Multi-attributive border approximation area comparison (MABAC) method based on normal q-rung orthopair fuzzy environment

2021 ◽  
pp. 1-27
Author(s):  
Peide Liu ◽  
Qian Pan ◽  
Hongxue Xu
Keyword(s):  
Membership Function ◽  
Fuzzy Numbers ◽  
Strong Stability ◽  
Decision Makers ◽  
Uncertain Information ◽  
Intuitionistic Fuzzy Number ◽  
Attribute Weights ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Evaluation Information

The normal intuitionistic fuzzy number (NIFN), which membership function and non-membership function are expressed by normal fuzzy numbers (NFNs), can better describe the normal distribution phenomenon in the real world, but it cannot deal with the situation where the sum of membership function and non-membership function is greater than 1. In order to make up for this defect, based on the idea of q-rung orthopair fuzzy numbers (q-ROFNs), we put forward the concept of normal q-rung orthopair fuzzy numbers (q-RONFNs), and its remarkable characteristic is that the sum of the qth power of membership function and the qth power of non-membership function is less than or equal to 1, so it can increase the width of expressing uncertain information for decision makers (DMs). In this paper, firstly, we give the basic definition and operational laws of q-RONFNs, propose two related operators to aggregate evaluation information from DMs, and develop an extended indifference threshold-based attribute ratio analysis (ITARA) method to calculate attribute weights. Then considering the multi-attributive border approximation area comparison (MABAC) method has strong stability, we combine MABAC with q-RONFNs, put forward the q-RONFNs-MABAC method, and give the concrete decision steps. Finally, we apply the q-RONFNs-MABAC method to solve two examples, and prove the effectiveness and practicability of our proposed method through comparative analysis.

Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators

2020 ◽  
Vol 39 (3) ◽  
pp. 4427-4441
Author(s):  
Bin Xu
Keyword(s):  
Network Security ◽  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Computer Network ◽  
Information Aggregation ◽  
Security Evaluation ◽  
Uncertain Information ◽  
Intuitionistic Fuzzy ◽  
Computer Network Security

The concept of fuzzy number intuitionistic fuzzy sets (FNIFSs) is designed to effectively depict uncertain information in decision making problems which fundamental characteristic of the FNIFS is that the values of its membership function and non-membership function are depicted with triangular fuzzy numbers (TFNs). The dual Hamy mean (DHM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this paper, we used the dual Hamy mean (DHM) operator and dual weighted Hamy mean (WDHM) operator with fuzzy number intuitionistic fuzzy numbers (FNIFNs) to propose the fuzzy number intuitionistic fuzzy dual Hamy mean (FNIFDHM) operator and fuzzy number intuitionistic fuzzy weighted dual Hamy mean (FNIFWDHM) operator. Then the MADM methods are proposed along with these operators. In the end, we utilize an applicable example for computer network security evaluation to prove the proposed methods.

scholarly journals Multi Objective Multi Mode Project Management Problem in Triangular Fuzzy Environment

2020 ◽  
Vol 9 (2) ◽  
pp. 1772-1781
Keyword(s):  
Project Management ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Decision Makers ◽  
Programming Approach ◽  
Management Problem ◽  
Linguistic Variables ◽  
Multi Objective ◽  
Fuzzy Environment ◽  
Multi Mode

Execution of any project with optimum duration, cost, quality and risk is very significant for project administrators in recent very competitive commercial situation. Sometimes it is not possible to have detailed earlier statistics about project criteria. In such situations, estimation of different Decision makers are considered in linguistic variables and altered into triangular fuzzy numbers as fuzzy numbers have ability to deal with vagueness. In this paper, we frame a new multi-mode multi objective critical path problem and suggest a possibilistic methodology to find critical path for a project where three decision makers’ views are considered as three modes of execution in terms of linguistic variables. We have formulated model of multiple mode in project network problem and find its solution with fuzzy programming approach with exponential membership and linear membership function. The proposed approach is useful to solve multi-mode project management problem which calculates optimal critical path according to four criteria- time, cost, risk and quality with three activities modes of execution in fuzzy environment.

