This document presents an article from the International Journal of Fuzzy System Applications that proposes a new method called the PSK method for solving type-1 and type-3 fuzzy transportation problems. In transportation problems, supplies, demands, and costs are usually certain values, but the article considers problems where these values may be uncertain and represented by fuzzy numbers like triangular or trapezoidal fuzzy numbers. The PSK method transforms the fuzzy transportation problem into a crisp one using an existing ranking procedure so that conventional solution methods can be applied. The method differs from solving certain transportation problems only in the allocation step. The PSK method and a new operation for multiplying trapezoidal fuzzy numbers are proposed to find an optimal solution with both crisp and fuzzy components
Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b
International Journal of Fuzzy System Applications editorial board and research articles
1.
2. Abbas Al-Refaie, University of Jordan, Jordan
Ahmad Taher Azar, Benha University, Egypt
P. Balasubramaniam, Gandhigram Rural University, India
Zeungnam Bien, UNIST, Korea
Asli Celikyilmaz, University of California-Berkeley, USA
Keeley Crockett, Manchester Metropolitan University, UK
Ali Ebrahimnejad, Islamic Azad University, Iran
K. Honda, Osaka Prefecture University, Japan
Jun-ichi Horiuch, Kitami Institute of Technology, Japan
Richard Jensen, The University of Wales, Aberystwyth, UK
Erich Peter Klement, Johannes Kepler University, Austria
Rudolf Kruse, Otto-von-Guericke-Universität Magdeburg, Germany
Salim Labiod, University of Jijel, Algeria
Yongming Li, Shaanxi Normal University, China
T. Warren Liao, Louisiana State Univeristy, USA
Pawan Lingras, Saint Mary’s University, Canada
Peide Liu, Shandong University, China
Yan-Jun Liu, Liaoning University of Technology, China
Yeh Ching Nee, National University of Singapore, Singapore
Jianbin Qiu, Harbin Institute of Technology, China
Chai Quek, Nanyang Technological University, Singapore
Elisabeth Rakus-Andersson, Blekinge Institute of Technology, Sweden
Soheil Salahshour, Islamic Azad University Mobarakeh Branch, Iran
Ismail Burhan Turksen, TOBB Economy and Technology University, Turkey
Pandian Vasant, Universiti Teknologi PETRONAS, Malaysia
Michael Voskoglou, Graduate Technological Educational Institute (T.E.I.), Greece
Hsiao-Fan Wang, National Tsing Hua University, China
Mao-Jiun J. Wang, National Tsing Hua University, Taiwan
Frank Werner, Otto-von-Guericke University, Germany
Chien-Wei Wu, National Taiwan University of Science and Technology, Taiwan
Tai-Shi Wu, National Taipei University, Taiwan
Zeshui Xu, PLA University of Science and Technology, China
Mesut Yavuz, Shenandoah University, USA
Gaofeng Yu, Sanming University, China
International Editorial Review Board
EDITOR-IN-CHIEF
Deng-Feng Li, Fuzhou University, China
INTERNATIONAL ADVISORY BOARD
Ronald R. Yager, Iona College, USA
Lotfi A. Zadeh, California University at Berkeley, USA
Hans-Jürgen Zimmermann, European Laboratory for Intelligent Techniques Engineering, Inform GmbH, Germany
ASSOCIATE EDITORS
Mark Burgin, UCLA, USA
Mingzhi Chen, Fuzhou University, China
Volume 5 • Issue 4 • October-December 2016 • ISSN: 2156-177X • eISSN: 2156-1761
An official publication of the Information Resources Management Association
International Journal of Fuzzy System Applications
5. International Journal of Fuzzy System Applications
Volume 5 • Issue 4 • October-December 2016
122
for general transportation problems. An Introduction to Operations Research Taha (2008) deals the
transportation problem.
In today’s real world problems such as in corporate or in industry many of the distribution
problems are imprecise in nature due to variations in the parameters. To deal quantitatively with
imprecise information in making decision, 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 Bellman and Zadeh (1970). The fuzzy set deals with
the degree of membership (belongingness) of an element in the set. In a fuzzy set the membership
value (level of acceptance or level of satisfaction) lies between 0 and 1 where as in crisp set the
element belongs to the set represent 1 and the element not belongs to the set represent 0.
Due to the applications of fuzzy set theory, several authors like Oheigeartaigh (1982) presented
an algorithm for solving transportation problems where the availabilities and requirements are fuzzy
sets with linear or triangular membership functions. Chanas et al. (1984) presented a fuzzy linear
programming model for solving transportation problems with fuzzy supply, fuzzy demand and crisp
costs. Chanas et al. (1993) formulated the fuzzy transportation problems in three different situations and
proposed method for solving the formulated fuzzy transportation problems. Chanas and Kuchta (1996)
proposed the concept of the optimal solution for the transportation problem with fuzzy coefficients
expressed as fuzzy numbers, and developed an algorithm for obtaining the optimal solution.
