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.

2. Khaled Abdelghany, Southern Methodist University, USA
Anil Aggarwal, University of Baltimore, USA
Ahad Ali, Lawrence Technological University, USA
Mohammad Amini, The University of Memphis, USA
Adedeji Badiru, Air Force Institute of Technology, USA
Lihui Bai, Valparaiso University, USA
Xuegang Ban, Rensselaer Polytechnic Institute, USA
Sankarshan Basu, Indian Institute of Management Bangalore, India
Melike Baykal-Gursoy, Rutgers University, USA
Sherry Borener, Federal Aviation Administration, USA
Denis Borenstein, Federal University of Rio Grande do Sul, Brazil
Robert Brigantic, Pacific Northwest National Laboratory, USA
Dirk Briskorn, Universität Siegen, Germany
Kevin Byrnes, Johns Hopkins University, USA
Muricio Cabrera Rios, University of Puerto Rico – Mayagüez, Puerto Rico
Mei Cao, University of Wisconsin-Superior, USA
Gary Chao, Kutztown University, USA
Dean Chatfield, Old Dominion University, USA
Chialin Chen, Queen’s University, Canada
Lijian Chen, University of Louisville, USA
Feng Cheng, IBM T.J. Watson Research Center, USA
Jagpreet Chhatwal, Merck Research Laboratories, USA
Wen Chiang, University of Tulsa, USA
David Chin, Federal Aviation Administration, USA
David Ciemnoczolowski, Union Pacific Railroad, USA
Barry Cobb, Virginia Military Institute, USA
Nagihan Çömez, Bilkent University, Tokelau
Louis Cox Jr., University of Colorado, USA
Lauren Davis, North Carolina A&T State University, USA
Ivan Derpich, University of Santiago of Chile, Chile
Jin Dong, IBM China Research Lab, Chile
Matt Drake, Duquesne University, USA
International Editorial Review Board
EDITOR-IN-CHIEF
John Wang, Montclair State University, USA
ASSOCIATE EDITORS
Sungzoon Cho, Seoul National University, Korea
Theodore Glickman, The George Washington University, USA
Manoj Jha, Morgan State University, USA
Eva Lee, Georgia Institute of Technology, USA
Panos Pardalos, University of Florida, USA
Roman Polyak, George Mason University, USA
Jasenkas Rakas, University of California at Berkeley, USA
Ravi Ravindran, Pennsylvania State University, USA
Kathryn Stecke, University of Texas at Dallas, USA
Volume 7 • Issue 2 • April-June 2016 • ISSN: 1947-9328 • eISSN: 1947-9336
An official publication of the Information Resources Management Association
International Journal of Operations Research and Information
Systems

3. Parijat Dube, IBM T.J. Watson Research Center, USA
Banu Ekren, Izmir University of Economics, Turkey
Sandra Eksioglu, Mississippi State University, USA
Ali Elkamel, University of Waterloo, Canada
Murat Erkoc, University of Miami, USA
Barry Ezell, Old Dominion University, USA
Javier Faulin, Public University of Navarre, Spain
Yudi Fernando, Universiti Sains Malaysia, Malaysia
William P. Fox, Naval Postgraduate School, USA
Hise Gibson, INFORMS, USA
Genady Grabarnik, IBM TJ Watson Research, USA
Scott Grasman, Rochester Institute of Technology, USA
Nalan Gulpinar, Warwick Business School, UK
Roger Gung, Response Analytics Inc., USA
Zhinling Guo, University of Maryland-Baltimore County, USA
Ülkü Gürler, Bilkent University, Turkey
Alexander Gutfraind, Los Alamos National Laboratory, USA
Peter Hahn, University of Pennsylvania, USA
Mohammed Hajeeh, Kuwait Institute for Scientific Research, Kuwait
Steven Harper, James Madison University, USA
Michael Hirsch, Raytheon Inc., USA
Samuel Hohmann, University Health System Consortium, USA
Xiangling Hu, Grand Valley State University, USA
Dariusz Jakóbczak, Technical University of Koszalin, Poland
Manoj Jha, Morgan State University, USA
Alan Johnson, Air Force Institute of Technology, USA
Burcu Keskin, The University of Alabama, USA
Adlar Kim, Massachusetts Institute of Technology, USA
Rex Kincaid, College of William & Mary, USA
Saroj Koul, Jindal Global Business School, India
Deepak Kulkarni, NASAAmes Research Center, USA
Nanda Kumar, University of Texas at Dallas, USA