scholarly journals Possibilistic Distribution for Selection of Critical Path in Multi Objective Multi-Mode Problem with Trapezoidal Fuzzy Number

2019 ◽  
Vol 8 (4) ◽  
pp. 10833-10842
Keyword(s):  
Fuzzy Numbers ◽  
Critical Path ◽  
Fuzzy Programming ◽  
Decision Makers ◽  
Programming Approach ◽  
Management Problem ◽  
Linguistic Variables ◽  
Multi Objective ◽  
Fuzzy Environment ◽  
Multi Mode

Execution of any project with optimum duration, cost, quality and risk is very significant for project administrators in recent very competitive commercial situation. Sometimes it is not possible to have detailed earlier statistics about project criteria. In such situations, estimation of different Decision makers are considered in linguistic variables and altered into triangular fuzzy numbers as fuzzy numbers have ability to deal with vagueness. In this paper, we frame a new multi-mode multi objective critical path problem and suggest a possibilistic methodology to find critical path for a project where three decision makers’ views are considered as three modes of execution in terms of linguistic variables. In this paper have formulated model of multiple mode in project network problem and find its solution with fuzzy programming approach with exponential membership and linear membership function. The proposed approach is useful to solve multi-mode project management problem which calculates optimal critical path according to four criteria- time, cost, risk and quality with three activities modes of execution in fuzzy environment

A GMCDM approach with linguistic Z-numbers based on TOPSIS and Choquet integral considering risk preference

2020 ◽  
Vol 39 (3) ◽  
pp. 4285-4298
Author(s):  
Ran Tao ◽  
Fuyuan Xiao
Keyword(s):  
Decision Making ◽  
Supplier Selection ◽  
Choquet Integral ◽  
Risk Preference ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Uncertain Information ◽  
Human Knowledge ◽  
Mcdm Method ◽  
Evaluation Information

Group multi-criteria decision-making (GMCDM) is an important part of decision theory, which is aimed to assess alternatives according to multiple criteria by collecting the wisdom of experts. However, in the process of evaluating, because of the limitation of human knowledge and the complexity of problems, an efficient GMCDM approach under uncertain environment still need to be further explored. Thus, in this paper, a novel GMCDM approach with linguistic Z-numbers based on TOPSIS and Choquet integral is proposed. Firstly, since linguistic Z-numbers performs better in coping with uncertain information, it is used to express the evaluation information. Secondly, TOPSIS, one of the most useful and systematic multi-criteria decision-making (MCDM) method, is adopted as the framework of the proposed approach. Thirdly, frequently it exists interaction between criteria, so Choquet integral is introduced to capture this kind of influence. What’s more, viewing that decision makers (DMs) show different preferences for uncertainty, the risk preference is regarded as a vital parameter when calculating the score of linguistic Z-numbers. An application in supplier selection is illustrated to demonstrate the effectiveness of the proposed approach. Finally, a further comparison and discussion of the proposed GMCDM method is given.

scholarly journals Some q-Rung Picture Fuzzy Dombi Hamy Mean Operators with Their Application to Project Assessment

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 468 ◽  
Author(s):  
Jiahuan He ◽  
Xindi Wang ◽  
Runtong Zhang ◽  
Li Li
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Project Assessment ◽  
Fuzzy Environment ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation

