scholarly journals MADM Problems with Correlation Coefficient of Trapezoidal Fuzzy Intuitionistic Fuzzy Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
John Robinson ◽  
Henry Amirtharaj
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Intuitionistic Fuzzy Sets ◽  
Weighted Averaging ◽  
Arithmetic Operations ◽  
Numerical Illustration ◽  
Intuitionistic Fuzzy

This paper discusses on the notion of trapezoidal fuzzy intuitionistic fuzzy sets (TzFIFSs) and some of the arithmetic operations of the same. Correlation coefficient of TzFIFS is proposed based on the membership, nonmembership, and hesitation degrees. The weighted averaging (WA) operator and the weighted geometric (WG) operator are proposed for TzFIFSs. Based on these operators and the correlation coefficient defined for the TzFIFS, new multiattribute decision making (MADM) models are proposed and numerical illustration is given.

Extended TOPSIS with Correlation Coefficient of Triangular Intuitionistic Fuzzy Sets for Multiple Attribute Group Decision Making

2011 ◽  
Vol 3 (3) ◽  
pp. 15-41 ◽  
Author(s):  
John Robinson P. ◽  
Henry AmirtharajE. C.
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Weighted Averaging ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Magdm Problems

This paper extends the technique for order preference by similarity to ideal solution (TOPSIS) for solving multi-attribute group decision making (MAGDM) problems under triangular intuitionistic fuzzy sets by using its correlation coefficient. In situations where the information or the data is of the form of triangular intuitionistic fuzzy numbers (TIFNs), some arithmetic aggregation operators have to be defined, namely the triangular intuitionistic fuzzy ordered weighted averaging (TIFOWA) operator and the triangular intuitionistic fuzzy hybrid aggregation (TIFHA) operator. An extended TOPSIS model is developed to solve the MAGDM problems using a new type of correlation coefficient defined for TIFNs based on the triangular intuitionistic fuzzy weighted arithmetic averaging (TIFWAA) operator and the TIFHA operator. With an illustration this proposed model of MAGDM with the correlation coefficient of TIFNs is compared with the other existing methods.

Vague Correlation Coefficient of Interval Vague Sets and its Applications to Topsis in MADM Problems

2014 ◽  
pp. 140-173
Author(s):  
John Robinson P. ◽  
Henry Amirtharaj E. C.
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Intuitionistic Fuzzy Sets ◽  
New Method ◽  
Numerical Illustration ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Statistical Confidence ◽  
Order Preference ◽  
Novel Method

Various attempts are made by researchers on the study of vagueness of data through Intuitionistic Fuzzy sets and Vague sets, and also it is shown that Vague sets are Intuitionistic Fuzzy sets. However, there are algebraic and graphical differences between Vague sets and Intuitionistic Fuzzy sets. In this chapter, an attempt is made to define the correlation coefficient of Interval Vague sets lying in the interval [0,1], and a new method for computing the correlation coefficient of interval Vague sets lying in the interval [-1,1] using a-cuts over the vague degrees through statistical confidence intervals is also presented by an example. The new method proposed in this work produces a correlation coefficient in the form of an interval. The proposed method produces a correlation coefficient in the form of an interval from a trapezoidal shaped fuzzy number derived from the vague degrees. This chapter also aims to develop a new method based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to solve MADM problems for Interval Vague Sets (IVSs). A TOPSIS algorithm is constructed on the basis of the concepts of the relative-closeness coefficient computed from the correlation coefficient of IVSs. This novel method also identifies the positive and negative ideal solutions using the correlation coefficient of IVSs. A numerical illustration explains the proposed algorithms and comparisons are made with some existing methods.

New Einstein Hybrid Aggregation Operators for Intuitionistic Fuzzy Sets and Applications in Multi-Criteria Decision-Making

2019 ◽  
pp. 252-283
Author(s):  
Bhagawati Prasad Joshi ◽  
Abhay Kumar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Decision Maker ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Processes

The fusion of multidimensional intuitionistic fuzzy information plays an important part in decision making processes under an intuitionistic fuzzy environment. In this chapter, it is observed that existing intuitionistic fuzzy Einstein hybrid aggregation operators do not follow the idempotency and boundedness. This leads to sometimes illogical and even absurd results to the decision maker. Hence, some new intuitionistic fuzzy Einstein hybrid aggregation operators such as the new intuitionistic fuzzy Einstein hybrid weighted averaging (IFEHWA) and the new intuitionistic fuzzy Einstein hybrid weighted geometric (IFEHWG) were developed. The new IFEHWA and IFEHWG operators can weigh the arguments as well as their ordered positions the same as the intuitionistic fuzzy Einstein hybrid aggregation operators do. Further, it is validated that the defined operators are idempotent, bounded, monotonic and commutative. Then, based on the developed approach, a multi-criteria decision-making (MCDM) procedure is given. Finally, a numerical example is conducted to demonstrate the proposed method effectively.

