Ordering Of Intuitionistic Fuzzy Numbers Using Centroid Of Centroids Of Intuitionistic Fuzzy Number

2017 ◽  
Vol 52 (5) ◽  
pp. 276-287
Author(s):  
B.Pardha saradhi ◽  
◽  
M.V.Mad huri ◽  
N.Ravi Shankar
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy

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.

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.

Arithmetic Behaviors of P-Norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers with Application to Circuit Analysis

2017 ◽  
Vol 6 (3) ◽  
pp. 6-58
Author(s):  
Sanhita Banerjee ◽  
Tapan Kumar Roy
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Circuit Analysis ◽  
Extension Principle ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Given ◽  
Trapezoidal Intuitionistic Fuzzy Number ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

P-norm Generalized Trapezoidal Intuitionistic Fuzzy Number is the most generalized form of Fuzzy as well as Intuitionistic Fuzzy Number. It has a huge application while solving various problems in imprecise environment. In this paper the authors have discussed some basic arithmetic operations of p-norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers using two different methods (extension principle method and vertex method) and have solved a problem of circuit analysis taking the given data as p-norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers.

scholarly journals An unknown Transit technique for Solving Generalized Trapezoidal Intuitionistic Fuzzy Transportation Problems using Centroid of Centroids

2021 ◽  
Vol 12 (3) ◽  
pp. 5121-5128
Author(s):  
Indira Singuluri Et. al.
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Ranking Function ◽  
Intuitionistic Fuzzy Number ◽  
Numerical Illustration ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Trapezoidal Intuitionistic Fuzzy Number ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

In the present day by day life circumstances TP we habitually face the circumstance of unreliability in addition to unwillingness due to various unmanageable segments. To deal with unreliability and unwillingness multiple researchers have recommended the intuitionistic fuzzy (IF) delineation for material. This paper proposes the approach used by generalized trapezoidal intuitionistic fuzzy number to solve these transport problem, i.e. capacity and demand are considered as real numbers and charge of transport from origin to destination is considered as generalized trapezoidal intuitionistic fuzzy numbers as charge of product per unit. The generalized trapezoidal intuitionistic fuzzy numbers ranking function is used on the basis of IFN'S centroid of centroids. Through the traditional optimization process, we generate primary basic feasible solution and foremost solution. The numerical illustration shows efficacy of technique being suggested. A fresh technique is implemented to seek foremost solution using ranking function of a fuzzy TP of generalized trapezoidal intuitionistic fuzzy number. Without finding a IBFS, this approach explicitly provides optimal solution for GTrIFTP. Finally, for ranking function we apply a proposed GTrIFTP method illustrated Numerical example.

A METHOD FOR FINDING CRITICAL PATH WITH SYMMETRIC OCTAGONAL INTUITIONISTIC FUZZY NUMBERS

2020 ◽  
Vol 9 (11) ◽  
pp. 9273-9286
Author(s):  
N. Rameshan ◽  
D.S. Dinagar
Keyword(s):  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Membership Functions ◽  
Intuitionistic Fuzzy Number ◽  
Lower And Upper Bounds ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Membership Function

The concept of this paper represents finding fuzzy critical path using octagonal fuzzy number. In project scheduling, a new method has been approached to identify the critical path by using Symmetric Octagonal Intuitionistic Fuzzy Number (SYMOCINTFN). For getting a better solution, we use the fuzzy octagonal number rather than other fuzzy numbers. The membership functions of the earliest and latest times of events are by calculating lower and upper bounds of the earliest and latest times considering octagonal fuzzy duration. The resulting conditions omit the negative and infeasible solution. The membership function takes up an essential role in finding a new solution. Based on membership function, fuzzy number can be identified in different categories such as Triangular, Trapezoidal, pentagonal, hexagonal, octagonal, decagonal, hexa decagonal fuzzy numbers etc.

scholarly journals A Novel Method of Ranking Intuitionistic Fuzzy Numbers using Value and θ Multiple of Ambiguity at Flexibility Parameters

2021 ◽  
Author(s):  
Rituparna Chutia
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Number ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Novel Method ◽  
Flexibility Parameters

