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 A Simple Method for Solving Fully Intuitionistic Fuzzy Real Life Assignment Problem

2016 ◽  
Vol 7 (2) ◽  
pp. 39-61 ◽  
Author(s):  
P. Senthil Kumar ◽  
R. Jahir Hussain
Keyword(s):  
Assignment Problem ◽  
Fuzzy Numbers ◽  
Graphical Representation ◽  
Real Life ◽  
New Method ◽  
Simple Method ◽  
Optimal Cost ◽  
Intuitionistic Fuzzy Numbers ◽  
Numerical Example ◽  
Intuitionistic Fuzzy

In solving real life assignment problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representations for the data. So, in this paper, the authors consider the assignment problem having uncertainty and hesitation in cost/time/profit. They formulate the problem and utilize triangular intuitionistic fuzzy numbers (TIFNs) to deal with uncertainty and hesitation. The authors propose a new method called PSK (P.Senthil Kumar) method for finding the intuitionistic fuzzy optimal cost/time/profit for fully intuitionistic fuzzy assignment problem (FIFAP). The proposed method gives the optimal object value in terms of TIFN. The main advantage of this method is computationally very simple, easy to understand. Finally the effectiveness of the proposed method is illustrated by means of a numerical example which is followed by graphical representation of the finding.

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.

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.

Developing Management from Islamic Perspectives (MIP) as a Formal Academic Discipline

2009 ◽  
Vol 26 (1) ◽  
pp. 46-69
Author(s):  
Shamas-Ur-Rehman Toor
Keyword(s):  
Literature Review ◽  
Academic Discipline ◽  
Real Life ◽  
Growth Potential ◽  
Future Research ◽  
Business Practices ◽  
Research Directions ◽  
International Consortium ◽  
Future Research Directions ◽  
Scholarly Attention

Management from Islamic Perspectives (MIP) is an emerging field that has begun to attract scholarly attention. However, the research undertaken so far has been rather fragmented and lack a clear agenda. This paper presents a literature review of the field and the areas of current focus. Although the field has a huge growth potential, I argue that it faces several challenges and problems as it develops further. I outline these potential pitfalls, suggest how to develop MIP as a formal discipline, and explain how to integrate it within real-life business practices. The article closes with a call for research to be conducted in a more organized fashion through an international consortium of researchers as well as recommendations for future research directions.

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.

Developing Management from Islamic Perspectives (MIP) as a Formal Academic Discipline

2009 ◽  
Vol 26 (1) ◽  
pp. 46-69
Author(s):  
Shamas-Ur-Rehman Toor
Keyword(s):  
Literature Review ◽  
Academic Discipline ◽  
Real Life ◽  
Growth Potential ◽  
Future Research ◽  
Business Practices ◽  
Research Directions ◽  
International Consortium ◽  
Future Research Directions ◽  
Scholarly Attention

Management from Islamic Perspectives (MIP) is an emerging field that has begun to attract scholarly attention. However, the research undertaken so far has been rather fragmented and lack a clear agenda. This paper presents a literature review of the field and the areas of current focus. Although the field has a huge growth potential, I argue that it faces several challenges and problems as it develops further. I outline these potential pitfalls, suggest how to develop MIP as a formal discipline, and explain how to integrate it within real-life business practices. The article closes with a call for research to be conducted in a more organized fashion through an international consortium of researchers as well as recommendations for future research directions.

scholarly journals Managing cost uncertainties in transportation and assignment problems

1998 ◽  
Vol 2 (1) ◽  
pp. 65-104 ◽  
Author(s):  
V. Adlakha ◽  
H. Arsham
Keyword(s):  
Time Lag ◽  
Real Life ◽  
Optimal Solution ◽  
Global Market ◽  
Solution Algorithm ◽  
Assignment Problems ◽  
The Stability ◽  
Order Assignment ◽  
Cost Parameters ◽  
The Cost

