scholarly journals A Novel Multiattribute Decision-Making Method Based on Point–Choquet Aggregation Operators and Its Application in Supporting the Hierarchical Medical Treatment System in China

2018 ◽  
Vol 15 (8) ◽  
pp. 1718
Author(s):  
Runtong Zhang ◽  
Yuping Xing ◽  
Jun Wang ◽  
Xiaopu Shang ◽  
Xiaomin Zhu
Keyword(s):  
Decision Making ◽  
Medical Treatment ◽  
Choquet Integral ◽  
Aggregation Operators ◽  
Treatment System ◽  
Medical Resources ◽  
New Class ◽  
Fuzzy Point ◽  
Fuzzy Environment ◽  
Novel Approach

The hierarchical medical treatment system is an efficient way to solve the problem of insufficient and unbalanced medical resources in China. Essentially, classifying the different degrees of diseases according to the doctor’s diagnosis is a key step in pushing forward the hierarchical medical treatment system. This paper proposes a framework to solve the problem where diagnosis values are given as picture fuzzy numbers (PFNs). Point operators can reduce the uncertainty of doctor’s diagnosis and get intensive information in the process of decision making, and the Choquet integral operator can consider correlations among symptoms. In order to take full advantage of these two kinds of operators, in this paper, we firstly define some point operators under the picture fuzzy environment, and further propose a new class of picture fuzzy point–Choquet integral aggregation operators. Moreover, some desirable properties of these operators are also investigated in detail. Then, a novel approach based on these operators for multiattribute decision-making problems in the picture fuzzy context is introduced. Finally, we give an example to illustrate the applicability of the new approach in assisting hierarchical medical treatment system. This is of great significance for integrating the medical resources of the whole society and improving the service efficiency of the medical service system.

scholarly journals Heronian Means as Aggregation Operators for Multi-Attribute Decision Making Applications

2018 ◽  
Author(s):  
Xiaopu Shang ◽  
Jun Wang ◽  
Anupam Nanda ◽  
Weizi Li
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Novel Approach ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Heronian Mean

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

scholarly journals Convex Aggregation Operators and Their Applications to Multi-Hesitant Fuzzy Multi-Criteria Decision-Making

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 207 ◽  
Author(s):  
Ye Mei ◽  
Juanjuan Peng ◽  
Junjie Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Choquet Integral ◽  
Convex Combination ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Novel Approach ◽  
Ordered Weighted Average

Hesitant fuzzy sets (HFSs), which were generalized from fuzzy sets, constrain the membership degree of an element to be a set of possible values between zero and one; furthermore, if two or more decision-makers select the same value, it is only counted once. However, a situation where the evaluation value is repeated several times differs from one where the value appears only once. Multi-hesitant fuzzy sets (MHFSs) can deal effectively with a case where some values are repeated more than once in a MHFS. In this paper, the novel convex combination of multi-hesitant fuzzy numbers (MHFNs) is introduced. Some aggregation operators based on convex operation, such as generalized multi-hesitant fuzzy ordered weighted average (GMHFOWA) operator, generalized multi-hesitant fuzzy hybrid weighted average (GMHFHWA) operator, generalized multi-hesitant fuzzy prioritized weighted average (GMHFPWA) operator and generalized multi-hesitant fuzzy Choquet integral weighted average (GMHFCIWA) operator, are developed and corresponding properties are discussed in detail. Then, based on the proposed aggregation operators, a novel approach for multi-criteria decision-making (MCDM) problem is proposed for ranking alternatives. Finally, an example is provided to verify the developed approach and demonstrate its validity and feasibility and the study is supported by a sensitivity analysis and a comparison analysis.

scholarly journals Complex T-Spherical Fuzzy Aggregation Operators with Application to Multi-Attribute Decision Making

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1311 ◽  
Author(s):  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Miin-Shen Yang
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
The Novel ◽  
Fuzzy Environment ◽  
Novel Approach ◽  
Operational Laws ◽  
Comparison Results ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making

In this paper, the novel approach of complex T-spherical fuzzy sets (CTSFSs) and their operational laws are explored and also verified with the help of examples. CTSFS composes the grade of truth, abstinence, and falsity with a condition that the sum of q-power of the real part (also for imaginary part) of the truth, abstinence, and falsity grades cannot be exceeded from a unit interval. Additionally, to examine the interrelationships among the complex T-spherical fuzzy numbers (CTSFNs), we propose two aggregation operators, called complex T-spherical fuzzy weighted averaging (CTSFWA) and complex T-spherical fuzzy weighted geometric (CTSFWG) operators. A multi-attribute decision making (MADM) problem is resolved based on CTSFNs by using the proposed CTSFWA and CTSFWG operators. To examine the proficiency and reliability of the explored works, we use an example to make comparisons between the proposed operators and some existing operators. Based on the comparison results, the proposed CTSFWA and CTSFWG operators are well suited in the fuzzy environment with legitimacy and prevalence by contrasting other existing operators.

