On Hesitant Fuzzy Reducible Weighted Bonferroni Mean and Its Generalized Form for Multicriteria Aggregation

Due to convenience and powerfulness in dealing with vagueness and uncertainty of real situation, hesitant fuzzy set has received more and more attention and has been a hot research topic recently. To differently process and effectively aggregate hesitant fuzzy information and capture their interrelationship, in this paper, we propose the hesitant fuzzy reducible weighted Bonferroni mean (HFRWBM) and present its four prominent characteristics, namely, reductibility, monotonicity, boundedness, and idempotency. Then, we further investigate its generalized form, that is, the generalized hesitant fuzzy reducible weighted Bonferroni mean (GHFRWBM). Based on the discussion of model parameters, some special cases of the HFRWBM and GHFRWBM are studied in detail. In addition, to deal with the situation that multicriteria have connections in hesitant fuzzy information aggregation, a three-step aggregation approach has been proposed on the basis of the HFRWBM and GHFRWBM. In the end, we apply the proposed aggregation operators to multicriteria aggregation and give an example to illustrate our results.

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Covering-based compound mean operators arising from Heronian and Bonferroni mean operators in fuzzy and intuitionistic fuzzy environments

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-211457 ◽

2021 ◽

pp. 1-12

Author(s):

Yun Bo Tian ◽

Zhen Ming Ma

Keyword(s):

Multiple Attribute Decision Making ◽

Aggregation Operators ◽

Research Topic ◽

Fuzzy Information ◽

Bonferroni Mean ◽

Intuitionistic Fuzzy ◽

Multiple Attribute ◽

Special Cases ◽

The Common ◽

Aggregation Technique

Both Heronian mean (HM) operators and Bonferroni mean (BM) operators can capture the interrelationship between input arguments and have been a hot research topic as a useful aggregation technique in fuzzy and intuitionistic fuzzy environments. In this paper, associated with the common characters of these operators we propose the covering-based compound mean operators in fuzzy environments to capture various interrelationships between input arguments, some desirable properties and special cases of the proposed mean operators are provided. Then, conditions under which these covering-based compound mean operators can be directly used to aggregate the membership degrees and nonmembership degrees of intuitionistic fuzzy information, are provided. In particular, novel intuitionistic fuzzy HM operators and intuitionistic fuzzy BM operators are directly derived from the classical ones. We list the detailed steps of multiple attribute decision making with the developed aggregation operators, and give a comparison of the new extensions of BM operators by this paper with the corresponding existing ones to prove the rationality and effectiveness of the proposed method.

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Pythagorean Hesitant Fuzzy Information Aggregation and Their Application to Multi-Attribute Group Decision-Making Problems

Journal of Intelligent Systems ◽

10.1515/jisys-2017-0231 ◽

2018 ◽

Vol 29 (1) ◽

pp. 154-171 ◽

Cited By ~ 6

Author(s):

Muhammad Sajjad Ali Khan ◽

Saleem Abdullah ◽

Asad Ali ◽

Khaista Rahman

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Information Aggregation ◽

Weighted Averaging ◽

Hesitant Fuzzy Set ◽

Fuzzy Information ◽

New Approach ◽

Fuzzy Environment ◽

Multidimensional Evaluation

Abstract In this paper, we introduce the concept of the Pythagorean hesitant fuzzy set (PHFS), which is the generalization of the intuitionistic hesitant fuzzy set under the restriction that the square sum of its membership degrees is ≤1. In decision making with PHFSs, aggregation operators play a key role because they can be used to synthesize multidimensional evaluation values represented as Pythagorean hesitant fuzzy values into collective values. Under PHFS environments, Pythagorean hesitant fuzzy ordered weighted averaging and Pythagorean fuzzy ordered weighted geometric operators are used to aggregate the Pythagorean hesitant fuzzy values. The main advantage of these operators is that they provide more accurate and valuable results. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean hesitant fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, we compare the proposed approach to the existing methods.

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Archimedean Copula-Based Hesitant Fuzzy Information Aggregation Operators for Multiple Attribute Decision Making

Mathematical Problems in Engineering ◽

10.1155/2020/6284245 ◽

2020 ◽

Vol 2020 ◽

pp. 1-21 ◽

Cited By ~ 1

Author(s):

Ju Wu ◽

Lianming Mou ◽

Fang Liu ◽

Haobin Liu ◽

Yi Liu

Keyword(s):