In a fast changing global market, a manager is concerned with cost uncertainties of the cost matrix in transportation problems (TP) and assignment problems (AP).A time lag between the development and application of the model could cause cost parameters to assume different values when an optimal assignment is implemented. The manager might wish to determine the responsiveness of the current optimal solution to such uncertainties. A desirable tool is to construct a perturbation set (PS) of cost coeffcients which ensures the stability of an optimal solution under such uncertainties.The widely-used methods of solving the TP and AP are the stepping-stone (SS) method and the Hungarian method, respectively. Both methods fail to provide direct information to construct the needed PS. An added difficulty is that these problems might be highly pivotal degenerate. Therefore, the sensitivity results obtained via the available linear programming (LP) software might be misleading.We propose a unified pivotal solution algorithm for both TP and AP. The algorithm is free of pivotal degeneracy, which may cause cycling, and does not require any extra variables such as slack, surplus, or artificial variables used in dual and primal simplex. The algorithm permits higher-order assignment problems and side-constraints. Computational results comparing the proposed algorithm to the closely-related pivotal solution algorithm, the simplex, via the widely-used pack-age Lindo, are provided. The proposed algorithm has the advantage of being computationally practical, being easy to understand, and providing useful information for managers. The results empower the manager to assess and monitor various types of cost uncertainties encountered in real-life situations. Some illustrative numerical examples are also presented.

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.

scholarly journals On the Resilience of Ant Algorithms. Experiment with Adapted MMAS on TSP

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 752
Author(s):  
Elena Nechita ◽  
Gloria Cerasela Crişan ◽  
Laszlo Barna Iantovics ◽  
Yitong Huang
Keyword(s):  
Real Life ◽  
Future Research ◽  
Heuristic Methods ◽  
Ant System ◽  
Research Directions ◽  
Ant Algorithms ◽  
Software Applications ◽  
Communication Processes ◽  
Future Research Directions ◽  
Broad Outline

This paper focuses on the resilience of a nature-inspired class of algorithms. The issues related to resilience fall under a very wide umbrella. The uncertainties that we face in the world require the need of resilient systems in all domains. Software resilience is certainly of critical importance, due to the presence of software applications which are embedded in numerous operational and strategic systems. For Ant Colony Optimization (ACO), one of the most successful heuristic methods inspired by the communication processes in entomology, performance and convergence issues have been intensively studied by the scientific community. Our approach addresses the resilience of MAX–MIN Ant System (MMAS), one of the most efficient ACO algorithms, when studied in relation with Traveling Salesman Problem (TSP). We introduce a set of parameters that allow the management of real-life situations, such as imprecise or missing data and disturbances in the regular computing process. Several metrics are involved, and a statistical analysis is performed. The resilience of the adapted MMAS is analyzed and discussed. A broad outline on future research directions is given in connection with new trends concerning the design of resilient systems.

Initial attempt to optimize the operation of a hydrometric network using branch and bound algorithm

1988 ◽  
Vol 15 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Patrice M. Pelletier ◽  
Slobodan P. Simonovic
Keyword(s):  
Heuristic Algorithm ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Traveling Salesman ◽  
Future Research ◽  
Initial Attempt ◽  
Research Directions ◽  
New Approach ◽  
Future Research Directions ◽  
Field Area

The paper presents a new approach developed to formulate and solve the problem of field operation of a hydrometric network. In present practice, optimization techniques are not used for solving this problem. In the initial attempt, documented in the paper, the traveling salesman algorithm is used to find the optimal solution. Assumptions used and experience gained during the research are addressed in the paper. For the Dauphin hydrometric field area in Manitoba, an "optimal" solution has been obtained and presented. Based on the analysis of the results, conclusions were drawn about future research directions incorporating development of an effective heuristic algorithm for solving the traveling hydrometric technician problem. Key words: operation, hydrometric network, optimization, heuristic algorithm, traveling salesman algorithm.

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