The recently proposed q-rung picture fuzzy set (q-RPFSs) can describe complex fuzzy and uncertain information effectively. The Hamy mean (HM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this study, we extend HM to q-rung picture fuzzy environment, propose novel q-rung picture fuzzy aggregation operators, and demonstrate their application to multi-attribute group decision-making (MAGDM). First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules of q-rung picture fuzzy numbers (q-RPFNs). Second, we propose some new aggregation operators of q-RPFNs based on the newly-developed operations, i.e., the q-rung picture fuzzy Dombi Hamy mean (q-RPFDHM) operator, the q-rung picture fuzzy Dombi weighted Hamy mean (q-RPFDWHM) operator, the q-rung picture fuzzy Dombi dual Hamy mean (q-RPFDDHM) operator, and the q-rung picture fuzzy Dombi weighted dual Hamy mean (q-RPFDWDHM) operator. Properties of these operators are also discussed. Third, a new q-rung picture fuzzy MAGDM method is proposed with the help of the proposed operators. Finally, a best project selection example is provided to demonstrate the practicality and effectiveness of the new method. The superiorities of the proposed method are illustrated through comparative analysis.

A Multi-Criteria Intuitionistic Fuzzy Group Decision Making Method for Supplier Selection with VIKOR Method

2012 ◽  
Vol 2 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Razieh Roostaee ◽  
Mohammad Izadikhah ◽  
Farhad Hosseinzadeh Lotfi ◽  
Mohsen Rostamy-Malkhalifeh
Keyword(s):  
Decision Making ◽  
Supplier Selection ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Decision Makers ◽  
Uncertain Information ◽  
Vikor Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Right

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain, and is typically a multi-criteria group decision problem. In many practical situations, there usually exists incomplete and uncertain information, and the decision makers cannot easily express their judgments on the candidates with exact and crisp values. Therefore, in this paper an extended VIKOR method for group decision making with intuitionistic fuzzy numbers is proposed to solve the supplier selection problem under incomplete and uncertain information environment. In other researches in this area, the weights of each decision makers and in many of them the weights of criteria are pre-determined, but these weights have been calculated in this paper by using the decision matrix of each decision maker. Also, normalized Hamming distance is proposed to calculate the distance between intuitionistic fuzzy numbers. Finally, a numerical example for supplier selection is given to clarify the main results developed in this paper.

scholarly journals Multiattribute Decision Making Method Based on Intuitionistic Linguistic Aggregation Operator

2016 ◽  
Vol 4 (6) ◽  
pp. 574-586
Author(s):  
Jing Chen ◽  
Zhongxing Wang
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Uncertain Information ◽  
Real Numbers ◽  
Distribution Law ◽  
Attribute Weights ◽  
Weighted Arithmetic ◽  
Averaging Operator ◽  
Operational Laws ◽  
Arithmetic Averaging Operator

AbstractIn this paper, some new operational laws for intuitionistic linguistic numbers are defined via Archimedean t-norm and s-norm. The prominent feature of these operations is that these operations are closed. Some main properties of these operations, like commutativity, associativity and distribution law, are investigated. Based on these operational laws, intuitionistic linguistic weighted arithmetic averaging operator is given to aggregate intuitionistic linguistic information. Furthermore, in order to reduce uncertain information of intuitionistic linguistic number, hesitancy degree is divided into degrees of membership and non-membership in proportions, and new expected function and score function are built and used to rank intuitionistic linguistic numbers. Finally, an approach is proposed to solve multiattribute decision making problems in which attribute weights are real numbers and attribute values are intuitionistic linguistic numbers, and a real example is provided to show the effectiveness and applicability of the new method.

Appraisement and benchmarking of supply chain performance extent

2015 ◽  
Vol 5 (1) ◽  
pp. 2-30 ◽  
Author(s):  
Santosh Kumar Sahu ◽  
Saurav Datta ◽  
Siba Sankar Mahapatra
Keyword(s):  
Decision Making ◽  
Supply Chain ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Supply Chain Performance ◽  
Triangular Fuzzy Numbers ◽  
Subjective Judgment ◽  
Content Type ◽  
Grey Relation ◽  
Evaluation Information

