scholarly journals Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1058 ◽  
Author(s):  
Muhammad Akram ◽  
Sumera Naz ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Social Economy ◽  
Hesitant Fuzzy Set ◽  
Attribute Weights ◽  
Fuzzy Environment ◽  
Relative Closeness ◽  
Multiple Attribute ◽  
Maximizing Deviation Method ◽  
Deviation Method

With the development of the social economy and enlarged volume of information, the application of multiple-attribute decision-making (MADM) has become increasingly complex, uncertain, and obscure. As a further generalization of hesitant fuzzy set (HFS), simplified neutrosophic hesitant fuzzy set (SNHFS) is an efficient tool to process the vague information and contains the ideas of a single-valued neutrosophic hesitant fuzzy set (SVNHFS) and an interval neutrosophic hesitant fuzzy set (INHFS). In this paper, we propose a decision-making approach based on the maximizing deviation method and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) to solve the MADM problems, in which the attribute weight information is incomplete, and the decision information is expressed in simplified neutrosophic hesitant fuzzy elements. Firstly, we inaugurate an optimization model on the basis of maximizing deviation method, which is useful to determine the attribute weights. Secondly, using the idea of the TOPSIS, we determine the relative closeness coefficient of each alternative and based on which we rank the considered alternatives to select the optimal one(s). Finally, we use a numerical example to show the detailed implementation procedure and effectiveness of our method in solving MADM problems under simplified neutrosophic hesitant fuzzy environment.

scholarly journals Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment

2015 ◽  
Vol 24 (1) ◽  
pp. 23-36 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Neutrosophic Set ◽  
Fuzzy Environment ◽  
Cosine Measure ◽  
Multiple Attribute

AbstractOn the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging (SVNHFWA) operator and a single-valued neutrosophic hesitant fuzzy weighted geometric (SVNHFWG) operator and investigate their properties. Furthermore, a multiple-attribute decision-making method is established on the basis of the SVNHFWA and SVNHFWG operators and the cosine measure under a single-valued neutrosophic hesitant fuzzy environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

scholarly journals New Distance Measures for Dual Hesitant Fuzzy Sets and Their Application to Multiple Attribute Decision Making

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 191
Author(s):  
Wang ◽  
Li ◽  
Zhang ◽  
Han
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
Attribute Weights ◽  
Multiple Attribute

Multiple attribute decision making (MADM) is full of uncertainty and vagueness due to intrinsic complexity, limited experience and individual cognition. Representative decision theories include fuzzy set (FS), intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) and so on. Compared with IFS and HFS, DHFS has more advantages in dealing with uncertainties in real MADM problems and possesses good symmetry. The membership degrees and non-membership degrees in DHFS are simultaneously permitted to represent decision makers’ preferences by a given set having diverse possibilities. In this paper, new distance measures for dual hesitant fuzzy sets (DHFSs) are developed in terms of the mean, variance and number of elements in the dual hesitant fuzzy elements (DHFEs), which overcomes some deficiencies of the existing distance measures for DHFSs. The proposed distance measures are effectively applicable to solve MADM problems where the attribute weights are completely unknown. With the help of the new distance measures, the attribute weights are objectively determined, and the closeness coefficients of each alternative can be objectively obtained to generate optimal solution. Finally, an evaluation problem of airline service quality is conducted by using the distance-based MADM method to demonstrate its validity and applicability.

scholarly journals AN EXTENDED COPRAS MODEL FOR MULTIPLE ATTRIBUTE GROUP DECISION MAKING BASED ON SINGLE-VALUED NEUTROSOPHIC 2-TUPLE LINGUISTIC ENVIRONMENT

2021 ◽  
Vol 0 (0) ◽  
pp. 1-16
Author(s):  
Guiwu Wei ◽  
Jiang Wu ◽  
Yanfeng Guo ◽  
Jie Wang ◽  
Cun Wei
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Construction Project ◽  
Numerical Example ◽  
Attribute Weights ◽  
Multiple Attribute ◽  
Maximizing Deviation Method ◽  
Deviation Method

In this article, we develop the COPRAS model to solve the multiple attribute group decision making (MAGDM) under single-valued neutrosophic 2-tuple linguistic sets (SVN2TLSs). Firstly, we introduce the relevant knowledge about SVN2TLSs in a nutshell, such as the definition, the operation laws, a few of fused operators and so on. Then, combine the traditional COPRAS model with SVN2TLNs, and structure as well as elucidate the computing steps of the SVN2TLNCOPRAS pattern. Furthermore, in this article, we propose a method for determining attribute weights in different situations relying on the maximizing deviation method with SVN2TLNs. Last but not least, a numerical example about assessing the safety of construction project has been designed. And for further demonstrating the advantage of the new designed method, we also select a number of existed methods to have comparisons.

Multiple-attribute decision making method based on power generalized maclaurin symmetric mean operators under normal wiggly hesitant fuzzy environment

2021 ◽  
pp. 1-26
Author(s):  
Peide Liu ◽  
Pei Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Hesitant Fuzzy Set ◽  
Uncertain Information ◽  
Fuzzy Environment ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Special Cases ◽  
The Impact

A normal wiggly hesitant fuzzy set is a very useful tool to mine the potential uncertain information given by decision makers, which is considered as an extension of hesitant fuzzy set and can improve the effectiveness of decision making. Power average operator can relieve the impact on decision result of unreasonable data, and the generalized Maclaurin symmetric mean operator (GMSM) is an extension of Maclaurin symmetric mean operator with wider range of applications, which can consider the relationship among decision attributes. By integrating the advantages of them, in this paper, we develop the normal wiggly hesitant fuzzy power GMSM (NWHFPGMSM) operator and its weighted form based on the distance measure of two normal wiggly hesitant fuzzy elements, then we further discuss their properties and some special cases. Thus, a new multi-attribute decision making method based on the NWHFPGMSM operator under normal wiggly hesitant fuzzy environment is proposed. Finally, we select some examples to illustrate the effectiveness and superiority of the proposed method in this paper through comparison and analysis with other methods.

Extended TOPSIS method based on the entropy measure and probabilistic hesitant fuzzy information and their application in decision support system

2021 ◽  
pp. 1-12
Author(s):  
Muhammad Naeem ◽  
Muhammad Ali Khan ◽  
Saleem Abdullah ◽  
Muhammad Qiyas ◽  
Saifullah Khan
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Group Decision ◽  
Hesitant Fuzzy Set ◽  
Entropy Measure ◽  
Fuzzy Information ◽  
Score Functions ◽  
Fuzzy Environment ◽  
Basic Operating

Probabilistic hesitant fuzzy Set (PHFs) is the most powerful and comprehensive idea to support more complexity than developed fuzzy set (FS) frameworks. In this paper, it can explain a novel, improved TOPSIS-based method for multi-criteria group decision-making (MCGDM) problem through the Probabilistic hesitant fuzzy environment, in which the weights of both experts and criteria are completely unknown. Firstly, we discuss the concept of PHFs, score functions and the basic operating laws of PHFs. In fact, to compute the unknown weight information, the generalized distance measure for PHFs was defined based on the Probabilistic hesitant fuzzy entropy measure. Second, MCGDM will be presented with the PHF information-based decision-making process.

scholarly journals Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 280 ◽  
Author(s):  
Harish Garg ◽  
Gagandeep Kaur
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Weight Vector ◽  
Aggregation Operators ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Maximum Deviation ◽  
Dual Hesitant Fuzzy Set ◽  
Deviation Method

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.

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

2018 ◽  
Vol 29 (1) ◽  
pp. 154-171 ◽  
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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