Chang Won Lee, Hanyang University, Korea, Democratic People’s Republic Of
Hyoung-Gon Lee, Massachusetts Institute of Technology, USA
Loo Lee, National University of Singapore, Singapore
Fei Li, George Mason University, USA
Feng Li, IBM China Research Laboratory, China
Jian Li, Northeastern Illinois University, USA
Jing Li, Arizona State University, USA
Kunpeng Li, Utica College, USA
Xueping Li, University of Tennessee, Knoxville, USA
Igor Linkov, US Army Engineer Research & Devel. Center, USA
Dengpan Liu, University of Alabama in Huntsville, USA
George Liu, Intel Corporation, China
Tie Liu, IBM China Research Laboratory, China
Leonardo Lopes, University of Arizona, USA
Dimitrios Magos, Technological Educational Institute of Athens, Greece
Kaye McKinzie, U.S. Army, USA
Yefim Michlin, Israel Institute of Technology, Israel
Somayeh Moazeni, Princeton University, USA
Soumyo Moitra, Carnegie Mellon University, USA
Okesola Moses Olusola, Oludoy Dynamix Consulting Ltd, Nigeria
B.P.S. Murthi, University of Texas at Dallas, USA
Nagen Nagarur, Binghamton University, USA
Olufemi Omitaomu, Oak Ridge National Laboratory, USA
Mohammad Oskoorouchi, California State University San Marcos, USA
Kivanc Ozonat, HP Labs, USA
Dessislava Pachamanova, Babson College, USA
Julia Pahl, University of Hamburg, Germany
Alexander Paz, University of Nevada Las Vegas, USA
Francois Pinet, Irstea - Clermont Ferrand, France
Tania Querido, Linear Options Consulting, LCC, USA
International Editorial Review Board
Continued

4. Michael Racer, University of Memphis, USA
H. Charles Ralph, Clayton State University, USA
Marion Rauner, University of Vienna, Austria
Joe Roise, North Carolina State University, USA
Kedar Sambhoos, CUBRC, USA
Enzo Sauma Pontificia, Universidad Catolica de Chile, Chile
Hsu-Shih Shih, Tamkang University, Taiwan
Laura Shwartz, IBM T.J. Watson Research Center, USA
Sebastian Sitarz, University of Silesia, Poland
Young-Jun Son, The University of Arizona, USA
Huaming Song, Nanjing University of Science & Technology, China
Qin Su, Xi’an Jiaotong University, China
Yang Sun, California State University - Sacramento, USA
Durai Sundaramoorthi, Washington University in St. louis, USA
Pei-Fang Tsai, State University of New York at Binghamton, USA
M. Ali Ülkü, Dalhousie University, Canada
Bruce Wang, Texas A&M University, USA
Jiamin Wang, Long Island University, USA
Kaibo Wang, ASQ Certified Six Sigma Black Belt, China
Yitong Wang, Tsinghua University, China
Ue-Pyng Wen, National Tsing Hua University, Taiwan
Harris Wu, Old Dominion University, USA
Changyuan Yan, PNC Bank, USA
Justin Yates, Texas A&M University, USA
Mesut Yavuz, Shenandoah University, USA
Xugang Ye, Johns Hopkins University and Microsoft, USA
Donghun Yoon, Keio University, Japan
Banu Yukse-Ozkaya, Hacettepe University, Turkey
Muhong Zhang, Arizona State University, USA
Kangyuan Zhu, CSSI, Inc., USA
Yuntao Zhu, Arizona State University, USA
Jun Zhuang, SUNY Buffalo, USA
International Editorial Review Board
Continued

5. The International Journal of Operations Research and Information Systems is indexed or listed in the following: ACM
Digital Library; Bacon’s Media Directory; Cabell’s Directories; DBLP; Google Scholar; IAOR Online; INSPEC;
JournalTOCs; Library & Information Science Abstracts (LISA); MediaFinder; The Standard Periodical Directory; Ulrich’s
Periodicals Directory
Research Articles
1 Application of SARIMAX Model to Forecast Daily Sales in Food Retail Industry
Nari Sivanandam Arunraj, Deggendorf Institute of Technology, Deggendorf, Germany
Diane Ahrens, Deggendorf Institute of Technology, Deggendorf, Germany
Michael Fernandes, Deggendorf Institute of Technology, Deggendorf, Germany
21 AEGISi: Attribute Experimentation Guiding Improvement Searches Inline Framework
Michael Racer, Marketing & Supply Chain Management Department, University of Memphis, Memphis, TN, USA
Robin Lovgren, Department of Mathematics and Computer Science, Belmont University, Nashville, TN, USA
