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

2013 ◽  
Vol 2013 ◽  
pp. 1-33 ◽  
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.

scholarly journals Interval-Valued Pythagorean Hesitant Fuzzy Set and Its Application to Multiattribute Group Decision-Making

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Maoyin Zhang ◽  
Tingting Zheng ◽  
Wanrong Zheng ◽  
Ligang Zhou
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Score Function ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
Interval Numbers ◽  
Operational Laws ◽  
Interval Valued

Pythagorean hesitant fuzzy sets are widely watched because of their excellent ability to deal with uncertainty, imprecise and vague information. This paper extends Pythagorean hesitant fuzzy environments to interval-valued Pythagorean hesitant fuzzy environments and proposes the concept of interval-valued Pythagorean hesitant fuzzy set (IVPHFS), which allows the membership of each object to be a set of several pairs of possible interval-valued Pythagorean fuzzy elements. Furthermore, we develop a series of aggregation operators for interval-valued Pythagorean hesitant fuzzy information and apply them to multiattribute group decision-making (MAGDM) problems. Then, some desired operational laws and properties of IVPHFSs are studied. Especially, considering an interval-valued Pythagorean fuzzy element (IVPHFE) is formed by several pairs of interval values, this paper proposes the concepts of score function and accuracy function in the form of two interval numbers which can retain interval-valued Pythagorean fuzzy information as much as possible. Then, the relationship among these operators is discussed by comparing the interval numbers. Eventually, an illustrative example fully shows the feasibility, practicality, and effectiveness of the proposed approach.

scholarly journals Interval-Valued Probabilistic Hesitant Fuzzy Set Based Muirhead Mean for Multi-Attribute Group Decision-Making

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 342 ◽  
Author(s):  
Krishankumar ◽  
Ravichandran ◽  
Ahmed ◽  
Kar ◽  
Peng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Partial Information ◽  
Programming Model ◽  
Hesitant Fuzzy Set ◽  
Occurrence Probability ◽  
Source Selection ◽  
Interval Valued

As a powerful generalization to fuzzy set, hesitant fuzzy set (HFS) was introduced, which provided multiple possible membership values to be associated with a specific instance. But HFS did not consider occurrence probability values, and to circumvent the issue, probabilistic HFS (PHFS) was introduced, which associates an occurrence probability value with each hesitant fuzzy element (HFE). Providing such a precise probability value is an open challenge and as a generalization to PHFS, interval-valued PHFS (IVPHFS) was proposed. IVPHFS provided flexibility to decision makers (DMs) by associating a range of values as an occurrence probability for each HFE. To enrich the usefulness of IVPHFS in multi-attribute group decision-making (MAGDM), in this paper, we extend the Muirhead mean (MM) operator to IVPHFS for aggregating preferences. The MM operator is a generalized operator that can effectively capture the interrelationship between multiple attributes. Some properties of the proposed operator are also discussed. Then, a new programming model is proposed for calculating the weights of attributes using DMs’ partial information. Later, a systematic procedure is presented for MAGDM with the proposed operator and the practical use of the operator is demonstrated by using a renewable energy source selection problem. Finally, the strengths and weaknesses of the proposal are discussed in comparison with other methods.

scholarly journals OPERATOR-OPERATOR PADA HIMPUNAN KABUR HESITANT BERNILAI INTERVAL

2019 ◽  
Vol 8 (1) ◽  
pp. 17
Author(s):  
Awanda Amelia Maron ◽  
Yudiantri Asdi
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Hesitant Fuzzy Set ◽  
Interval Valued

