scholarly journals Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-Making

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-28 ◽  
Author(s):  
Yuchu Qin ◽  
Xiaolan Cui ◽  
Meifa Huang ◽  
Yanru Zhong ◽  
Zhemin Tang ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Intuitionistic Fuzzy Number ◽  
Specific Context ◽  
Intuitionistic Fuzzy ◽  
Special Cases ◽  
Magdm Problems ◽  
Interval Valued

Two important tasks in multiattribute group decision-making (MAGDM) are to describe the attribute values and to generate a ranking of all alternatives. A superior tool for the first task is linguistic interval-valued intuitionistic fuzzy number (LIVIFN), and an effective tool for the second task is aggregation operator (AO). To date, nearly ten AOs of LIVIFNs have been presented. Each AO has its own features and can work well in its specific context. But there is not yet an AO of LIVIFNs that can offer desirable generality and flexibility in aggregating attribute values and capturing attribute interrelationships and concurrently reduce the influence of unreasonable attribute values. To this end, a linguistic interval-valued intuitionistic fuzzy Archimedean power Muirhead mean operator and its weighted form, which have such capabilities, are presented in this paper. Firstly, the generalised expressions of the AOs are established by a combination of the Muirhead mean operator and the power average operator under the Archimedean T-norm and T-conorm operations of LIVIFNs. Then the properties of the AOs are explored and proved, their specific expressions are constructed, and the special cases of the specific expressions are discussed. After that, a new method for solving the MAGDM problems based on LIVIFNs is designed on the basis of the weighted AO. Finally, the designed method is illustrated via a practical example, and the presented AOs are evaluated via experiments and comparisons.

scholarly journals Multiple Attribute Group Decision-Making Based on Power Heronian Aggregation Operators under Interval-Valued Dual Hesitant Fuzzy Environment

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Shenqing Jiang ◽  
Wei He ◽  
Fangfang Qin ◽  
Qingqing Cheng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Fuzzy Environment ◽  
Multiple Attribute ◽  
Special Cases ◽  
Magdm Problems ◽  
Interval Valued ◽  
Heronian Mean

In this paper, we focus on new methods to deal with multiple attribute group decision-making (MAGDM) problems and a new comparison law of interval-valued dual hesitant fuzzy elements (IVDHFEs). More explicitly, the interval-valued dual hesitant fuzzy 2nd-order central polymerization degree (IVDHFCP2) function is introduced, for the case that score values of different IVDHFEs are identical. This function can further compare different IVDHFEs. Then, we develop a series of interval-valued dual hesitant fuzzy power Heronian aggregation operators, i.e., the interval-valued dual hesitant fuzzy power Heronian mean (IVDHFPHM) operator, the interval-valued dual hesitant fuzzy power geometric Heronian mean (IVDHFPGHM) operator, and their weighted forms. Some desirable properties and their special cases are discussed. These proposed operators can simultaneously reflect the interrelationship of aggregated arguments and reduce the influence of unreasonable evaluation values. Finally, two approaches for interval-valued dual hesitant fuzzy MAGDM with known or unknown weight information are presented. An illustrative example and comparative studies are given to verify the advantages of our methods. A sensitivity analysis of the decision results is analyzed with different parameters.

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 INTUITIONISTIC FUZZY ORDERED PRECISE WEIGHTED AGGREGATION OPERATOR AND ITS APPLICATION IN GROUP DECISION MAKING

2014 ◽  
Vol 20 (4) ◽  
pp. 648-672 ◽  
Author(s):  
Wei Zhou ◽  
Jian Min He
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Scale Invariance ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Aggregation ◽  
Interval Valued

An important research topic related to the theory and application of the interval-valued intuitionistic fuzzy weighted aggregation operators is how to determine their associated weights. In this paper, we propose a precise weight-determined (PWD) method of the monotonicity and scale-invariance, just based on the new score and accuracy functions of interval-valued intuitionistic fuzzy number (IIFN). Since the monotonicity and scale-invariance, the PWD method may be a precise and objective approach to calculate the weights of IIFN and interval-valued intuitionistic fuzzy aggregation operator, and a more suitable approach to distinguish different decision makers (DMs) and experts in group decision making. Based on the PWD method, we develop two new interval-valued intuitionistic fuzzy aggregation operators, i.e. interval-valued intuitionistic fuzzy ordered precise weighted averaging (IIFOPWA) operator and interval-valued intuitionistic fuzzy ordered precise weighted geometric (IIFOPWG) operator, and study their desirable properties in detail. Finally, we provide an illustrative example.