38 A Simple Method for Solving Fully Intuitionistic Fuzzy Real Life Assignment Problem
Senthil P. Kumar, PG & Research Department of Mathematics, Jamal Mohamed College (Autonomous),
Tiruchirappalli, India
Jahir R. Hussain, PG & Research Department of Mathematics, Jamal Mohamed College (Autonomous),
Tiruchirappalli, India
62 Optimal Transportation and Spatial Integration of Regional Palm Oil Markets in Nigeria
L.O.E. Nwauwa, Department of Agricultural Economics, Faculty of Agriculture, University of Ibadan, Ibadan,
Nigeria
K.O. Adenegan, Department of Agricultural Economics, Faculty of Agriculture, University of Ibadan, Ibadan,
Nigeria
M.A.Y. Rahji, Department of Agricultural Economics, Faculty of Agriculture, University of Ibadan, Ibadan,
Nigeria
T.T. Awoyemi, Department of Agricultural Economics, Faculty of Agriculture, University of Ibadan, Ibadan,
Nigeria
83 Supply Chain Coordination Under Service Level Constraint and Controllable Lead Time
Prashant Jindal, Department of Applied Mathematics, Gautam Buddha University, Greater Noida, India
Anjana Solanki, Department of Applied Mathematics, Gautam Buddha University, Greater Noida, India
Copyright
The International Journal of Operations Research and Information Systems (IJORIS) (ISSN 1947-9328; eISSN 1947-9336), Copyright ©
2016 IGI Global. All rights, including translation into other languages reserved by the publisher. No part of this journal may be reproduced or used in
any form or by any means without written permission from the publisher, except for noncommercial, educational use including classroom teaching
purposes. Product or company names used in this journal are for identification purposes only. Inclusion of the names of the products or companies does
not indicate a claim of ownership by IGI Global of the trademark or registered trademark. The views expressed in this journal are those of the authors
but not necessarily of IGI Global.
Volume 7 • Issue 2 • April-June-2016 • ISSN: 1947-9328 • eISSN: 1947-9336
An official publication of the Information Resources Management Association
International Journal of Operations Research and Information
Systems
Table of Contents

6. DOI: 10.4018/IJORIS.2016040103
Copyright © 2016, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
International Journal of Operations Research and Information Systems
Volume 7 • Issue 2 • April-June 2016
A Simple Method for Solving
Fully Intuitionistic Fuzzy Real
Life Assignment Problem
P. Senthil Kumar, PG & Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli,
Tamil Nadu, India
R. Jahir Hussain, PG & Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli,
Tamil Nadu, India
ABSTRACT
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
suggestedtheintuitionisticfuzzyrepresentationsforthedata.So,inthispaper,theauthorsconsider
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.TheauthorsproposeanewmethodcalledPSK(P.SenthilKumar)methodforfindingthe
intuitionisticfuzzyoptimalcost/time/profitforfullyintuitionisticfuzzyassignmentproblem(FIFAP).
The proposed method gives the optimal object value in terms ofTIFN.The main advantage of this
methodiscomputationallyverysimple,easytounderstand.Finallytheeffectivenessoftheproposed
methodisillustratedbymeansofanumericalexamplewhichisfollowedbygraphicalrepresentation
of the finding.
Keywords
Fully Intuitionistic Fuzzy Assignment Problem, Intuitionistic Fuzzy Set, Optimal Assignment, PSK Method,
Triangular Intuitionistic Fuzzy Number
1. INTRODUCTION
AssignmentProblem(AP)isusedworldwideinsolvingrealworldproblems.Anassignmentproblem
plays an important role in assigning of persons to jobs, drivers to trucks, trucks to routes, operators
to machines, or problems to research teams, etc.The assignment problem is a special kind of linear
programming problem (LPP) in which the aim of the decision maker (DM) is to assign n number
of jobs to n number of machines (persons) at a minimum cost/minimum time/ maximum profit.