Chen dan Xu memperkenalkan tentang relasi preference hesitant bernilai interval dalam proses pengambilan keputusan kelompok(Group Decision Making/GDM ) [2]. Pada proses GDM digunakan operator-operator untuk mengumpulkan informasi Interval-valued Hesitant Fuzzy Set (IVHFS) [2]. Konsep himpunan kabur hesitant bernilai interval banyak digunakan pada teori pengambilan keputusan. akan tetapi pada penelitian ini hanya dibatasi kajian aljabar yaitu dikaji tentang sifat-sifat operasi pada elemen kabur hesitant bernilai interval dan bentuk operator-operator pada IVHFS. Operasi ring sum, ring product, irisan dan gabungan pada elemen kabur hesitant bernilai interval memenuhi sifat-sifat aljabar yaitu sifat komutatif, sifat asosiatif, sifat distributif. Bentuk operator-operator pada himpunan kabur hesitant bernilai interval yaitu operator GIVHFWA, GIVHFWG dan operator GIVHFOWA, GIVHFOWG.Kata Kunci :himpunan kabur hesitant bernilai interval, sifat-sifat operasi, operator

Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making

2018 ◽  
Vol 29 (1) ◽  
pp. 393-408 ◽  
Author(s):  
Khaista Rahman ◽  
Saleem Abdullah ◽  
Muhammad Sajjad Ali Khan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Multiple Attribute ◽  
Interval Valued

Abstract In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.

scholarly journals Induced Interval-Valued Intuitionistic Fuzzy Hybrid Aggregation Operators with TOPSIS Order-Inducing Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Jun-Ling Zhang ◽  
Xiao-Wen Qi
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Special Cases ◽  
Wide Range ◽  
Induced Aggregation ◽  
Interval Valued

Two induced aggregation operators with novelly designed TOPSIS order-inducing variables are proposed: Induced Interval-valued Intuitionistic Fuzzy Hybrid Averaging (I-IIFHA) operator and Induced Interval-valued Intuitionistic Fuzzy Hybrid Geometric (I-IIFHG) operator. The merit of two aggregation operators is that they can consider additional preference information of decision maker’s attitudinal characteristics besides argument-dependent information and argument-independent information. Some desirable properties of I-IIFHA and I-IIFHG are studied and theoretical analysis also shows that they can include a wide range of aggregation operators as special cases. Further, we extend these operators to form a novel group decision-making method for selecting the most desirable alternative in multiple attribute multi-interest group decision-making problems with attribute values and decision maker’s interest values taking the form of interval-valued intuitionistic fuzzy numbers, and application research to real estate purchase selection shows its practicality.

scholarly journals Interval-Valued Hesitant Fuzzy Multiattribute Group Decision Making Based on Improved Hamacher Aggregation Operators and Continuous Entropy

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Jun Liu ◽  
Ning Zhou ◽  
Li-Hua Zhuang ◽  
Ning Li ◽  
Fei-Fei Jin
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Ordered Weighted Averaging ◽  
Cowa Operator ◽  
Interval Valued

Under the interval-valued hesitant fuzzy information environment, we investigate a multiattribute group decision making (MAGDM) method with continuous entropy weights and improved Hamacher information aggregation operators. Firstly, we introduce the axiomatic definition of entropy for interval-valued hesitant fuzzy elements (IVHFEs) and construct a continuous entropy formula on the basis of the continuous ordered weighted averaging (COWA) operator. Then, based on the Hamachert-norm andt-conorm, the adjusted operational laws for IVHFEs are defined. In order to aggregate interval-valued hesitant fuzzy information, some new improved interval-valued hesitant fuzzy Hamacher aggregation operators are investigated, including the improved interval-valued hesitant fuzzy Hamacher ordered weighted averaging (I-IVHFHOWA) operator and the improved interval-valued hesitant fuzzy Hamacher ordered weighted geometric (I-IVHFHOWG) operator, the desirable properties of which are discussed. In addition, the relationship among these proposed operators is analyzed in detail. Applying the continuous entropy and the proposed operators, an approach to MAGDM is developed. Finally, a numerical example for emergency operating center (EOC) selection is provided, and comparative analyses with existing methods are performed to demonstrate that the proposed approach is both valid and practical to deal with group decision making problems.

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