Decision making method for evaluating logistics companies based on the ordered representation of the polygonal fuzziness1

2020 ◽  
Vol 39 (3) ◽  
pp. 3151-3166
Author(s):  
Xiaoping Li ◽  
Yujie Tao ◽  
Yanhong Li
Keyword(s):  
Decision Making ◽  
Euclidean Distance ◽  
Fuzzy Numbers ◽  
Decision Matrix ◽  
Arithmetic Average ◽  
Weighted Arithmetic ◽  
Relative Closeness ◽  
Negative Ideal Solution ◽  
Arbitrary Precision ◽  
Polygonal Fuzzy Numbers

A polygonal fuzzy numbers can describe fuzzy information by means of finite ordered real numbers. It not only overcomes the complexity of traditional fuzzy number operations, but also keeps some good properties of trapezoidal fuzzy numbers, and it can approximate general fuzzy numbers with arbitrary precision. In this paper, a weighted arithmetic average operator is defined by the ordered representation and its operations of the polygonal fuzzy numbers, and a new Euclidean distance for measuring the polygonal fuzzy numbers is given. Secondly, in view of cost attribute and benefit attributes, the polygonal fuzzy decision matrix is normalized, and the weighted Euclidean distance is used to solve the positive (negative) ideal solution and the relative closeness of the decision matrix, and then a new decision method is given. Finally, the effectiveness of the proposed decision-making method is illustrated by an example of the evaluation of logistics companies by shopping websites.

scholarly journals A Heterogeneous Multiattribute Group Decision-Making Method Based on Intuitionistic Triangular Fuzzy Information

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Jun Xu ◽  
Jiu-Ying Dong ◽  
Shu-Ping Wan ◽  
De-Yan Yang ◽  
Yi-Feng Zeng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Entropy Method ◽  
Triangular Fuzzy Numbers ◽  
Decision Matrix ◽  
Interval Numbers ◽  
Attribute Weights ◽  
Relative Closeness

How to aggregate decision information in heterogeneous multiattribute group decision making (HMAGDM) is vital. The aim of this paper is to develop an approach to aggregating decision data into intuitionistic triangular fuzzy numbers (ITFNs) for heterogeneous MAGDM problems with real numbers (RNs), interval numbers (INs), triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), and triangular intuitionistic fuzzy number (TIFNs). Using the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS) and geometry entropy method, we first present a general approach to aggregating heterogeneous information into ITFNs, which takes the group consistency of experts into account. Based on the collective intuitionistic triangular fuzzy decision matrix and extended TOPSIS, a multiple objective mathematical program is constructed to determine the optimal attribute weights. Subsequently, a new method to solve HMAGDM problems is presented based on the aforementioned discussion. A trustworthy service selection example is provided to verify the practicality and effectiveness of the proposed method.

A Multi-Attribute Decision-Making Model Using Interval-Valued Intuitionistic Fuzzy Numbers and Attribute Correlation

2018 ◽  
Vol 14 (1) ◽  
pp. 21-34 ◽  
Author(s):  
Sha Fu ◽  
Xi-long Qu ◽  
Hang-jun Zhou ◽  
Guo-bing Fan
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Reference Points ◽  
Intuitionistic Fuzzy Numbers ◽  
Arithmetic Average ◽  
Attribute Weight ◽  
Intuitionistic Fuzzy ◽  
Weighted Arithmetic ◽  
Interval Valued ◽  
Attribute Correlation

This article describes a decision analysis method with attribute correlation and attribute values of interval-valued intuitionistic fuzzy numbers (IVIFN). This considers the correlation between attributes and undetermined attribute weight information was put forward against the case where solution attribute values are interval-valued intuitionistic fuzzy numbers. To achieve a comprehensive consideration of the undetermined evaluation attribute weight information, experts' positive and negative ideal solutions against each attribute are taken as reference points, attribute weight is obtained via decision making trial and evaluation laboratory (DEMATEL) method according to the direct relation matrix provided by experts against attribute sets. On this basis, evaluation information is aggregated by using weighted arithmetic average operators. Then, the closeness degree formula of interval-valued intuitionistic fuzzy numbers relative to the maximum IVIFN is provided by combining the Euclidean distance of IVIFN, thus determining closeness degree and making an ordering of all solutions. Finally, the feasibility and validity of the method proposed in this study are verified via a case analysis of the best information system decision-making.