Information Aggregation ◽

Multiple Attribute Decision Making ◽

Aggregation Operators ◽

Archimedean Copula ◽

Fuzzy Information ◽

Fuzzy Environment ◽

Operational Laws ◽

Multiple Attribute ◽

Special Cases ◽

Effective Use

In view of the good properties of copulas and their effective use in various fuzzy environments, the goal of the current study is to develop a series of aggregation operators for hesitant fuzzy information based on Archimedean copula and cocopula, which are applied to the MADM problems. Firstly, operational laws of hesitant fuzzy elements on the basis of copulas and cocopulas are defined which can show the relevance between hesitant fuzzy values. Secondly, four aggregation operators (AC-HFWA, AC-GHFWA, AC-HFWG, and AC-GHFWG) under hesitant fuzzy environment are developed according to the proposed operational laws. The properties of these operators are also studied in detail, including idempotence, monotonicity, boundedness, etc. Subsequently, five special cases of copula are also given and the special forms of aggregation operator are obtained. In the end, an example is used to illustrate the application of the proposed approach in MADM problems. The influences of different generated functions and parameters are shown, and the feasibility of the proposed method is validated through comparative analyses.

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Interval-Valued Dual Hesitant Fuzzy Heronian Mean Aggregation Operators and their Application to Multi-Attribute Decision Making

International Journal of Computational Intelligence and Applications ◽

10.1142/s1469026818500050 ◽

2018 ◽

Vol 17 (01) ◽

pp. 1850005 ◽

Cited By ~ 7

Author(s):

Yuqi Zang ◽

Xiaodong Zhao ◽

Shiyong Li

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Aggregation Operators ◽

Hesitant Fuzzy Set ◽

Fuzzy Information ◽

New Approach ◽

Dual Hesitant Fuzzy Set ◽

Multi Attribute Decision Making ◽

Interval Valued ◽

Heronian Mean

The interval-valued dual hesitant fuzzy set (IVDHFS) can depict the imprecise, vague and indeterminate information and Heronian mean (HM) has the prominent characteristic of capturing the correlation of the aggregated arguments. In this paper, we investigate multi-attribute decision making (MADM) problems based on HM, in which the attribute values are assumed in the form of interval-valued dual hesitant fuzzy information. Firstly, we briefly present some concepts of IVDHFS and HM. Then, we propose the interval-valued dual hesitant fuzzy Heronian mean (IVDHFHM) operator and the interval-valued dual hesitant fuzzy geometric Heronian mean (IVDHFGHM) operator. We also prove that they satisfy some desirable properties. Further, we consider the importance of the input arguments and derive the interval-valued dual hesitant fuzzy weighted Heronian mean (IVDHFWHM) operator and the interval-valued dual hesitant fuzzy weighted geometric Heronian mean (IVDHFWGHM) operator, and then develop the procedure of MADM. Finally, an illustrate example is given to demonstrate the practicality and effectiveness of the new approach.

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Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making

The Scientific World JOURNAL ◽

10.1155/2014/648516 ◽

2014 ◽

Vol 2014 ◽

pp. 1-15 ◽

Cited By ~ 4

Author(s):

Chunyong Wang ◽

Qingguo Li ◽

Xiaoqiang Zhou ◽

Tian Yang

Keyword(s):

Decision Making ◽

Information Aggregation ◽

Multiple Attribute Decision Making ◽

Aggregation Operators ◽

Fuzzy Information ◽

Fuzzy Environment ◽

Operational Laws ◽

Multiple Attribute ◽

Special Cases ◽

Fuzzy Aggregation

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.

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Probabilistic Interval-Valued Hesitant Fuzzy Information Aggregation Operators and Their Application to Multi-Attribute Decision Making

Algorithms ◽

10.3390/a11080120 ◽

2018 ◽

Vol 11 (8) ◽

pp. 120 ◽

Cited By ~ 11

Author(s):

Wenying Wu ◽

Ying Li ◽

Zhiwei Ni ◽

Feifei Jin ◽

Xuhui Zhu

Keyword(s):

Decision Making ◽

Information Aggregation ◽

Aggregation Operators ◽

Weighted Averaging ◽

Hesitant Fuzzy Set ◽

Fuzzy Information ◽

Proposed Model ◽

Multi Attribute Decision Making ◽

Definition Of ◽

Interval Valued

Based on the probabilistic interval-valued hesitant fuzzy information aggregation operators, this paper investigates a novel multi-attribute group decision making (MAGDM) model to address the serious loss of information in a hesitant fuzzy information environment. Firstly, the definition of probabilistic interval-valued hesitant fuzzy set will be introduced, and then, using Archimedean norm, some new probabilistic interval-valued hesitant fuzzy operations are defined. Secondly, based on these operations, the generalized probabilistic interval-valued hesitant fuzzy ordered weighted averaging (GPIVHFOWA) operator, and the generalized probabilistic interval-valued hesitant fuzzy ordered weighted geometric (GPIVHFOWG) operator are proposed, and their desirable properties are discussed. We further study their common forms and analyze the relationship among these proposed operators. Finally, a new probabilistic interval-valued hesitant fuzzy MAGDM model is constructed, and the feasibility and effectiveness of the proposed model are verified by using an example of supplier selection.

