A New Method for Ranking Canonical Intuitionistic Fuzzy Numbers

2013 ◽  
pp. 609-616 ◽  
Author(s):  
Zuming Peng ◽  
Qiang Chen
Keyword(s):  
Fuzzy Numbers ◽  
New Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy

A New Method for Ranking Intuitionistic Fuzzy Numbers

2011 ◽  
Vol 2 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Cui-Ping Wei ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Ranking Method ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Additional Information ◽  
Intuitionistic Fuzzy ◽  
Possibility Degree

In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making problems.

A New Method for Ranking Intuitionistic Fuzzy Numbers

2013 ◽  
pp. 45-51
Author(s):  
Cui-Ping Wei ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Ranking Method ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Additional Information ◽  
Intuitionistic Fuzzy ◽  
Possibility Degree

In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making problems.

scholarly journals A Simple Method for Solving Fully Intuitionistic Fuzzy Real Life Assignment Problem

2016 ◽  
Vol 7 (2) ◽  
pp. 39-61 ◽  
Author(s):  
P. Senthil Kumar ◽  
R. Jahir Hussain
Keyword(s):  
Assignment Problem ◽  
Fuzzy Numbers ◽  
Graphical Representation ◽  
Real Life ◽  
New Method ◽  
Simple Method ◽  
Optimal Cost ◽  
Intuitionistic Fuzzy Numbers ◽  
Numerical Example ◽  
Intuitionistic Fuzzy

In solving real life assignment problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representations for the data. So, in this paper, the authors consider the assignment problem having uncertainty and hesitation in cost/time/profit. They formulate the problem and utilize triangular intuitionistic fuzzy numbers (TIFNs) to deal with uncertainty and hesitation. The authors propose a new method called PSK (P.Senthil Kumar) method for finding the intuitionistic fuzzy optimal cost/time/profit for fully intuitionistic fuzzy assignment problem (FIFAP). The proposed method gives the optimal object value in terms of TIFN. The main advantage of this method is computationally very simple, easy to understand. Finally the effectiveness of the proposed method is illustrated by means of a numerical example which is followed by graphical representation of the finding.

scholarly journals Some Normal Intuitionistic Fuzzy Heronian Mean Operators Using Hamacher Operation and Their Application

2018 ◽  
Author(s):  
Guofang Zhang ◽  
Zhiming Zhang ◽  
Hang Kong
Keyword(s):  
Decision Making ◽  
Normal Distribution ◽  
Fuzzy Numbers ◽  
New Method ◽  
Arithmetical Operation ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Einstein Operation ◽  
Heronian Mean

Hamacher operation which is generalization of the Algebraic and Einstein operation, can widely provide a large number of arithmetical operation with respect to uncertainty information, and Heronian mean can deal with correlations of the input arguments or different criteria and don’t make calculation redundancy, meanwhile, the normal intuitionistic fuzzy numbers (NIFNs) can depict distinctively normal distribution information in practical decision making. In this paper, a multi-criteria group decision-making (MCGDM) problem is researched under the NIFNs environment, and a new MCGDM approach is introduced on the basis of the Hamacher operation. Firstly, according to Hamacher t-conorm and t-norm, some operational laws of NIFNs are presented. Secondly, it is noticed that Heronian mean can’t only once take into account mutual relation between attribute values once, but also consider the correlation between input argument and itself. Therefore, we develop some operators and study their properties in order to aggregate normal intuitionistic fuzzy numbers information, these operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM) and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we apply the proposed operators to the MCGDM problem and present a new method. The main characteristics of this new method involve that: (1) it is suitable to make decision under the normal intuitionistic fuzzy numbers environment and more reliable and reasonable to aggregate the normal distribution information. (2) it utilizes Hamacher operation which can provide more reliable and flexible decision-making results and offer an effective and powerful mathematic tool for the MAGDM under uncertainty. (3) it uses the Heronian mean operator which can considers relationships between the input arguments or the attributes and don’t brings subsequently about redundancy. Lastly, an application is given for showing the feasibility and effectiveness of the presented method in this paper.

scholarly journals A New Method for Ranking of Intuitionistic Fuzzy Numbers

2011 ◽  
Vol 3 (6) ◽  
pp. 1-2 ◽  
Author(s):  
S. Sagaya Roseline ◽  
◽  
E. C. Henry Amirtharaj
Keyword(s):  
Fuzzy Numbers ◽  
New Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy

Interval-valued intuitionistic fuzzy multiple attribute decision making and their applications

2021 ◽  
Vol 25 (2) ◽  
pp. 251-277
Author(s):  
Hong-Jun Wang
Keyword(s):  
Supplier Selection ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Green Supply Chain Management ◽  
Green Supply Chain ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operator Interval ◽  
Multiple Attribute ◽  
Interval Valued

In this paper, we expand the Muirhead mean (MM) operator and dual Muirhead mean (DMM) operator with interval-valued intuitionistic fuzzy numbers (IVIFNs) to propose the interval -valued intuitionistic fuzzy Muirhead mean (IVIFMM) operator, interval-valued intuitionistic fuzzy weighted Muirhead mean (IVIFWMM) operator, interval-valued intuitionistic fuzzy dual Muirhead mean (IVIFDMM) operator and interval-valued intuitionistic fuzzy weighted dual Muirhead mean (IVIFWDMM) operator. Then the MADM methods are proposed with these operators. In the end, we utilize an applicable example for green supplier selection in green supply chain management to prove the proposed methods.

scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

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