Group decision making method for residents to choose livable cities depicted by n-intuitionistic polygonal fuzzy sets1

2020 ◽  
Vol 39 (3) ◽  
pp. 3503-3518
Author(s):  
Guijun Wang ◽  
Jie Zhou
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Arithmetic Operation ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Fuzzy Information ◽  
Decision Matrix ◽  
Arithmetic Average

The polygonal fuzzy set is an effective tool to express a class of fuzzy information with the help of finite ordered real numbers. It can not only guarantee the closeness of arithmetic operation of the polygonal fuzzy sets, but also has good linearity and intuitiveness. Firstly, the concept of the n-intuitionistic polygonal fuzzy set (n-IPFS) is proposed based on the intuitionistic fuzzy set and the polygonal fuzzy set. The ordered representation and arithmetic operation of n-IPFS are given by an example. Secondly, a new aggregation method for multi attribute fuzzy information is given based on the n-IPFS operations and the weighted arithmetic average operator, and the ranking criteria of n-IPFS are obtained by using the score function and the accuracy function. Finally, a new group decision making method is proposed for urban residents to choose the livable city problem based on the decision matrix of the n-IPFS, and the effectiveness of the proposed method is explained by an actual example.

scholarly journals Hybrid Weighted Arithmetic and Geometric Aggregation Operator of Neutrosophic Cubic Sets for MADM

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 278 ◽  
Author(s):  
Lilian Shi ◽  
Yue Yuan
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Arithmetic Average ◽  
Weighted Arithmetic ◽  
Geometric Average ◽  
Multi Attribute Decision Making

Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neutrosophic cubic hybrid weighted arithmetic and geometric aggregation (NCHWAGA) operator and investigates its suitability and effectiveness. Then, we established a MADM method based on the NCHWAGA operator. Finally, a MADM problem with neutrosophic cubic information was provided to illustrate the application and effectiveness of the proposed method.

scholarly journals A Heterogeneous MCDM Framework for Sustainable Supplier Evaluation and Selection Based on the IVIF-TODIM Method

2019 ◽  
Vol 11 (18) ◽  
pp. 5057 ◽  
Author(s):  
Ren-Jie Mao ◽  
Jian-Xin You ◽  
Chun-Yan Duan ◽  
Lu-Ning Shao
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Third Party ◽  
Multi Criteria Decision Making ◽  
Interval Numbers ◽  
Intuitionistic Fuzzy Numbers ◽  
Sustainability Performance ◽  
Intuitionistic Fuzzy ◽  
Relative Closeness ◽  
Interval Valued

The third-party platform named ECO system is used by many transnational companies to monitor the sustainability performance of their global suppliers because of its easiness and shareability. Nonetheless, methods used in this platform for evaluating and calculating the sustainability performance of the alternative suppliers are criticized for their lack of accuracy. In response to these problems, this paper presents a heterogeneous multi-criteria decision-making (MCDM) method based on interval-valued intuitionistic fuzzy--an acronym in Portuguese for interactive multi-criteria decision making (IVIF--TODIM) to improve the efficiency of the evaluation model. Considering the varying features of evaluation criteria, i.e., either quantitative or qualitative, the evaluation values under different criteria are expressed in their appropriate information types. In this paper, a general method based on the relative closeness to the technique for order preference by similarity to ideal solution (TOPSIS) method is applied for aggregating the heterogeneous assessment information, including crisp numbers, interval numbers, and triangular fuzzy numbers (TFNs), into interval-valued intuitionistic fuzzy numbers (IVIFNs). Then, the TODIM (an acronym in Portuguese for interactive multi-criteria decision making) is extended and employed to prioritize the alternative suppliers. Finally, the applicability and effectiveness of the proposed method is verified by a practical example of polymer manufacturing company and a comparison analysis with existing methods.

