下,将幂几何(PG)算子和几何Heronian平均(GHM)算子相结合,提出区间毕达哥拉斯模糊幂几何-几何Heronian平均(IVPFPG-GHM)算子和区间毕达哥拉斯模糊加权幂几何-几何Heronian平均(IVPFWPG-GHM)算子。在模糊信息聚合过程中,新算子不仅能体现属性间的关联性,而且能最大限度地避免专家“奇异值”(过大或过小)带来的干扰。此外,还研究了它们的基本性质。最后,给出基于IVPFWPG-GHM算子的多属性群决策(MAGDM)方法,并以实例说明其可行性与合理性。

关键词: 区间毕达哥拉斯模糊数, 幂几何算子, 几何Heronian平均算子, 区间毕达哥拉斯模糊幂几何-几何Heronian平均算子, 多属性群决策

CLC Number:

C934

LI Jin-jun, TI Ting-ting, BAO Yu-e, CHEN Ming-hao. Interval-Valued Pythagorean Fuzzy Power Geometric-Geometric Heronian Mean Operators and Their Application in Multiple Attribute Group Decision Making[J]. Operations Research and Management Science, 2021, 30(12): 78-83.

李进军, 李婷婷, 包玉娥, 陈明浩. 区间毕达哥拉斯模糊幂几何-几何Heronian平均算子及其在多属性群决策中的应用[J]. 运筹与管理, 2021, 30(12): 78-83.

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Interval-Valued Pythagorean Fuzzy Power Geometric-Geometric Heronian Mean Operators and Their Application in Multiple Attribute Group Decision Making

区间毕达哥拉斯模糊幂几何-几何Heronian平均算子及其在多属性群决策中的应用

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