Advances in Fuzzy Sets and Systems

The Advances in Fuzzy Sets and Systems publishes original research papers in the field of fuzzy sets and systems, covering topics such as artificial intelligence, robotics, decision-making, and data analysis. It also welcomes papers on variants of fuzzy sets and algorithms for computational work.

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AN INTUITIONISTIC FUZZY LOGARITHMIC MEASUREMENT FOR TRAVELLING SALESMAN PROBLEM

Authors

  • M. K. Sharma
  • Dhanpal Singh
  • Nitesh Dhiman

Keywords:

intuitionistic fuzzy logic, intuitionistic travelling salesman problem, difficulty, logarithm measurement.

DOI:

https://doi.org/10.17654/0973421X22008

Abstract

We introduce a novel method to obtain a comprehensive technique to several paths of intuitionistic fuzzy logic-based travelling salesman problem and identify the minimal path which will optimize the objective function. In this work, we will use a logarithm function for the measurement of difficult problem. The intuitionistic fuzzy logic approach is used to verify the shortest track for the travelling salesman problems. First, we use the concept of difficulty and then apply this concept to introduce logarithmic intuitionistic fuzzy travelling salesman problem. The planned methodology is demonstrated with an example.

Received: March 2, 2022
Accepted: April 11, 2022

References

L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.

A. Kumar and A. Gupta, Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions, Fuzzy Information and Engineering 3(1) (2011), 3-21.

S. Mukherjee and K. Basu, Application of fuzzy ranking method for solving assignment problems with fuzzy costs, International Journal of Computational and Applied Mathematics 5 (2010), 359-368.

D. Dubois and H. Prade, Fuzzy Sets and Systems Theory and Applications, Academic Press, New York, 1980.

A. Kumar and A. Gupta, Assignment and Travelling salesman problems with coefficient as LR fuzzy parameter, International Journal of Applied Science and Engineering 10(3) (2012), 155-170.

J. J. Buckley, Possibilistic linear programming with triangular fuzzy numbers, Fuzzy Sets and Systems 26 (1988), 135-138.

C. B. Chen and C. M. Klein, A simple approach to ranking a group of aggregated fuzzy utilities, IEEE Trans Syst., Man Cybern. B, SMC-27 (1997), 26-35.

S. H. Chen, Ranking fuzzy numbers with maximizing set and minimizing set and systems, Fuzzy Sets and Systems 17 (1985), 113-129.

S. Jain, An algorithm for fractional transshipment problem, International Journal of Mathematical Modeling Simulation & Applications 3 (2010), 62-67.

J. Majumdar and A. K. Bhunia, Genetic algorithm for asymmetric travelling salesman problem with imprecise travel times, J. Comput. Appl. Math. 235 (2011), 3063-3078.

R. Fischer and K. Richter, Solving a multi objective travelling salesman problem by dynamic programming, Optimization 13 (1982), 247-253.

K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1) (1986), 87-96.

N. Dhiman and M. K. Sharma, Calculus of new intuitionistic fuzzy generator: In generated intuitionistic fuzzy sets and its applications in medical diagnosis, International Journal of Advanced and Applied Sciences 7 (2020), 125-130.

G. J. Klir and B. Yuan, Fuzzy Sets & Fuzzy Logic Theory and Applications, Pearson Education, Inc., 1995.

P. Rajarajeswary, A. S. Sudha and R. Karthika, A new operation on hexagonal fuzzy number, International Journal of Fuzzy Logic Systems 3 (2013), 15-26.

P. Rajarajeswary and A. S. Sudha, Ordering generalized hexagonal fuzzy numbers using Rank, Mode, Divergence and Spread, IOSR Journal of Mathematics 10 (2014), 15-22.

D. S. Dinagar and U. H. Narayanan, On determinant of hexagonal fuzzy number matrices, Int. J. Math. Appl. 4 (2016), 357-363.

M. S. A. Christi and B. Kasthuri, Transportation problem with pentagonal intuitionistic fuzzy numbers solved using ranking technique and Russell’s method, Int. J. Eng. Res. Appl. 6 (2016), 82-86.

H. Basirzadeh, An approach for solving fuzzy transportation problem, Appl. Math. 5 (2011), 1549-1566.

P. Pandian and G. Natarajan, A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems, Appl. Math. Sci. 4 (2010), 79-90.

P. Pandian and G. Natarajan, An optimal more-for-less solution to fuzzy transportation problems with mixed constraints, Appl. Math. Sci. 4 (2010), 1405-1415.

A. N. Gani, A. E. Samuel and D. Anuradha, Simplex type algorithm for solving fuzzy transportation problem, Tamsui Oxf. J. Inf. Math. Sci. 27 (2011), 89-98.

D. S. Dinagar and K. Palanivel, On trapezoidal membership functions in solving transportation problem under fuzzy Environment, Int. J. Comput. Phys. Sci. 1 (2009), 1-12.

D. S. Dinagar and K. Palanivel, The transportation problem in fuzzy invironment, Int. J. Algorithms Comput. Math. 2 (2009), 65-71.

S. T. Liu and C. Kao, Solving fuzzy transportation problems based on extension principle, European J. Oper. Res. 153 (2004), 661-674.

M. Tavana, K. K. Damghani and A. R. Abtahi, A hybrid fuzzy group decision support framework for advanced-technology prioritization at NASA, Expert Syst. Appl. 40 (2013), 480-491.

J. L. Verdegay, A dual approach to solve the fuzzy linear programming problem, Fuzzy Sets and Systems 14 (1984), 131-144.

S. C. Fang, C.-F Hu, H. F. Wang and S.-Y. Wu, Linear programming with fuzzy coefficients in constraints, Comput. Math. Appl. 37 (1999), 63-76.

Y. R. Fan, G. H. Huang, Y. P. Li, M. F. Cao and G. H. Cheng, A fuzzy linear programming approach for municipal solid-waste management under uncertainty, Eng. Optim. 41(12) (2009), 1081-1101.

H. I. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems 1 (1978), 45-55.

S. Chanas, A concept of the optimal solution of the transportation problem with fuzzy cost coefficients, Fuzzy Sets and Systems 82 (1996), 299-305.

A. Ojha, B. Das S. K. Mondal and M. Maiti, A multi-item transportation problem with fuzzy tolerance, Appl. Soft. Comput. 13 (2013), 3703-3712.

M. Oheigeartaigh, A fuzzy transportation algorithm, Fuzzy Sets and Systems 8 (1982), 235-243.

J. Sadeghi S. Sadeghi and S. T. A. Niaki, Optimizing a hybrid vendor-managed inventory and transportation problem with fuzzy demand: an improved particle swarm optimization algorithm, Inform. Sci. 272 (2014), 126-144.

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Published

2022-05-14

Issue

Vol. 27 No. 1 (2022)

Section

Articles

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How to Cite

AN INTUITIONISTIC FUZZY LOGARITHMIC MEASUREMENT FOR TRAVELLING SALESMAN PROBLEM. (2022). Advances in Fuzzy Sets and Systems, 27(1), 151-167. https://doi.org/10.17654/0973421X22008

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