New Einstein Hybrid Aggregation Operators for Intuitionistic Fuzzy Sets and Applications in Multi-Criteria Decision-Making

2019 ◽  
pp. 252-283
Author(s):  
Bhagawati Prasad Joshi ◽  
Abhay Kumar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Decision Maker ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Processes

The fusion of multidimensional intuitionistic fuzzy information plays an important part in decision making processes under an intuitionistic fuzzy environment. In this chapter, it is observed that existing intuitionistic fuzzy Einstein hybrid aggregation operators do not follow the idempotency and boundedness. This leads to sometimes illogical and even absurd results to the decision maker. Hence, some new intuitionistic fuzzy Einstein hybrid aggregation operators such as the new intuitionistic fuzzy Einstein hybrid weighted averaging (IFEHWA) and the new intuitionistic fuzzy Einstein hybrid weighted geometric (IFEHWG) were developed. The new IFEHWA and IFEHWG operators can weigh the arguments as well as their ordered positions the same as the intuitionistic fuzzy Einstein hybrid aggregation operators do. Further, it is validated that the defined operators are idempotent, bounded, monotonic and commutative. Then, based on the developed approach, a multi-criteria decision-making (MCDM) procedure is given. Finally, a numerical example is conducted to demonstrate the proposed method effectively.

scholarly journals Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information

2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Muhammad Akram ◽  
Naveed Yaqoob ◽  
Ghous Ali ◽  
Wathek Chammam
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Ordered Weighted Averaging ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Electre I ◽  
Geometric Operator

An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.

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 A Novel Multi-Attribute Decision Making Method Based on The Double Hierarchy Hesitant Fuzzy Linguistic Generalized Power Aggregation Operator

Information ◽  
2019 ◽  
Vol 10 (11) ◽  
pp. 339 ◽  
Author(s):  
Liu ◽  
Zhao ◽  
Li ◽  
Wang ◽  
Wang
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Linguistic Context ◽  
Practical Application ◽  
Linguistic Expression ◽  
Novel Approach ◽  
Linguistic Term ◽  
Multi Attribute Decision Making ◽  
Complex Decision ◽  
Fuzzy Linguistic

. A double hierarchy hesitant fuzzy linguistic term set (DHHFLT) is deemed as an effective and powerful linguistic expression which models complex linguistic decision information more accurately by using two different hierarchy linguistic term sets. The purpose of this paper is to propose a multi-attribute decision making method to tackle complex decision issues in which attribute values are represented as double hierarchy hesitant fuzzy linguistic numbers, and there are some extreme or unreasonable data in the attribute values. To do this, firstly, four double hierarchy hesitant fuzzy linguistic generalized power aggregation operators are introduced, including the double hierarchy hesitant fuzzy linguistic generalized power average (DHHFLGPA) operator, the double hierarchy hesitant fuzzy linguistic generalized power geometric (DHHFLGPG) operator, and their weighted forms. Thereafter, several favorable properties, as well as representative cases of the proposed operators, are investigated in detail. Moreover, by virtue of the proposed operators, a novel approach is developed for coping with multi-attribute decision making cases in the double hierarchy hesitant fuzzy linguistic context. Finally, an illustrated example is given to demonstrate the practical application of the presented approach, an availability verification is given to show its validity, and a comparative analysis is also conducted to highlight the advantages of the proposed approach.

Additive Intuitionistic Fuzzy Aggregation Operators Based on Fuzzy Measure

2016 ◽  
Vol 24 (01) ◽  
pp. 1-12 ◽  
Author(s):  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Probability Measure ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Fuzzy Measure ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Aggregation ◽  
The World ◽  
Multi Attribute Decision Making

Intuitionistic fuzzy sets can describe the uncertainty and complexity of the world flexibly, so it has been widely used in multi-attribute decision making. Traditional intuitionistic fuzzy aggregation operators are usually based on the probability measure, namely, they consider that the attributes of objects are independent. But in actual situations, it is difficult to ensure the independence of attributes, so these operators are unsuitable in such situations. Fuzzy measure is able to depict the relationships among the attributes more comprehensively, so it can complement the traditional probability measure in dealing with the multi-attribute decision making problems. In this paper, we first analyze the existing intuitionistic fuzzy operators based on fuzzy measure, then introduce two novel additive intuitionistic fuzzy aggregation operators based on the Shapley value and the Choquet integral, respectively, and show their advantages over other ones.

scholarly journals Interval-Valued Intuitionistic Fuzzy Multicriteria Group Decision Making Based on VIKOR and Choquet Integral

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Chunqiao Tan ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Choquet Integral ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Problem ◽  
Multicriteria Group Decision Making ◽  
Interval Valued

An effective decision making approach based on VIKOR and Choquet integral is developed to solve multicriteria group decision making problem with conflicting criteria and interdependent subjective preference of decision makers in a fuzzy environment where preferences of decision makers with respect to criteria are represented by interval-valued intuitionistic fuzzy sets. First, an interval-valued intuitionistic fuzzy Choquet integral operator is given. Some of its properties are investigated in detail. The extended VIKOR decision procedure based on the proposed operator is developed for solving the multicriteria group decision making problem where the interactive criteria weight is measured by Shapley value. An illustrative example is given for demonstrating the applicability of the proposed decision procedure for solving the multi-criteria group decision making problem in interval-valued intuitionistic fuzzy environment.

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