Extension of VIKOR Method for Multi-Attribute Group Decision Making with Incomplete Weights

2014 ◽  
Vol 513-517 ◽  
pp. 721-724 ◽  
Author(s):  
Chen Guang Xu ◽  
Dong Xiao Liu ◽  
Min Li
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Fuzzy Decision ◽  
Vikor Method ◽  
Decision Matrix ◽  
Intuitionistic Fuzzy ◽  
Magdm Problems ◽  
Interval Valued

In this paper, we First utilize the induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision makers into a collective interval-valued intuitionistic fuzzy decision matrix. Based on the basic ideal of traditional VIKOR method, we establish an optimization model to determine the weights of attributes. Then, calculation steps based on the collective interval-valued intuitionistic fuzzy decision matrix and traditional VIKOR method for solving the MAGDM problems with interval-valued intuitionistic fuzzy assessments and partially known weight information are given. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

Extension of VIKOR Method for Multi-Attribute Group Decision Making with Interval-Valued Intuitionistic Fuzzy Assessments and Incomplete Weights

2014 ◽  
Vol 513-517 ◽  
pp. 725-728 ◽  
Author(s):  
Chen Guang Xu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Fuzzy Decision ◽  
Vikor Method ◽  
Decision Matrix ◽  
Intuitionistic Fuzzy ◽  
Magdm Problems ◽  
Interval Valued

In this paper, we investigate the multi-attribute group decision making (MAGDM) problems in which all the information provided by the decision makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFN), and the information about attribute weights is partially known. First, we utilize the induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision makers into a collective interval-valued intuitionistic fuzzy decision matrix. Based on the basic ideal of traditional VIKOR method, we establish an optimization model to determine the weights of attributes. Then, calculation steps based on the collective interval-valued intuitionistic fuzzy decision matrix and traditional VIKOR method for solving the MAGDM problems with interval-valued intuitionistic fuzzy assessments and partially known weight information are given. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

scholarly journals A Novel Approach to Multi-Attribute Group Decision-Making based on Interval-Valued Intuitionistic Fuzzy Power Muirhead Mean

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 441 ◽  
Author(s):  
Wuhuan Xu ◽  
Xiaopu Shang ◽  
Jun Wang ◽  
Weizi Li
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Intuitionistic Fuzzy ◽  
Novel Approach ◽  
Maclaurin Symmetric Mean ◽  
Magdm Problems ◽  
Interval Valued

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method.

Taxonomy method for multiple attribute group decision making based on interval-valued intuitionistic fuzzy with entropy

2021 ◽  
pp. 1-15
Author(s):  
Lu Xiao ◽  
Guiwu Wei ◽  
Yanfeng Guo ◽  
Xudong Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Set ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Proposed Model ◽  
Multiple Attribute ◽  
Magdm Problems ◽  
Interval Valued

Interval-valued intuitionistic fuzzy set (IVIFS) is a flexible method to deal with uncertainty and fuzziness. For the past few years, extensive researches about the multi-attribute group decision making (MAGDM) problems based on IVIFSs has been extensively studied in many fields. In this study, the Taxonomy method based on IVIFSs (IVIF-Taxonomy) was proposed for MAGDM problems. For the sake of the objectivity of attribute weight, entropy is introduced into the proposed model. The IVIF-Taxonomy method fully considers the weight of the decision makers (DMs) and the homogeneity of the chosen alternatives, making it more realistic. In addition, we apply IVIF-Taxonomy method to fund selection to verify the validity of IVIF-Taxonomy method. Finally, the trustworthy of IVIF-Taxonomy method is proved by comparing with the aggregate operator, IVIF-TOPSIS method, IVIF-GRA method and modified IVIF-WASPAS method.

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