In literature, to find the solution to assignment problems, Kuhn (1955) proposed the Hungarian
method for solving the assignment problem.Thompson (1981) discussed a recursive method for
solving assignment problem. Avis and Devroye (1985) presented an analysis of a decomposition
heuristicfortheassignmentproblem.Balinski(1986)didacompetitive(dual)simplexmethodforthe
assignmentproblem.Paparrizos(1991)developedanefficientexteriorpointsimplextypealgorithm
for the assignment problem. Barr et al. (1977) gave the alternating basis algorithm for assignment
problems.Pingetal.(1997)discussedanewalgorithmfortheassignmentproblemwhichtheyalso
called an alternative to the Hungarian Method. Their assignment algorithm is based on a 2n*2n
matrixwhereoperatorsareperformedonthematrixuntilanoptimalsolutionisfound.LinandWen
39

7. International Journal of Operations Research and Information Systems
Volume 7 • Issue 2 • April-June 2016
40
(2004) proposed an efficient algorithm based on a labeling method for solving the linear fractional
programming case. Singh (2012) discussed note on assignment algorithm with easy method of
drawing lines to cover all zeros.
However,inreallifesituations,theparameterofassignmentproblemisinimpreciseinsteadof
fixedrealnumbersbecausetime/cost/profitfordoingajobbyafacility(machine/person)mightvary
duetodifferentreasons.Todealquantitativelywithimpreciseinformationinmakingdecision,Zadeh
(1965) introduced the fuzzy set theory and has applied it successfully in various fields. The use of
fuzzy set theory becomes very rapid in the field of optimization after the pioneering work done by
BellmanandZadeh(1970).Thefuzzysetdealswiththedegreeofmembership(belongingness)ofan
elementinthesetbutitdoesnotconsiderthenon-membership(non-belongingness)ofanelementin
theset.Inafuzzyset,themembershipvalue(levelofacceptanceorlevelofsatisfaction)liesbetween
0and1whereasincrispsettheelementbelongstothesetthatrepresents1andtheelementnotin
the set that represents 0.
Therefore the applications of fuzzy set theory enabled many authors to solve assignment,
transportationandlinearprogrammingproblemsbyusingfuzzyrepresentationfordata.Kumaret
al. (2009) proposed a method for solving fully fuzzy assignment problems using triangular fuzzy
numbers.MukherjeeandBasu(2010)presentedanapplicationoffuzzyrankingmethodforsolving
assignmentproblemswithfuzzycosts.KumarandGupta(2012)investigatedassignmentandtravelling
salesman problems with cost coefficients as LR fuzzy parameters. De and Yadav (2012) evolved a
general approach for solving assignment problems involving with fuzzy costs coefficients.Thorani
and Shankar (2013) did fuzzy assignment problem with generalized fuzzy numbers. Kumar and
Kaur (2011) presented methods for solving fully fuzzy transportation problems based on classical
transportationmethods.Ebrahimnejadetal.(2011)proposedboundedprimalsimplexalgorithmfor
bounded linear programming with fuzzy cost coefficients. Nasseri and Ebrahimnejad (2011) did
sensitivityanalysisonlinearprogrammingproblemswithtrapezoidalfuzzyvariables.Pattnaik(2015)
presenteddecisionmakingapproachtofuzzylinearprogrammingproblemswithpostoptimalanalysis.
Intheassignmentproblem,theperformingtimeofeachjobtotheworkersisnotknownexactly.