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Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Operators and Their Application in Multiple-Attribute Decision-Making

Complexity ◽

10.1155/2018/3606245 ◽

2018 ◽

Vol 2018 ◽

pp. 1-25 ◽

Cited By ~ 9

Author(s):

Wei Yang ◽

Jiarong Shi ◽

Yong Liu ◽

Yongfeng Pang ◽

Ruiyue Lin

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Multiple Attribute Decision Making ◽

Aggregation Operators ◽

Investment Company ◽

Pythagorean Fuzzy Set ◽

Bonferroni Mean ◽

Multiple Attribute ◽

Special Cases ◽

Geometric Bonferroni Mean

The aim of this paper is to develop partitioned Pythagorean fuzzy interaction Bonferroni mean operators based on the Pythagorean fuzzy set, Bonferroni mean, and interaction between membership and nonmembership. Several new aggregation operators are developed including the Pythagorean fuzzy interaction partitioned Bonferroni mean (PFIPBM) operator, the Pythagorean fuzzy weighted interaction partitioned Bonferroni mean (PFWIPBM) operator, the Pythagorean fuzzy interaction partitioned geometric Bonferroni mean (PFIPGBM) operator, and the Pythagorean fuzzy weighted interaction partitioned geometric Bonferroni mean (PFWIPGBM) operator. Some main properties and some special particular cases of the new operators are studied. Many existing operators are the special cases of new aggregation operators. Moreover, a multiple-attribute decision-making method based on the proposed operator has been developed and the investment company selection problem is presented to illustrate feasibility and practical advantages of the new method.

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Interval-Valued Dual Hesitant Fuzzy Hamacher Aggregation Operators for Multiple Attribute Decision Making

Journal of Systems Science and Information ◽

10.21078/jssi-2019-227-30 ◽

2019 ◽

Vol 7 (3) ◽

pp. 227-256

Author(s):

Chao Jiang ◽

Shenqing Jiang ◽

Jianlan Chen

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Multiple Attribute Decision Making ◽

Aggregation Operators ◽

Hesitant Fuzzy Set ◽

Dual Hesitant Fuzzy Set ◽

Operation Rules ◽

Multiple Attribute ◽

Special Cases ◽

Interval Valued

AbstractAs an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given, and an numerical example is provided to demonstrate that the developed approach is both valid and practical.

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Some Hesitant Fuzzy Hamacher Power-Aggregation Operators for Multiple-Attribute Decision-Making

Mathematics ◽

10.3390/math7070594 ◽

2019 ◽

Vol 7 (7) ◽

pp. 594 ◽

Cited By ~ 1

Author(s):

Mi Jung Son ◽

Jin Han Park ◽

Ka Hyun Ko

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Multiple Attribute Decision Making ◽

Aggregation Operators ◽

Decision Makers ◽

Hesitant Fuzzy Set ◽

Fuzzy Information ◽

New Approach ◽

Multiple Attribute

As an extension of the fuzzy set, the hesitant fuzzy set is used to effectively solve the hesitation of decision-makers in group decision-making and to rigorously express the decision information. In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm. Some desirable properties of these operators is shown, and the interrelationships between them are given. Furthermore, the relationships between the proposed aggregation operators and the existing hesitant fuzzy power-aggregation operators are discussed. Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems. Finally, a practical example is provided to illustrate the effectiveness of the developed approach, and the advantages of our approach are analyzed by comparison with other existing approaches.

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Interval-Valued Intuitionistic Hesitant Fuzzy Aggregation Operators and Their Application in Group Decision-Making

Journal of Applied Mathematics ◽

10.1155/2013/670285 ◽

2013 ◽

Vol 2013 ◽

pp. 1-33 ◽

Cited By ~ 18

Author(s):

Zhiming Zhang

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Aggregation Operators ◽

Hesitant Fuzzy Set ◽

Mathematical Tool ◽

Fuzzy Information ◽

Intuitionistic Fuzzy ◽

Interval Valued

Hesitant fuzzy sets, permitting the membership of an element to be a set of several possible values, can be used as an efficient mathematical tool for modelling people’s hesitancy in daily life. In this paper, we extend the hesitant fuzzy set to interval-valued intuitionistic fuzzy environments and propose the concept of interval-valued intuitionistic hesitant fuzzy set, which allows the membership of an element to be a set of several possible interval-valued intuitionistic fuzzy numbers. The aim of this paper is to develop a series of aggregation operators for interval-valued intuitionistic hesitant fuzzy information. Then, some desired properties of the developed operators are studied, and the relationships among these operators are discussed. Furthermore, we apply these aggregation operators to develop an approach to multiple attribute group decision-making with interval-valued intuitionistic hesitant fuzzy information. Finally, a numerical example is provided to illustrate the application of the developed approach.

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