The PSK Method for Solving Fully Intuitionistic Fuzzy Assignment Problems With Some Software Tools

2020 ◽  
pp. 149-202 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Linear Programming ◽  
Comparative Study ◽  
Assignment Problem ◽  
Linear Programming Problem ◽  
Real Life ◽  
Computer Code ◽  
Assignment Problems ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Software Packages

The assignment problem (AP) is a particular case of a linear programming problem that deals with the allocation of various resources for various activities on a 1-to-1 basis. It does so in such a manner that the profit or sale involved in the process is maximum and cost or time is minimum. Generally, the profit/sale/cost/time is called the parameter of the AP and this is not a crisp number due to some uncontrollable factors. They can also involve uncertainty and hesitation. Therefore, to solve the AP under an intuitionistic fuzzy environment in this chapter, the author proposes the PSK (P. Senthil Kumar) method. Numerous theorems which are related to intuitionistic fuzzy assignment problem is proposed and is proved by PSK. By using the PSK method, the real-life related fully intuitionistic fuzzy assignment problems are solved. The proposed results are verified by both LINGO 17.0 and TORA software packages. In addition to verifying the efficiency and realism of the proposed method, the computer code based on LINGO 17.0 is presented. Results, discussion, comparative study, and the advantages of the PSK method are given. The chapter ends with the conclusion and future studies.

Computationally Simple and Efficient Method for Solving Real-Life Mixed Intuitionistic Fuzzy 3D Assignment Problems

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Assignment Problem ◽  
Graphical Representation ◽  
Real Life ◽  
Optimal Solution ◽  
Future Research ◽  
Assignment Problems ◽  
3 Dimensional ◽  
Intuitionistic Fuzzy ◽  
Comparison Results ◽  
Future Research Directions

This article addresses the 3-dimensional mixed intuitionistic fuzzy assignment problems (3D-MIFAPs). In this article, firstly, the author formulates an assignment problem (AP) and assumes the parameters are in uncertainty with hesitation. Secondly, based on the nature of the parameter the author defines various types of solid assignment problem (SAP) in uncertain environment. Thirdly, to solve 3D-MIFAP the PSK method for finding an optimal solution of fully intuitionistic fuzzy assignment problem (FIFAP) is extended by the author. Fourthly, the author presents the proofs of the proposed theorems and corollary. Fifthly, the proposed approach is illustrated with three numerical examples and the optimal objective value of 3D-MIFAP is obtained in the form of intuitionistic fuzzy number and the solution is checked with MATLAB and their coding are also given by the author. Sixthly, the author presents the comparison results and their graphical representation, merits and demerits of the proposed and existing methods and finally the author presents conclusion and future research directions.

scholarly journals The Knowledge of Expert Opinion in Intuitionistic Fuzzy Linear Programming Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
A. Nagoorgani ◽  
J. Kavikumar ◽  
K. Ponnalagu
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Real Life ◽  
Fuzzy Linear Programming ◽  
Limited Resources ◽  
Fuzzy Data ◽  
Intuitionistic Fuzzy ◽  
Competing Demands ◽  
Intuitionistic Fuzzy Data

In real life, information available for certain situations is vague and such uncertainty is unavoidable. One possible solution is to consider the knowledge of experts on the parameters involved as intuitionistic fuzzy data. We examine a linear programming problem in which all the coefficients are intuitionistic in nature. An approach is presented to solve an intuitionistic fuzzy linear programming problem. In this proposed approach, a procedure for allocating limited resources effectively among competing demands is developed. An example is given to highlight the illustrated study.

scholarly journals Computer Oriented Interior Point Algorithm for Solving Linear Programming Problem with Application

2017 ◽  
Vol 65 (1) ◽  
pp. 41-47
Author(s):  
Farhana Ahmed Simi ◽  
Md Ainul Islam
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Linear Programming Problem ◽  
Large Scale ◽  
Real Life ◽  
Computer Code ◽  
Interior Point Algorithm ◽  
Hand Calculation ◽  
Diet Problem ◽  
Do So

In this paper, we study the interior point algorithm for solving linear programming (LP) problem developed by Narendra Karmarkar. As interior point algorithm for LP problem involves tremendous calculations, it is quite impossible to do so by hand calculation. To fulfill the requirement we develop computer code in MATLAB for LP which is based on this algorithm procedure. To illustrate the purpose, we formulate a real life sizeable large-scale linear program for diet problem and solve it using our computer code for interior point algorithm in MATLAB. Dhaka Univ. J. Sci. 65(1): 41-47, 2017 (January)

scholarly journals Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment

2020 ◽  
Vol 9 (1) ◽  
pp. 1-34 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Reduction Method ◽  
Real Life ◽  
Optimal Solution ◽  
Assignment Problems ◽  
New Approach ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Computing Procedure ◽  
Fuzzy Representation ◽  
Objective Value

When people solve real-life SAP they 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 SAP under uncertain environment. He formulates the IFSAP and utilizes the TIFN to deal with uncertainty and hesitation. The SAP has uncertainty and hesitation in cost/time/profit/production is known as FIFSAP. The PSK (P. Senthil Kumar) method for finding an optimal solution for FIFAP is extended to solve the FIFSAP and the optimal objective value of FIFSAP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution/assignment of FIFSAP is obtained without using the Hungarian method and intuitionistic fuzzy reduction method. Moreover, the proposed method is computationally very simple and easy to understand. The numerical example is presented to demonstrate computing procedure. The results affirm efficiency of the proposed method.

scholarly journals Linear Programming Approach for Solving Balanced and Unbalanced Intuitionistic Fuzzy Transportation Problems

2018 ◽  
Vol 9 (2) ◽  
pp. 73-100 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Linear Programming ◽  
Comparative Study ◽  
Real Life ◽  
Programming Approach ◽  
Programming Technique ◽  
Distribution Method ◽  
Numerical Examples ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy ◽  
Linear Programming Technique

In this article, two methods are presented, proposed method 1 and proposed method 2. Proposed method 1 is based on linear programming technique and proposed method 2 is based on modified distribution method. Both of the methods are used to solve the balanced and unbalanced intuitionistic fuzzy transportation problems. The ideas of the proposed methods are illustrated with the help of real life numerical examples which is followed by the results and discussion and comparative study is given. The proposed method is computationally very simple when compared to the existing methods, it is shown to be and easier form of evaluation when compared to current methods.

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.

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