This may be due to lack of experience, interest, capacity, understanding, etc. In such situation the
DM cannot predict performing time exactly. Hence the decision maker may hesitate.The fuzzy set
dealswiththebelongingnessofanelementinthesetbutitdoesnotconsiderthenon-belongingness
(rejectionslevel)ofanelementintheset.So,tocountertheseuncertaintieswithhesitation,Atanassov
(1983) proposed the intuitionistic fuzzy set (IFS) which is more reliable than the fuzzy set proposed
by Zadeh (1965).The major advantage of intuitionistic fuzzy set over fuzzy set is that IFS separates
thedegreeofmembership(belongingness)andthedegreeofnonmembership(nonbelongingness)
ofanelementintheset.WiththehelpofIFStheory,decisionmakercandecideaboutthedegreeof
acceptance,degreeofnonacceptanceanddegreeofhesitationforsomequantity.Incaseofassignment
problem,theDMcandecideaboutthelevelofacceptanceandnon-acceptancefortheassignment
cost/profit/time.Duetothis,theapplicationofIFStheorybecomesverypopularinprojectschedules,
transportation problems, decision making theory and network flow problems etc.
In literature, due to the lack of uncertainty of the parameter of the fuzzy assignment problem,
many authors have solved assignment problem with intuitionistic fuzzy version. Mukherjee and
Basu (2012) presented the solution of a class of intuitionistic fuzzy assignment problem by using
similarity measures. Jose and Kuriakose (2013) discussed algorithm for solving an assignment
model in intuitionistic fuzzy context. Kumar and Hussain (2014) presented a method for finding an
optimalsolutionofanassignmentproblemundermixedintuitionisticfuzzyenvironment.Kumarand
Bajaj (2014) evolved on solution of interval valued intuitionistic fuzzy assignment problem using
similaritymeasureandscorefunction.KumarandHussain(2014)didamethodforsolvingbalanced
intuitionisticfuzzyassignmentproblem.DinagarandThiripurasundari(2014)foundanewmethod
for finding the cost of fuzzy assignment problem using genetic algorithm of artificial intelligence.
Prabakaran andGanesan(2014)presentedfuzzyHungarianmethodforsolvingintuitionisticfuzzy

8. 21 more pages are available in the full version of this
document, which may be purchased using the "Add to Cart"
button on the product's webpage:
www.igi-global.com/article/a-simple-method-for-solving-fully-
intuitionistic-fuzzy-real-life-assignment-
problem/146835?camid=4v1
This title is available in InfoSci-Journals, InfoSci-Journal
Disciplines Business, Administration, and Management.
Recommend this product to your librarian:
www.igi-global.com/e-resources/library-
recommendation/?id=2
Related Content
Managing Risk in Small and Medium Enterprises (SMEs) Supply Chains’
Using Quality Function Deployment (QFD) Approach
Mohd. Nishat Faisal (2013). International Journal of Operations Research and
Information Systems (pp. 64-83).
www.igi-global.com/article/managing-risk-small-medium-
enterprises/76673?camid=4v1a
Component-Based Decision Trees: Empirical Testing on Data Sets of
Account Holders in the Montenegrin Capital Market
Ljiljana Kašelan and Vladimir Kašelan (2015). International Journal of Operations
Research and Information Systems (pp. 1-18).
www.igi-global.com/article/component-based-decision-
trees/133602?camid=4v1a
Data Envelopment Analysis with Fuzzy Parameters: An Interactive Approach
Adel Hatami-Marbini, Saber Saati and Madjid Tavana (2011). International Journal of
Operations Research and Information Systems (pp. 39-53).
www.igi-global.com/article/data-envelopment-analysis-fuzzy-
parameters/55860?camid=4v1a

9. Measuring Performance of Dynamic and Network Structures by SBM Model
N. Aghayi, Z. Ghelej Beigi, K. Gholami and F. Hosseinzadeh Lotfi (2014). Handbook
of Research on Strategic Performance Management and Measurement Using Data
Envelopment Analysis (pp. 527-558).
www.igi-global.com/chapter/measuring-performance-of-dynamic-and-
network-structures-by-sbm-model/121504?camid=4v1a

10. International Journal of Operations Research and Information Systems
Volume 7 • Issue 2 • April-June 2016
55
REFERENCES
Aggarwal, S., & Gupta, C. (2014). Algorithm for solving intuitionistic fuzzy transportation problem with
generalized trapezoidal intuitionistic fuzzy number via new ranking method. arXiv preprint arXiv:1401.3353.
Antony, R. J. P., Savarimuthu, S. J., & Pathinathan, T. (2014). Method for solving the transportation problem
using triangular intuitionistic fuzzy number. International Journal of Computing Algorithm, 3, 590–605.