Purpose – Supply chain performance (SCP) extent can be attributed as a function of multiple criteria/attributes. Most of the criterions/attributes being intangible in nature; SCP appraisement relies on the subjective judgment of the decision makers. Moreover, quantitative appraisement of SCP appears to be very difficult due to involvement of ill-defined (vague) performance measures as well as metrics. The purpose of this paper is to develop an efficient decision support system (DSS) to facilitate SCP appraisement, benchmarking and related decision making. Design/methodology/approach – This study explores the concept of fuzzy logic in order to tackle incomplete and inconsistent subjective judgment of the decision makers’ whilst evaluating supply chain’s overall performance. Grey relational analysis has been adopted in the later stage to derive appropriate ranking of alternative companies/enterprises (in the same industry) in view of ongoing SCP extent. Findings – In this work, a performance appraisement index system has been postulated to gather evaluation information (weights and ratings) in relation to SCP measures and metrics. Combining the concepts of fuzzy set theory, entropy, ideal and grey relation analysis, a fuzzy grey relation method for SCP benchmarking problem has been presented. First, triangular fuzzy numbers and linguistic evaluation information characterized by triangular fuzzy numbers have been used to evaluate the importance weights of all criteria and the superiority of all alternatives vs various criteria above the alternative level. Then, the concept of entropy has been utilized to solve the adjusted integration weight of all objective criteria above the alternative level. Moreover, using the concept of the grey ration grades, various alternatives have been ranked accordingly. Originality/value – Finally, an empirical example of selecting most appropriate company has been used to demonstrate the ease of applicability of the aforesaid approach. The study results showed that this method appears to be an effective means for tackling multi-criteria decision-making problems in uncertain environments. Empirical data have been analysed and results obtained thereof, have been reported to exhibit application potential of the said fuzzy grey relation based DSS in appropriate situation.

RANKING-INTUITIONISTIC FUZZY NUMBERS

2004 ◽  
Vol 12 (03) ◽  
pp. 377-386 ◽  
Author(s):  
H. B. MITCHELL
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Sets ◽  
Test Cases ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Statistical Viewpoint

Intuitionistic fuzzy sets are a generalization of ordinary fuzzy sets which are characterized by a membership function and a non-membership function. In this paper we consider the problem of ranking a set of intuitionistic fuzzy numbers. We adopt a statistical viewpoint and interpret each intuitionistic fuzzy number as an ensemble of ordinary fuzzy numbers. This enables us to define a fuzzy rank and a characteristic vagueness factor for each intuitionistic fuzzy number. We show the reasonablesness of the results obtained by examining several test cases.

scholarly journals Extended TOPSIS Method for Supplier Selection under Picture Hesitant Fuzzy Environment Using Linguistic Variables

2021 ◽  
Vol 2021 ◽  
pp. 1-28
Author(s):  
Rabia Ambrin ◽  
Muhammad Ibrar ◽  
Manuel De La Sen ◽  
Ihsan Rabbi ◽  
Asghar Khan
Keyword(s):  
Fuzzy Numbers ◽  
Fuzzy Topsis ◽  
Vital Role ◽  
Decision Makers ◽  
Linguistic Variables ◽  
Comparison Analysis ◽  
Topsis Method ◽  
Practical Applications ◽  
Fuzzy Environment ◽  
Intuitionistic Fuzzy Topsis

The main purpose of this planned manuscript is to establish an algorithm for the solution of multiattribute decision-making (MADM) issues, where the experts utilizing linguistic variables provide the information about attributes in the form of picture hesitant fuzzy numbers. So, for the solution of these kinds of issues, we develop the TOPSIS algorithm under picture hesitant fuzzy environment using linguistic variables, which plays a vital role in practical applications, notably MADM issues, where the decision information is arranged by the decision-makers (DMs) in the form of picture hesitant fuzzy numbers. Finally, a sample example is given as an application and appropriateness of the planned method. At the end, we conduct comparison analysis of the planned method with picture fuzzy TOPSIS method and intuitionistic fuzzy TOPSIS method.

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