The logarithmic operational laws of intuitionistic fuzzy sets and intuitionistic fuzzy numbers

2017 ◽  
Vol 33 (6) ◽  
pp. 3241-3253 ◽  
Author(s):  
Zehua Li ◽  
Fuyi Wei
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operational Laws

scholarly journals A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers

2010 ◽  
Vol 2010 ◽  
pp. 1-25 ◽  
Author(s):  
Debashree Guha ◽  
Debjani Chakraborty
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Theoretical Development ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Intuitionistic Fuzzy

The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones.

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 Intuitionistic Fuzzy Sets in Multi-Criteria Group Decision Making Problems Using the Characteristic Objects Method

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1382 ◽  
Author(s):  
Shahzad Faizi ◽  
Wojciech Sałabun ◽  
Tabasam Rashid ◽  
Sohail Zafar ◽  
Jarosław Wątróbski
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Uncertain Data ◽  
Research Area ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy

Over the past few decades, several researchers and professionals have focused on the development and application of multi-criteria group decision making (MCGDM) methods under a fuzzy environment in different areas and disciplines. This complex research area has become one of the more popular topics, and it seems that this trend will be increasing. In this paper, we propose a new MCGDM approach combining intuitionistic fuzzy sets (IFSs) and the Characteristic Object Method (COMET) for solving the group decision making (GDM) problems. The COMET method is resistant to the rank reversal phenomenon, and at the same time it remains relatively simple and intuitive in practical problems. This method can be used for both symmetric and asymmetric information. The Triangular Intuitionistic Fuzzy Numbers (TIFNs) have been used to handle uncertain data. This concept can ensure the preference information about an alternative under specific criteria more comprehensively and allows for easy modelling of symmetrical or asymmetrical linguistic values. Each expert provides the membership and non-membership degree values of intuitionistic fuzzy numbers (IFNs). So this approach deals with a different kind of uncertainty than with hesitant fuzzy sets (HFSs). The proposed combination of COMET and IFSs required an adaptation of the matrix of expert judgment (MEJ) and allowed to capture the behaviour aspects of the decision makers (DMs). Therefore, we get more reliable solutions while solving MCGDM problems. Finally, the proposed method is presented in a simple academic example.

scholarly journals Attributes Weight Determination in Magdm Problems using Some Numerical Method Techniques

2019 ◽  
Vol 8 (6S4) ◽  
pp. 1502-1505
Keyword(s):  
Fuzzy Sets ◽  
Numerical Method ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy Numbers ◽  
Attribute Weight ◽  
Intuitionistic Fuzzy ◽  
Weight Data ◽  
Magdm Problems ◽  
Combined Matrix

Here MAGDM problems are explored. Attribute weight data given are in the form of problems involving numerical method solutions. The decision information during this study is in the shape of Intuitionistic Fuzzy Numbers (IFNs) derived from Intuitionistic Fuzzy Sets (IFSs). The IFOWA operator and IFHA operator are used for collecting the combined matrix. The modified Euler-Cauchy method and Heun method are used to calculate the unidentified weights. Effectiveness of the projected method is established using Numerical Illustrations.

scholarly journals Preference Attitude-Based Method for Ranking Intuitionistic Fuzzy Numbers and Its Application in Renewable Energy Selection

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Jian Lin ◽  
Fanyong Meng ◽  
Riqing Chen ◽  
Qiang Zhang
Keyword(s):  
Renewable Energy ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Sets ◽  
Ranking Method ◽  
Ranking Methods ◽  
Score Functions ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Feasible Domain

Many applications of intuitionistic fuzzy sets depend on ranking or comparing intuitionistic fuzzy numbers. This paper presents a novel ranking method for intuitionistic fuzzy numbers based on the preference attitudinal accuracy and score functions. The proposed ranking method considers not only the preference attitude of decision maker, but also all the possible values in feasible domain. Some desirable properties of preference attitudinal accuracy and score functions are verified in detail. A total order on the set of intuitionistic fuzzy numbers is established by using the proposed two functions. The proposed ranking method is also applied to select renewable energy. The advantage and validity of the proposed method are shown by comparing with some representative ranking methods.

