Intuitionistic Fuzzy Measures of Correlation Coefficient of Intuitionistic Fuzzy Numbers Under Weakest Triangular Norm

2019 ◽  
Vol 8 (1) ◽  
pp. 48-64 ◽  
Author(s):  
Mohit Kumar
Keyword(s):  
Correlation Coefficient ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Fuzzy Arithmetic ◽  
Triangular Norm ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Technology Level

The correlation coefficient of variables has wide applications in statistics and is often calculated in crisp or fuzzy environment. This article extends the application of correlation coefficient to intuitionistic fuzzy environment. In this article, a new method is proposed to measure the correlation coefficient of intuitionistic fuzzy numbers using weakest triangular norm based intuitionistic fuzzy arithmetic operations. Different from previous studies, the correlation coefficient computed in this article is an intuitionistic fuzzy number rather than a crisp or fuzzy number. It is well known that the weakest t-norm arithmetic operations effectively reduce fuzzy spreads (fuzzy intervals) and provide more exact results. Therefore, a simplified, effective and exact method based on weakest t-norm arithmetic operations is presented to compute the correlation coefficient of intuitionistic fuzzy numbers. To illustrate the proposed method, the correlation coefficient between the technology level and management achievement from a sample of 15 machinery firms in Taiwan is calculated using proposed approach.

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.

A Novel Ranking Approach to Solving Fully LR-Intuitionistic Fuzzy Transportation Problems

2018 ◽  
Vol 15 (01) ◽  
pp. 95-112 ◽  
Author(s):  
Abhishekh ◽  
A. K. Nishad
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Ranking Functions ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Fuzzy Transportation Problem

To the extent of our knowledge, there is no method in fuzzy environment to solving the fully LR-intuitionistic fuzzy transportation problems (LR-IFTPs) in which all the parameters are represented by LR-intuitionistic fuzzy numbers (LR-IFNs). In this paper, a novel ranking function is proposed to finding an optimal solution of fully LR-intuitionistic fuzzy transportation problem by using the distance minimizer of two LR-IFNs. It is shown that the proposed ranking method for LR-intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied ranking approach to solve an LR-intuitionistic fuzzy transportation problem in which all the parameters (supply, cost and demand) are transformed into LR-intuitionistic fuzzy numbers. The proposed method is illustrated with a numerical example to show the solution procedure and to demonstrate the efficiency of the proposed method by comparison with some existing ranking methods available in the literature.

scholarly journals On statistical convergent sequence spaces of intuitionistic Fuzzy numbers

2018 ◽  
Vol 36 (1) ◽  
pp. 235 ◽  
Author(s):  
Shyamal Debnath ◽  
Vishnu Narayan Mishra ◽  
Jayanta Debnath
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Inclusion Relations ◽  
Bounded Sequences

In the present paper we introduce the classes of sequence stcIFN, stc0IFN and st∞IFN of statistically convergent, statistically null and statistically bounded sequences of intuitionistic fuzzy number based on the newly defined metric on the space of all intuitionistic fuzzy numbers (IFNs). We study some algebraic and topological properties of these spaces and prove some inclusion relations too.

scholarly journals EXPERT ESTIMATES AVERAGING BY CONSTRUCTING INTUITIONISTIC FUZZY TRIANGLES

2015 ◽  
Vol 20 (3) ◽  
pp. 409-421 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Natalja Kosareva
Keyword(s):  
Decision Making ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Fuzzy Numbers ◽  
Fuzzy Arithmetic ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Probability Matrices

The problem of ranking (sorting) of m alternatives is considered when experts evaluate each alternative according to k criteria. Functions of arithmetic and geometric averages are constructed for decision making. We present a generalization of this scheme when there are evaluation matrices of several experts and this information is aggregated in the form of triangular intuitionistic fuzzy numbers. Fuzzy triangles were constructed with different uncertainty levels, experts decision matrices and the number of experts varied from 2 to 5. Moreover, method for construction of experts decision probability matrices is proposed in the paper. Ranking results obtained by performing Monte Carlo simulations. Probabilities of errors are compared for arithmetic, geometric, fuzzy arithmetic and fuzzy geometric averages.

scholarly journals A Value and Ambiguity-Based Ranking Method of Trapezoidal Intuitionistic Fuzzy Numbers and Application to Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xiang-tian Zeng ◽  
Deng-feng Li ◽  
Gao-feng Yu
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Implementation Process ◽  
Ranking Method ◽  
Comparison Analysis ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
A Value ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

The aim of this paper is to develop a method for ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) in the process of decision making in the intuitionistic fuzzy environment. Firstly, the concept of TrIFNs is introduced. Arithmetic operations and cut sets over TrIFNs are investigated. Then, the values and ambiguities of the membership degree and the nonmembership degree for TrIFNs are defined as well as the value-index and ambiguity-index. Finally, a value and ambiguity-based ranking method is developed and applied to solve multiattribute decision making problems in which the ratings of alternatives on attributes are expressed using TrIFNs. A numerical example is examined to demonstrate the implementation process and applicability of the method proposed in this paper. Furthermore, comparison analysis of the proposed method is conducted to show its advantages over other similar methods.

scholarly journals Group Replacement Strategy under Fuzzy Methods

2019 ◽  
Vol 9 (1S5) ◽  
pp. 250-254
Keyword(s):  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Active Role ◽  
Replacement Policy ◽  
Replacement Strategy ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Methods ◽  
Fuzzy Environment

Intuitionistic Fuzzy Numbers play an active role in finding an optimal solution for replacement problems under vague and uncertain situations. This paper gives a group replacement policy under fuzzy environment. Here all the costs and the number of units are taken as Triangular Intuitionistic Fuzzy Numbers (TIFNs). An example is used for illustration of the policy

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