Chanas and Kuchta (1998) developed a new method for solving fuzzy integer transportation
problem by representing the supply and demand parameters as L-R type fuzzy numbers. Saad and
Abbas (2003) proposed an algorithm for solving the transportation problems under fuzzy environment.
Liu and Kao (2004) presented a method for solving fuzzy transportation problems based on extension
principle. Chiang (2005) proposed a method to find the optimal solution of transportation problems
with fuzzy requirements and fuzzy availabilities. Gani and Razak (2006) obtained a fuzzy solution
for a two stage cost minimizing fuzzy transportation problem in which availabilities and requirements
are trapezoidal fuzzy numbers using a parametric approach. Das and Baruah (2007) discussed Vogel’s
approximation method to find the fuzzy initial basic feasible solution of fuzzy transportation problem
in which all the parameters (supply, demand and cost) are represented by triangular fuzzy numbers.
Li et al. (2008) proposed a new method based on goal programming approach for solving fuzzy
transportation problems with fuzzy costs.
Chen et al. (2008) proposed the methods for solving transportation problems on a fuzzy network.
Lin (2009) used genetic algorithm for solving transportation problems with fuzzy coefficients.
Dinagar and Palanivel (2009) investigated the transportation problem in fuzzy environment using
trapezoidal fuzzy numbers. De and Yadav (2010) modified the existing method (Kikuchi 2000) by
using trapezoidal fuzzy numbers instead of triangular fuzzy numbers. Pandian et al. (2010) proposed
a new algorithm for finding a fuzzy optimal solution for fuzzy transportation problem where all the
parameters are trapezoidal fuzzy numbers. Mohideen and Kumar (2010) did a comparative study on
transportation problem in fuzzy environment. Sudhakar et al. (2011) proposed a different approach for
solving two stage fuzzy transportation problems in which supplies and demands are trapezoidal fuzzy
numbers. Hadi Basirzadeh (2011) discussed an approach for solving fuzzy transportation problem
where all the parameters are trapezoidal fuzzy numbers. Gani et al. (2011) presented simplex type
algorithm for solving fuzzy transportation problem where all the parameters are triangular fuzzy
numbers. Nasseri and Ebrahimnejad (2011) did sensitivity analysis on linear programming problems
with trapezoidal fuzzy variables.
Biswas and Modak (2012) studied using fuzzy goal programming technique to solve multi-
objective chance constrained programming problems in a fuzzy environment. Saati et al. (2012)
presented a two-fold linear programming model with fuzzy data. Ebrahimnejad (2012) discussed
cost efficiency measures with trapezoidal fuzzy numbers in data envelopment analysis based on
ranking functions: application in insurance organization and hospital. Rani et al. (2014) presented a
method for unbalanced transportation problems in fuzzy environment taking all the parameters are
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8. Reference to this paper should be made as follows:
MLA
Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy
Transportation Problems." IJFSA 5.4 (2016): 121-146. Web. 16 Mar. 2017.
doi:10.4018/IJFSA.2016100106
APA
Kumar, P. S. (2016). PSK Method for Solving Type-1 and Type-3 Fuzzy
Transportation Problems. International Journal of Fuzzy System Applications
(IJFSA), 5(4), 121-146. doi:10.4018/IJFSA.2016100106
Chicago
Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy
Transportation Problems," International Journal of Fuzzy System Applications
(IJFSA) 5 (2016): 4, accessed (March 16, 2017),
doi:10.4018/IJFSA.2016100106
9. International Journal of Fuzzy System Applications
Volume 5 • Issue 4 • October-December 2016
144
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P. Senthil Kumar is an Assistant Professor in PG and Research Department of Mathematics at Jamal Mohamed
College (Autonomous), Tiruchirappalli, Tamil Nadu, India. He has six years of teaching experience. He received
his BSc, MSc and MPhil from Jamal Mohamed College, Tiruchirappalli in 2006, 2008, 2010 respectively. He
completed his BEd in Jamal Mohamed College of Teacher Education in 2009. He completed PGDCA in 2011
in the Bharathidasan University and PGDAOR in 2012 in the Annamalai University, Tamil Nadu, India. He has
submitted his PhD thesis in the area of intuitionistic fuzzy optimisation technique to the Bharathidasan University
in 2015. He has published many research papers in referred national and international journals like Springer, IGI
Global, etc. He also presented his research in Elsevier Conference Proceedings (ICMS-2014), MMASC-2012, etc.
His areas of interest include operations research, fuzzy optimisation, intuitionistic fuzzy optimisation, numerical
analysis and graph theory, etc.