Atanassov, K. (1983, June). Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia.
Atanassov,K.(1999).Intuitionisticfuzzysets:theoryandapplications.Springer.doi:10.1007/978-3-7908-1870-3
Avis,D.,&Devroye,L.(1985).Ananalysisofadecompositionheuristicfortheassignmentproblem.Operations
Research Letters, 3(6), 279–283. doi:10.1016/0167-6377(85)90001-X
Balinski, M. L. (1986). A competitive (dual) simplex method for the assignment problem. Mathematical
Programming, 34(2), 125–141. doi:10.1007/BF01580579
Ban, A. (2008). Trapezoidal approximations of intuitionistic fuzzy numbers expressed by value, ambiguity,
width and weighted expected value. Notes on Intuitionistic Fuzzy Sets, 14(1), 38–47.
Barr, R. S., Glover, F., & Klingman, D. (1977). The alternating basis algorithm for assignment problems.
Mathematical Programming, 13(1), 1–13. doi:10.1007/BF01584319
Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science, 17(B),
141-164.
Burillo, P., Bustince, H., & Mohedano, V. (1994, September). Some definitions of intuitionistic fuzzy number-
first properties. Proceedings of the FirstWorkshop on Fuzzy Based Expert System, Sofia, Bulgaria (pp. 53-55).
Chakraborty, D., Jana, D. K., & Roy, T. K. (2015). A new approach to solve multi-objective multi-choice multi-
item Atanassov’s intuitionistic fuzzy transportation problem using chance operator. Journal of Intelligent &
Fuzzy Systems, 28(2), 843–865.
Das, S., & Guha, D. (2013). Ranking of intuitionistic fuzzy number by centroid point. Journal of Industrial and
Intelligent Information, 1(2), 107–110. doi:10.12720/jiii.1.2.107-110
De, P. K., & Yadav, B. (2012). A general approach for solving assignment problems involving with fuzzy cost
coefficients. Modern Applied Science, 6(3), 2. doi:10.5539/mas.v6n3p2
Dinagar, D. S., &Thiripurasundari, K. (2014). A new method for finding the cost of fuzzy assignment problem
using genetic algorithm of artificial intelligence. International Electronic Journal of Pure and Applied
Mathematics, 8(4).
Dinagar,D.S.,&Thiripurasundari,K.(2014).Anavelmethodforsolvingfuzzytransportationprobleminvolving
intuitionistic trapezoidal fuzzy numbers. International Journal of Current Research, 6(6), 7038–7041.
Ebrahimnejad, A., Nasseri, S. H., & Mansourzadeh, S. M. (2011). Bounded Primal Simplex Algorithm for
Bounded Linear Programming with Fuzzy Cost Coefficients. International Journal of Operations Research
and Information Systems, 2(1), 96–120. doi:10.4018/joris.2011010105
Gani, A. N., & Abbas, S. (2012). Intuitionistic fuzzy transportation problem. Proceedings of the Heber
International Conference on Applications of Mathematics and Statistics (HICAMS) (pp. 528-535).
Grzegorzewski, P. (2003). Distance and orderings in a family of intuitionistic fuzzy numbers. InProceedings of
theThirdConferenceoftheEuropeanSocietyforFuzzyLogicandTechnology,Zittau,Germany(pp.223-227)3.
Guha, D., & Chakraborty, D. (2010). A theoretical development of distance measure for intuitionistic fuzzy
numbers. International Journal of Mathematics and Mathematical Sciences, 2010.
Jose, S., & Kuriakose, S. (2013). Algorithm for solving an assignment model in intuitionistic fuzzy context.
International Journal of Fuzzy Mathematics and Systems, 3(5), 345–349.
Kuhn, H. W. (1955). The Hungarian method for the assignment problem. Naval Research Logistics Quarterly,
2(1‐2), 83–97. doi:10.1002/nav.3800020109

11. International Journal of Operations Research and Information Systems
Volume 7 • Issue 2 • April-June 2016
56
Kumar, A., & Gupta, A. (2012). Assignment and travelling salesman problems with coefficients as LR fuzzy
parameters. International Journal of Applied Science and Engineering, 10(3), 155–170.
