scholarly journals Using Trapezoidal Intuitionistic Fuzzy Number to Find Optimized Path in a Network

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
P. Jayagowri ◽  
G. Geetha Ramani
Keyword(s):  
Network Flow ◽  
Relevant Literature ◽  
Real Life ◽  
Destination Node ◽  
Arc Length ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Trapezoidal Intuitionistic Fuzzy Number

In real life, information available on situations/issues/problems is vague, inexact, or insufficient and so the parameters involved therein are grasped in an uncertain way by the decision maker. But in real life such uncertainty is unavoidable. One possible way out is to consider the knowledge of experts about the parameters involved as fuzzy data. In a network, the arc length may represent time or cost. In Relevant literature reports there are several methods to solve such problems in network-flow. This paper proposes an optimized path for use in networks, using trapezoidal intuitionistic fuzzy numbers, assigned to each arc length in a fuzzy environment. It proposes a new algorithm to find the optimized path and implied distance from source node to destination node.

scholarly journals Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 218 ◽  
Author(s):  
Jinming Zhou ◽  
Tomas Baležentis ◽  
Dalia Streimikiene
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Real Life ◽  
Aggregation Operators ◽  
Harmonic Mean ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Selection Of

In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Weighted Bonferroni Harmonic Mean (IFNWBHM) and the Intuitionistic Fuzzy Ordered Normalized Weighted Bonferroni Harmonic Mean (IFNONWBHM). The paper winds up with an empirical example of multi-attribute group decision making (MAGDM) based on triangular intuitionistic fuzzy numbers. To serve this end, we apply the IFNWBHM aggregation operator.

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.

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 Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems

2021 ◽  
Author(s):  
Firoz Ahmad
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Practical Implication ◽  
Real Life ◽  
Future Research ◽  
Programming Approach ◽  
Solution Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiobjective Optimization Problems

AbstractThis study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.

Performance Efficiency of Public Health Sector Using Intuitionistic Fuzzy DEA

2020 ◽  
Vol 28 (02) ◽  
pp. 289-315
Author(s):  
Alka Arya ◽  
Shiv Prasad Yadav
Keyword(s):  
Public Health ◽  
Health Sector ◽  
Real Life ◽  
Output Data ◽  
Intuitionistic Fuzzy Numbers ◽  
Public Health Sector ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Fuzzy Input ◽  
Fuzzy Dea

Out of several generalizations of fuzzy set theory for various objectives, the notions of intuitionistic fuzzy sets (IFSs) is very useful in modeling real life problems. In existing fuzzy data envelopment analysis (FDEA) models, the inputs and outputs are limited to fuzzy input and fuzzy output data. In real life problems, the input data and output data can be considered as linguistic/vague characterized by intuitionistic fuzzy numbers (IFNs). So, in the present study, we extend FDEA to intuitionistic FDEA (IFDEA) in which the input and output data are taken as IFNs, in particular triangular IFNs (TIFNs). In this study, we develop models to measure the efficiencies of each DMU in intuitionistic fuzzy environment using α and β-cuts and we get IF interval efficiencies. The ranking of FNs has been studied by many authors and extended to IFNs because of its applicability in real life problems. The ranking of IF interval efficiency plays an important role in DEA where the interval analysis is essential. Further, in this paper a new method for ranking IF interval efficiencies has been proposed and compared with other existing methods. A new general minimax approach is proposed to compare and rank the IF efficiency intervals of DMUs. One numerical example is provided to show the applications of the proposed IFDEA model and the proposed ranking approach. Moreover, we present an application of the proposed approach to the public health sector.

scholarly journals PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems

2018 ◽  
Vol 7 (4) ◽  
pp. 62-99 ◽  
Author(s):  
P.Senthil Kumar
Keyword(s):  
Real Life ◽  
Optimal Solution ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Optimal Solution ◽  
Fuzzy Representation ◽  
Objective Value

This article proposes a method for solving intuitionistic fuzzy solid transportation problems (IFSTPs) in which only the transportation costs are represented in terms of intuitionistic fuzzy numbers (IFNs). The remaining parameters, namely: supply, demand and conveyance capacity, are all considered into crisp numbers. This type of STP is called a type-2 IFSTP. When solving the real life solid transportation problems (STPs) those tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this article, the author tried to categorise the STPs under the uncertain environment. He formulates the intuitionistic fuzzy STPs and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P.Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the type-2 IFSTP and the optimal objective value of type-2 IFSTP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution of type-2 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. A case study is presented to illustrate the procedure of the proposed method.

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 Trapezoidal Intuitionistic Fuzzy Multiattribute Decision Making Method Based on Cumulative Prospect Theory and Dempster-Shafer Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xihua Li ◽  
Fuqiang Wang ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Value Function ◽  
Cumulative Prospect Theory ◽  
Intuitionistic Fuzzy Numbers ◽  
Attribute Weight ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Fuzzy Environment ◽  
Shafer Theory

With respect to decision making problems under uncertainty, a trapezoidal intuitionistic fuzzy multiattribute decision making method based on cumulative prospect theory and Dempster-Shafer theory is developed. The proposed method reflects behavioral characteristics of decision makers, information fuzziness under uncertainty, and uncertain attribute weight information. Firstly, distance measurement and comparison rule of trapezoidal intuitionistic fuzzy numbers are used to derive value function under trapezoidal intuitionistic fuzzy environment. Secondly, the value function and decision weight function are used to calculate prospect values of attributes for each alternative. Then considering uncertain attribute weight information, Dempster-Shafer theory is used to aggregate prospect values for each alternative, and overall prospect values are obtained and thus the alternatives are sorted consequently. Finally, an illustrative example shows the feasibility of the proposed method.

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