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.

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.

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.

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.

scholarly journals Metric Properties between Trapezoidal Intuitionistic Fuzzy Numbers

2019 ◽  
Vol 8 (3) ◽  
pp. 3951-3954
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Interval Numbers ◽  
New Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Intuitionistic Fuzzy ◽  
Metric Distance ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

Generally ranking of fuzzy number is more essential for convertion of fuzzy number to crisp one. In this manuscript, a new approach to rank the trapezoidal intuitionistic fuzzy numbers using cuts is established. The metric distance of the interval numbers is extended to trapezoidal intuitionistic fuzzy numbers. By using both the ranking of trapezoidal intuitionistic fuzzy numbers and cuts there is abundant scope of investigating the numerical problems in optimization.

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.

scholarly journals Trapezoidal Hesitant Intuitionistic Fuzzy Numbers and Their Applications to Multiple-Criteria Decision Making Problems

2021 ◽  
Author(s):  
Irfan Deli
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Criteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Support Set ◽  
Deviation Degree ◽  
Degree Deviation ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

Abstract In this paper, we introduce an extension theory of the trapezoidal intuitionistic fuzzy numbers under intuitionistic hesitant fuzzy sets called trapezoidal hesitant intuitionistic fuzzy number (THIF-number). This new theory provides very effectively to model uncertainties of some events by several different trapezoidal intuitionistic fuzzy numbers based on the same support set in the set of real numbers R. Also, to demonstrate the application of this theory, a new multi-criteria decision-making(MCDM) method based on THIF-numbers is presented. To do this, we first propose operations of THIF-numbers with properties. We second give score, standard deviation degree, deviation degree of THIF-numbers to compare THIF-numbers. We third develop geometric operators and arithmetic operators of THIF-number. Finally, a numerical example is presented to illustrate the application of the developed method in THIF-numbers.

Sign in / Sign up

Export Citation Format

Share Document