scholarly journals Dombi Aggregation Operators of Linguistic Cubic Variables for Multiple Attribute Decision Making

Information ◽  
2018 ◽  
Vol 9 (8) ◽  
pp. 188 ◽  
Author(s):  
Xueping Lu ◽  
Jun Ye
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Optimal Choice ◽  
Decision Makers ◽  
Linguistic Variable ◽  
Operational Parameter ◽  
Arithmetic Average ◽  
Weighted Arithmetic ◽  
Multiple Attribute ◽  
Dombi Operations

A linguistic cubic variable (LCV) is comprised of interval linguistic variable and single-valued linguistic variable. An LCV contains decision-makers’ uncertain and certain linguistic judgments simultaneously. The advantage of the Dombi operators contains flexibility due to its changeable operational parameter. Although the Dombi operations have been extended to many studies to solve decision-making problems; the Dombi operations are not used for linguistic cubic variables (LCVs) so far. Hence, the Dombi operations of LCVs are firstly presented in this paper. A linguistic cubic variable Dombi weighted arithmetic average (LCVDWAA) operator and a linguistic cubic variable Dombi weighted geometric average (LCVDWGA) operator are proposed to aggregate LCVs. Then a multiple attribute decision making (MADM) method is developed in LCV setting on the basis of LCVDWAA and LCVDWGA operators. Finally, two illustrative examples about the optimal choice problems demonstrate the validity and the application of this method.

Interval Rough Neutrosophic TOPSIS Strategy for Multi-Attribute Decision Making

2020 ◽  
pp. 98-118
Author(s):  
Rumi Roy ◽  
Surapati Pramanik ◽  
Tapan Kumar Roy
Keyword(s):  
Decision Making ◽  
Euclidean Distance ◽  
Hamming Distance ◽  
Ideal Solution ◽  
Numerical Example ◽  
New Strategy ◽  
Order Preference ◽  
Multi Attribute Decision Making ◽  
Ranking Order ◽  
Negative Ideal Solution

In this chapter, the authors present a new strategy for multi-attribute decision making in interval rough neutrosophic environment. They define Hamming distance and Euclidean distance between interval rough neutrosophic numbers. They also define interval rough neutrosophic relative positive ideal solution (IRNRPIS) and interval rough neutrosophic relative negative ideal solution (IRNRNIS). Then the ranking order of the alternatives is obtained by the technique for order preference by similarity to ideal solution (TOPSIS) strategy. Finally, a numerical example is provided to demonstrate the applicability and effectiveness of the proposed interval rough neutrosophic TOPSIS strategy.

Introducing a new type of HFSs and its application in solving MAGDM problems

2021 ◽  
pp. 1-12
Author(s):  
Abazar Keikha
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Hesitant Fuzzy Sets ◽  
Vague Sets ◽  
Weighted Arithmetic ◽  
New Concepts ◽  
New Type ◽  
Magdm Problems

Uncertainty has long been explored as an objective and inalienable reality, and then modeled via different theories such as probability theory, fuzzy sets (FSs) theory, vague sets, etc. Hesitant fuzzy sets (HFSs) as a generalization of FSs, because of their flexibility and capability, extended and applied in many practical problems very soon. However, the above theories cannot meet all the scientific needs of researchers. For example, in some decision-making problems we encounter predetermined definite data, which have inductive uncertainties. In other words, the numbers themselves are crisp in nature, but are associated with varying degrees of satisfaction or fairness from the perspective of each decision-maker/judge. To this end, in this article, hesitant fuzzy numbers as a generalization of hesitant fuzzy sets will be introduced. Some concepts such as the operation laws, the arithmetic operations, the score function, the variance of hesitant fuzzy numbers, and a way to compare hesitant fuzzy numbers will be proposed. Mean-based aggregation operators of hesitant fuzzy numbers, i.e. hesitant fuzzy weighted arithmetic averaging (HWAA), hesitant fuzzy weighted geometric averaging (HWGA), hesitant fuzzy ordered weighted arithmetic averaging (HOWAA), and hesitant fuzzy ordered weighted geometric averaging (HOWGA) operators have been discussed in this paper, too. These new concepts will be used to model, and solve an uncertain multi-attribute group decision making (MAGDM) problem. The proposed method will be illustrated by a numerical example and the validity of the obtained solution will be checked by test criteria.