Vague Correlation Coefficient of Interval Vague Sets and its Applications to Topsis in MADM Problems

Fuzzy Systems ◽  
2017 ◽  
pp. 1110-1149
Author(s):  
John Robinson P. ◽  
Henry Amirtharaj E. C.
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Intuitionistic Fuzzy Sets ◽  
New Method ◽  
Numerical Illustration ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Statistical Confidence ◽  
Order Preference ◽  
Novel Method

Various attempts are made by researchers on the study of vagueness of data through Intuitionistic Fuzzy sets and Vague sets, and also it is shown that Vague sets are Intuitionistic Fuzzy sets. However, there are algebraic and graphical differences between Vague sets and Intuitionistic Fuzzy sets. In this chapter, an attempt is made to define the correlation coefficient of Interval Vague sets lying in the interval [0,1], and a new method for computing the correlation coefficient of interval Vague sets lying in the interval [-1,1] using a-cuts over the vague degrees through statistical confidence intervals is also presented by an example. The new method proposed in this work produces a correlation coefficient in the form of an interval. The proposed method produces a correlation coefficient in the form of an interval from a trapezoidal shaped fuzzy number derived from the vague degrees. This chapter also aims to develop a new method based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to solve MADM problems for Interval Vague Sets (IVSs). A TOPSIS algorithm is constructed on the basis of the concepts of the relative-closeness coefficient computed from the correlation coefficient of IVSs. This novel method also identifies the positive and negative ideal solutions using the correlation coefficient of IVSs. A numerical illustration explains the proposed algorithms and comparisons are made with some existing methods.

Novel Correlation Coefficient for Intuitionistic Fuzzy Sets and Its Application to Multi-Criteria Decision-Making Problems

2021 ◽  
Vol 10 (2) ◽  
pp. 39-58
Author(s):  
Ejegwa Paul Augustine
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Intuitionistic Fuzzy Sets ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Generalized Correlation

Correlation coefficient is an essential measuring operator in an intuitionistic fuzzy environment use in solving MCDM problems. In this paper, Xu et al.'s correlation coefficient for IFSs is generalized for an improved output. The objectives of this work are to generalize the triparametric correlation coefficient for IFSs proposed by Xu et al. and unravel its applicability in some MCDM problems. The generalized correlation coefficient for IFSs is characterized with some number of results. Some numerical illustrations are supplied to validate the preeminence of the generalized correlation coefficient for IFSs over some existing correlation coefficient measures. In addition, some MCDM problems such as determination of suitable lecturer for course allocation and personnel promotion exercise captured in intuitionistic fuzzy pairs are discussed with the aid of the proposed correlation coefficient.

An Approach to Multiple Attribute Decision Making with Triangular Intuitionistic Fuzzy Information

2016 ◽  
Vol 13 (10) ◽  
pp. 7285-7288
Author(s):  
Jinping Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Construction Projects ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Multiple Attribute

The aim of this paper is to investigate the multiple attribute decision making problems with triangular intuitionistic fuzzy information. Some operational laws of triangular intuitionistic fuzzy sets, score functions of triangular intuitionistic fuzzy sets are introduced. Based on these operational laws, some Einstein aggregation operators, including triangular intuitionistic fuzzy Einstein weighted averaging (TIFEWA) operator, triangular intuitionistic fuzzy Einstein ordered weighted averaging (TIFEOWA) operator and triangular intuitionistic fuzzy Einstein hybrid aggregation (TIFEHA) operator, are proposed. An approach to multiple attribute decision making with triangular intuitionistic fuzzy information is developed based on the TIFEWA operator. Finally, an illustrative example for evaluating the construction projects quality with triangular intuitionistic fuzzy information is given to verify the developed approach.

Sign in / Sign up

Export Citation Format

Share Document