A noval ranking approach based on incircle of triangular intuitionistic fuzzy numbers

2020 ◽  
Vol 39 (5) ◽  
pp. 6271-6278
Author(s):  
Gultekin Atalik ◽  
Sevil Senturk
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Fuzzy Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Linear Programming Problems ◽  
Relationship Of ◽  
Ranking Of Fuzzy Numbers

Since proposed by Zadeh in 1965, ordinary fuzzy sets help us to model uncertainty and developed many types such as type 2 fuzzy, intuitionistic fuzzy, hesitant fuzzy etc. Intuitionistic fuzzy sets include both membership and non-membership functions for their each element. Ranking of a number is to identify a relationship of scalar quantity between these numbers. Ranking of fuzzy numbers play an important role in modeling problems such as fuzzy decision making, fuzzy linear programming problems. In this study, a new ranking method for triangular intuitionistic fuzzy numbers is proposed. The method based on the incircle of the membership function and non-membership function of TIFN uses lexicographical order to rank intuitionistic fuzzy numbers. Two examples are provided to illustrate the applicability of the method. Also, a comparative study is performed to demonstrate the validity of the proposed method. The results indicate that proposed method is consistent with other methods in the literature. Also, the method overcomes the problems such as numbers being very small or close to each other.

scholarly journals Inclusion of uncertainty with different types of fuzzy numbers into DEMATEL

2021 ◽  
Vol 16 (1) ◽  
pp. 49-59
Author(s):  
Tjaša Šmidovnik ◽  
Petra Grošelj
Keyword(s):  
Complex System ◽  
Decision Making ◽  
Fuzzy Sets ◽  
Construction Projects ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Different Types

Nowadays the multi-criteria decision making is very complicated due to uncertainty, vagueness, limited sources, knowledge and time. The Decision-making Trial and Evaluation Laboratory (DEMATEL) method is a widely used multi-criteria decision-making method to analyze the structure of a complex system. It is useful in analysing the cause and effect relationships between the components of the system. Fuzzy sets can be used to include uncertainty in multi-criteria decision making. Linguistic assessments of decision makers can be translated into fuzzy numbers. In this study, fuzzy numbers, intuitionistic fuzzy numbers and neutrosophic fuzzy numbers were used for the decision makers evaluations in the DEMATEL method. The aim of this study was to evaluate how different types of fuzzy numbers affect the final results. An application of risk in construction projects was selected from the literature, where seven experts used a linguistic scale to evaluate different criteria. The results showed that there are only slight differences between the weights of the criteria with regard to the type of fuzzy numbers.

scholarly journals Some New Logarithmic Aggregation Operators and their Application to Group Decision Making Problem Based on t-Norm and t-Conorm

2021 ◽  
Author(s):  
khaista Rahman
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Weighted Averaging ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Decision Making Problem ◽  
Algebraic Operators

Abstract In this paper, a logarithmic operational law for intuitionistic fuzzy numbers is defined, in which the based1 is a real number such that1 ∈(0,1) with condition1 ≠ 1. Some properties of logarithmic operational laws have been studied and based on these, several Einstein averaging and Einstein geometric operators namely, logarithmic intuitionistic fuzzy Einstein weighted averaging (LIFEWA) operator, logarithmic intuitionistic fuzzy Einstein ordered weighted averaging (LIFEOWA) operator, logarithmic intuitionistic fuzzy Einstein hybrid averaging (LIFEHA) operator, logarithmic intuitionistic fuzzy Einstein weighted geometric (LIFEWG) operator, logarithmic intuitionistic fuzzy Einstein ordered weighted geometric (LIFEOWG) operator, and logarithmic intuitionistic fuzzy Einstein hybrid geometric (LIFEHG) operator have been introduced, which can overcome the weaknesses of algebraic operators. Furthermore, based on the proposed operators a multi-attribute group decision-making problem is established under logarithmic operational laws. Finally, an illustrative example is used to illustrate the applicability and validity of the proposed approach and compare the results with the existing methods to show the effectiveness of it.

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