Kumar, A., Gupta, A., & Kaur, A. (2009). Method for solving fully fuzzy assignment problems using triangular
fuzzy numbers. International Journal of Computer and Information Engineering, 3, 231–234.
Kumar, A., & Kaur, A. (2011). Methods for solving fully fuzzy transportation problems based on classical
transportation methods. International Journal of Operations Research and Information Systems, 2(4), 52–71.
doi:10.4018/joris.2011100104
Kumar, A., & Kaur, M. (2013). A ranking approach for intuitionistic fuzzy numbers and its application. Journal
of Applied Research and Technology, 11(3), 381–396. doi:10.1016/S1665-6423(13)71548-7
Kumar, G., & Bajaj, R. K. (2014). On Solution of Interval Valued Intuitionistic Fuzzy Assignment Problem
Using Similarity Measure and Score Function. International Journal of Mathematical, Computational. Physical
and Quantum Engineering, 8(4), 713–718.
Kumar, P. S., & Hussain, R. J. (2014). A method for solving balanced intuitionistic fuzzy assignment problem.
International Journal of Engineering Research and Applications, 4(3), 897–903.
Kumar, P. S., & Hussain, R. J. (2014). A method for finding an optimal solution of an assignment problem under
mixed intuitionistic fuzzy environment. Proceedings of International Conference on Mathematical Sciences
(ICMS-2014), Sathyabama University (pp. 417-421).
Kumar, P. S., & Hussain, R. J. (2015). Computationally simple approach for solving fully intuitionistic fuzzy
real life transportation problems. International Journal of System Assurance Engineering and Management,
2015(1). doi:10.1007/s13198-014-0334-2
Li, D. F., Nan, J. X., & Zhang, M. J. (2010). A ranking method of triangular intuitionistic fuzzy numbers and
application to decision making. International Journal of Computational Intelligence Systems, 3(5), 522–530.
doi:10.1080/18756891.2010.9727719
Lin, C. J., &Wen, U. P. (2004). A labeling algorithm for the fuzzy assignment problem. Fuzzy Sets and Systems,
142(3), 373–391. doi:10.1016/S0165-0114(03)00017-4
Mahapatra, G. S., & Roy, T. K. (2009). Reliability evaluation using triangular intuitionistic fuzzy numbers,
arithmetic operations. International Scholarly and Scientific Research & Innovation, 3(2), 422–429.
Mahapatra, G. S., & Roy,T. K. (2013). Intuitionistic fuzzy number and its arithmetic operation with application
on system failure. Journal of Uncertain Systems, 7(2), 92–107.
Mitchell, H. B. (2004). Ranking intuitionistic fuzzy numbers. International Journal of Uncertainty, Fuzziness
and Knowledge-based Systems, 12(3), 377–386. doi:10.1142/S0218488504002886
Mukherjee, S., & Basu, K. (2010). Application of fuzzy ranking method for solving assignment problems with
fuzzy costs. International Journal of Computational and Applied Mathematics, 5(3), 359–368.
Mukherjee, S., & Basu, K. (2012). Solution of a class of intuitionistic fuzzy assignment problem by using
similarity measures. Knowledge-Based Systems, 27, 170–179. doi:10.1016/j.knosys.2011.09.007
Nasseri, S. H., & Ebrahimnejad, A. (2011). Sensitivity Analysis on Linear Programming Problems with
Trapezoidal FuzzyVariables. [IJORIS]. International Journal of Operations Research and Information Systems,
2(2), 22–39. doi:10.4018/joris.2011040102
Nayagam, G., Lakshmana, V., Venkateshwari, G., & Sivaraman, G. (2008, June). Ranking of intuitionistic fuzzy
numbers. Proceedings of the IEEE International Conference on Fuzzy Systems FUZZ-IEEE 08 (pp. 1971-1974).
IEEE.
Nehi, H. M. (2010). A new ranking method for intuitionistic fuzzy numbers. International Journal of Fuzzy
Systems, 12(1), 80–86.
Nehi, H. M., & Maleki, H. R. (2005, July). Intuitionistic fuzzy numbers and it’s applications in fuzzy optimization
problem. Proceedings of the Ninth WSEAS International Conference on Systems, Athens, Greece (pp. 1-5).