Abstract In this paper a novel method of ordering intuitionistic fuzzy numbers, based on the notions of ‘value’ and θ-multiple of ‘ambiguity’ of an intuitionistic fuzzy number, is developed. Further, the flexibility parameters, of decision-making at (α, β)-levels, are used in the method. These parameters allow the decision-maker to take decisions at various (α, β)-levels of decision-making. Many a times, all the reasonable properties of ranking intuitionistic fuzzy numbers were never checked in the existing studies. However, in this study an utmost attempt is being made to study the reasonable properties thoroughly. Further, the existing methods are mostly based on intuition and the geometry of the intuitionistic fuzzy numbers. However, the proposed method completely complies with the reasonable properties of ranking intuitionistic fuzzy numbers as well as the coherent intuition and the geometry of the intuitionistic fuzzy numbers. Further, newer properties are also being developed in this study. These prove the novelty of the proposed method. Further, a few numerical examples are discussed that demonstrates the proposed method.

A New Interval-Valued Intuitionistic Fuzzy Numbers: Ranking Methodology and Application

2018 ◽  
Vol 14 (03) ◽  
pp. 363-381 ◽  
Author(s):  
S. K. Bharati ◽  
S. R. Singh
Keyword(s):  
Fuzzy Numbers ◽  
Optimal Solutions ◽  
Intuitionistic Fuzzy Number ◽  
Ranking Methods ◽  
Intuitionistic Fuzzy Numbers ◽  
Industrial Management ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Better Than ◽  
Real World Problems

Ranking of interval-valued intuitionistic fuzzy (IVIF) numbers is a most popular and elegant work in the area of decision-making of several real-world problems. Some limited methods have been presented concerning the ranking of IVIF sets in literature. In the present paper, we generalize the intuitionistic fuzzy (IF) number to interval-valued intuitionistic fuzzy number by defining interval membership and nonmembership functions instead of fixed-valued function and hence it will present uncertain situation better than IF numbers. It may also be applied in data analysis, industrial management, artificial intelligence, forecasting, time series and so on. In this paper, ranking methodology of IVIF numbers is presented, for this first we define the value and ambiguity of IVIF numbers. Proposed ranking method also is compared with existing ranking methods. Further, IVIF numbers are used to capture fuzziness and hesitation in transportation problem (TP), and we propose a new method to find optimal solutions of TP with IVIF number parameters and finally, a numerical example is given to demonstrate the proposed method.

scholarly journals New Results on Multiple Solutions for Intuitionistic Fuzzy Differential Equations

2016 ◽  
Vol 4 (6) ◽  
pp. 560-573 ◽  
Author(s):  
Lei Wang ◽  
Sicong Guo
Keyword(s):  
Differential Equations ◽  
Multiple Solutions ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Number ◽  
Hukuhara Difference ◽  
Intuitionistic Fuzzy Numbers ◽  
First Order ◽  
Intuitionistic Fuzzy ◽  
Cut Set ◽  
Selection Of

AbstractThe first-order fuzzy differential equations with intuitionistic fuzzy initial valued problem is studied. Firstly, with the help of (α, β)-cut set, the distance metric and the Hukuhara difference between intuitionistic fuzzy numbers are defined, and on this basis the concept of differentiability for the intuitionistic fuzzy number-valued functions is defined and a corresponding theorem is derived. Then, according to the selection of derivative the first order intuitionistic fuzzy differential equations is interpreted. Finally, an example of first-order linear intuitionistic fuzzy differential equations is solved, and the results show that there are four different solutions.

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.

Intutionistic Fuzzy Difference Equation

2017 ◽  
pp. 112-131
Author(s):  
Sankar Prasad Mondal ◽  
Dileep Kumar Vishwakarma ◽  
Apu Kumar Saha
Keyword(s):  
Difference Equation ◽  
Exact Solutions ◽  
Fuzzy Number ◽  
Linear Difference Equation ◽  
Initial Condition ◽  
Intuitionistic Fuzzy Number ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Trapezoidal Intuitionistic Fuzzy Number

In this chapter we solve linear difference equation with intuitionistic fuzzy initial condition. All possible cases are defined and solved them to obtain the exact solutions. The intuitionistic fuzzy numbers are also taken as trapezoidal intuitionistic fuzzy number. The problems are illustrated by two different numerical examples.

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