scholarly journals TOPSIS Hybrid Multiattribute Group Decision-Making Based on Interval Pythagorean Fuzzy Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
H. U. Jun ◽  
W. U. Junmin ◽  
W. U. Jie
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Comprehensive Evaluation ◽  
Weighted Average ◽  
Decision Makers ◽  
Relative Closeness ◽  
Order Preference ◽  
Pythagorean Fuzzy Numbers

Aiming at the mixed multiattribute group decision-making problem of interval Pythagorean fuzzy numbers, a weighted average (WA) operator model based on interval Pythagorean fuzzy sets is constructed. Furthermore, a decision-making method based on the technique for order preference by similarity to ideal solution (TOPSIS) method with interval Pythagorean fuzzy numbers is proposed. First, based on the completely unknown weights of decision-makers and attributes, interval Pythagorean fuzzy numbers are applied to TOPSIS group decision-making. Second, the interval Pythagorean fuzzy number WA operator is used to synthesize the evaluation matrices of multiple decision-makers into a comprehensive evaluation matrix, and the relative closeness of each scheme is calculated based on the TOPSIS decision-making method. Finally, an example is given to illustrate the rationality and effectiveness of the proposed method.

Weighted aggregation operators of fuzzy credibility cubic numbers and their decision making strategy for slope design schemes

2020 ◽  
Vol 01 ◽  
Author(s):  
Jun Ye ◽  
Shigui Du ◽  
Rui Yong ◽  
Fangwei Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Real World ◽  
Fuzzy Numbers ◽  
Aggregation Operators ◽  
Open Pit Mine ◽  
Open Pit ◽  
Weighted Arithmetic ◽  
Ranking Of Alternatives ◽  
Slope Design

Background: A fuzzy cubic set (FCS) is composed of a fuzzy set (FS) (certain fuzzy numbers) and an intervalvalued fuzzy set (IVFS) (uncertain fuzzy numbers) to describe the hybrid information of both. To enhance the credibility of both, they should be closely related to the measures/degrees of credibility owing to the vagueness and uncertainty of humans’ cognitions regarding the real world. Objective: This paper presents the notions of a fuzzy cubic credibility set (FCCS) and a fuzzy cubic credibility number (FCCN) as the new generalization of the FCS notion so as to enhance the credibility level of FCS by means of the credibility degrees of both FS and IVFS. Next, we define operations of FCCNs, an expected value of FCCN, and the FCCN weighted arithmetic averaging (FCCNWAA) and FCCN weighted geometric averaging (FCCNWGA) operators for decision making (DM) strategy. Method: A decision making (DM) strategy using the FCCNWAA or FCCNWGA operator is proposed to solve multicriteria DM problems in the environment of FCCNs. Then, the proposed DM strategy is applied to a DM example of slope design schemes for an open pit mine in the environment of FCCNs to reflect the feasibility of the proposed DM strategy. Result: By comparison with the fuzzy cubic DM strategy, the DM results with and without the degrees of credibility can impact on the ranking of alternatives in the DM example to reflect the effectiveness of the proposed DM strategy. Result: By comparison with the fuzzy cubic DM strategy, the DM results with and without the degrees of credibility can impact on the ranking of alternatives in the DM example to reflect the effectiveness of the proposed DM strategy. Conclusion: However, the highlighting advantage of this study is that the proposed DM strategy not only indicates the degrees of credibility regarding the assessed values of FCNs in the DM process but also enhances the DM reliability in the environment of FCCNs. Hence, the proposed DM strategy is superior to the fuzzy cubic DM strategy in the environment of FCCNs.

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