12. International Journal of Operations Research and Information Systems
Volume 7 • Issue 2 • April-June 2016
57
Paparrizos, K. (1991). An infeasible (exterior point) simplex algorithm for assignment problems. Mathematical
Programming, 51(1-3), 45–54. doi:10.1007/BF01586925
Pattnaik,M.(2015).Decisionmakingapproachtofuzzylinearprogramming(FLP)problemswithpostoptimal
analysis. International Journal of Operations Research and Information Systems, 6(4), 75–90. doi:10.4018/
IJORIS.2015100105
Ping, J. I., & Chu, K. F. (2002). A dual-matrix approach to the transportation problem. Asia-Pacific Journal of
Operational Research, 19(1), 35–45.
Prabakaran, K., & Ganesan, K. (2014). Fuzzy Hungarian method for solving intuitionistic fuzzy assignment
problems. International Journal of Scientific and Engineering Research, 5(9), 11–17.
Shabani, A., & Jamkhaneh, E. B. (2014). A new generalized intuitionistic fuzzy number. Journal of Fuzzy Set
Valued Analysis, 24, 1–10. doi:10.5899/2014/jfsva-00199
Shaw, A. K., & Roy, T. K. (2012). Some arithmetic operations on triangular intuitionistic fuzzy number and its
application on reliability evaluation. International Journal of Fuzzy Mathematics and Systems, 2(4), 363–382.
Singh,S.(2012).Noteonassignmentalgorithmwitheasymethodofdrawinglinestocoverallzeros.International
Journal of Operations Research and Information Systems, 3(3), 87–97. doi:10.4018/joris.2012070106
Singh, S. K., & Yadav, S. P. (2014). Efficient approach for solving type-1 intuitionistic fuzzy transportation
problem.InternationalJournalofSystemAssuranceEngineeringandManagement,1-9.doi:.10.1007/s13198-
014-0274-x
Srinivas, B., & Ganesan, G. (2015). A method for solving intuitionistic fuzzy assignment problem using Branch
and Bound Method, International Journal of Engineering Technology. Management and Applied Sciences,
3(2), 227–237.
Srinivas, B., & Ganesan, G. (2015). Optimal solution for intuitionistic fuzzy transportation problem via
Revised Distribution Method. International Journal of Mathematics Trends and Technology, 19(2), 150–161.
doi:10.14445/22315373/IJMTT-V19P519
Thompson,G.L.(1981).Arecursivemethodforsolvingassignmentproblems.JournalofScienceDirect-North-
Holland Mathematics Studies, 59, 319-343.
Thorani,Y. L. P., & Shankar, N. R. (2013). Fuzzy assignment problem with generalized fuzzy numbers. Applied
Mathematical Sciences, 7(71), 3511–3537.
Varghese, A., & Kuriakose, S. (2012). Centroid of an intuitionistic fuzzy number. Notes on Intuitionistic Fuzzy
Sets, 18(1), 19–24.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. doi:10.1016/S0019-9958(65)90241-X
P. Senthil Kumar is an Assistant Professor in PG and Research Department of Mathematics at Jamal Mohamed
College (Autonomous), Tiruchirappalli, Tamil Nadu, India. His research interests include operations research, fuzzy
optimization, intuitionistic fuzzy optimization, numerical analysis and graph theory. He received his BSc., MSc.,
MPhil degrees from Jamal Mohamed College, Tiruchirappalli, in 2006, 2008, 2010 respectively. He completed his
BEd in 2009 at Jamal Mohamed College of Teacher Education. He completed PGDCA in 2011 in the Bharathidasan
University and PGDAOR in 2012 in the Annamalai University, Tamil Nadu, India. He is now pursuing his PhD (Part
Time) in the area of Intuitionistic Fuzzy Optimization Technique. He has published research papers in referred
journals like Springer. He also presented his research in ELSEVIER conference proceedings.
R. Jahir Hussain received his MSc from AVC College (Autonomous), Mayiladudurai, MPhil and PhD from
Bharathidasan University, Tiruchirappalli, Tamilnadu. In 1996, he joined Jamal Mohamed College, Tiruchirappalli as
Lecturer in PG & Research Department of Mathematics. Now he is an Associate Professor. His activities currently
focus on Applications of Graph Theory. His research areas include Fuzzy Graph Theory and Fuzzy Optimization.