Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems
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This document presents a computationally simple method for solving fully intuitionistic fuzzy transportation problems, addressing uncertainty in supply, demand, and costs. The authors propose the PSK method, utilizing triangular intuitionistic fuzzy numbers to achieve optimal solutions with meaningful physical interpretations. A numerical example illustrates the effectiveness of the proposed approach, indicating its simplicity compared to existing methods.
Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems
- 1. 1 23 International Journal of System Assurance Engineering and Management ISSN 0975-6809 Int J Syst Assur Eng Manag DOI 10.1007/s13198-014-0334-2 Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems P. Senthil Kumar & R. Jahir Hussain
- 2. 1 23 Your article is protected by copyright and all rights are held exclusively by The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden. This e- offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com”.
- 3. ORIGINAL ARTICLE Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems P. Senthil Kumar • R. Jahir Hussain Received: 26 September 2014 / Revised: 18 December 2014 Ó The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2015 Abstract In solving real life transportation 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 intuition- istic fuzzy representation for the data. So, in this paper, we consider a transportation problem having uncertainty and hesitation in supply, demand and costs. We formulate the problem and utilize triangular intuitionistic fuzzy numbers (TrIFNs) to deal with uncertainty and hesitation. We pro- pose a new method called PSK method for finding the intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem in single stage. Also the new multiplication operation on TrIFN is proposed to find the optimal object value in terms of TrIFN. The main advan- tage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful. Finally the effectiveness of the proposed method is illustrated by means of a numerical example which is followed by graphical representation of the finding. Keywords Intuitionistic fuzzy set Á Triangular intuitionistic fuzzy number Á Fully intuitionistic fuzzy transportation problem Á PSK method Á Optimal solution 1 Introduction In several real life situations, there is a need for shipping the product from different origins (Factories) to different destinations (Warehouses). Here the aim of the decision maker (DM) is to find how much quantity of the product from which origin to which destination should be shipped subject to all the supply points are fully used and all the demand points are fully received in such a way that the total transportation cost is minimum for a minimization problem or total transportation profit is maximum for a maximization 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 quan- titatively 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 become 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 but it does not consider the non-membership (non-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 in the set represent 0. In conventional transportation problem supply, demand and costs are fixed crisp numbers. Therefore in this situation the DM can predict transportation cost exactly. On the con- trary in real world transportation problems, the availabilities and demands are not known exactly. These are uncertain quantities with hesitation due to various factors like lack of good communications, error in data, understanding of P. S. Kumar (&) Á R. J. Hussain PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamilnadu, India e-mail: [email protected] R. J. Hussain e-mail: [email protected] 123 Int J Syst Assur Eng Manag DOI 10.1007/s13198-014-0334-2 Author's personal copy
- 4. Reference to this paper should be made as follows: Kumar, P.S. & Hussain, R.J. Int J Syst Assur Eng Manag (2016) 7(Suppl 1): 90. https://doi.org/10.1007/s13198-014-0334-2 MLA Kumar, P. Senthil, and R. Jahir Hussain. "Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems." International journal of system assurance engineering and management 7.1 (2016): 90-101. DOI: 10.1007/s13198-014-0334-2 APA Kumar, P. S., & Hussain, R. J. (2016). Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems. International journal of system assurance engineering and management, 7(1), 90-101. DOI: 10.1007/s13198-014-0334-2 Chicago Kumar, P. Senthil, and R. Jahir Hussain. "Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems." International journal of system assurance engineering and management 7, no. 1 (2016): 90- 101. DOI: 10.1007/s13198-014-0334-2 Harvard Kumar, P.S. and Hussain, R.J., 2016. Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems. International journal of system assurance engineering and management, 7(1), pp.90-101. DOI: 10.1007/s13198-014-0334-2 Vancouver Kumar PS, Hussain RJ. Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems. International journal of system assurance engineering and management. 2016;7(1):90-101. DOI: 10.1007/s13198-014-0334-2
- 5. computationally very simple when compared to all the existing methods. Further, it can be concluded that the IFTP and MIFTP which can be solved by the existing methods (Hussain and Kumar 2012c); (Nagoor Gani and Abbas 2012); Antonyet al. (2014); Singh and Yadav (2014)) can also be solved by the proposed method. Acknowledgments The authors gratefully acknowledge the critical comments given by the learned reviewers which helped us to improve the manuscript. The first author would like to thank the people who helped continuously support the way to publish this paper. References Antony RJP, Savarimuthu SJ, Pathinathan T (2014) Method for solving the transportation problem using triangular intuitionistic fuzzy number. Int J Comput Algorithm 03:590–605 Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96 Bellman R, Zadeh LA (1970) Decision making in fuzzy environment. Manag Sci 17(B):141–164 Dinagar DS, Thiripurasundari K (2014) A navel method for solving fuzzy transportation problem involving intuitionistic trapezoidal fuzzy numbers. Int J Curr Res 6:7038–7041 Dinager DS, Palanivel K (2009) The transportation problem in fuzzy environment. Int J Algorithm Comput Math 2:65–71 Nagoor Gani A, Abbas S (2012) Mixed constraint intuitionistic fuzzy transportation problem. In: Proceedings in international confer- ence on mathematical modeling and applied soft computing (MMASC-2012), Coimbatore Institute of Technology, Coimba- tore, pp 832–843, 2012 Hussain RJ, Kumar PS (2012a) The transportation problem in an intuitionistic fuzzy environment. Int J Math Res 4:411–420 Hussain RJ, Kumar PS (2012b) Algorithmic approach for solving intuitionistic fuzzy transportation problem. Appl Math Sci 6:3981–3989 Hussain RJ, Kumar PS (2012c) The transportation problem with the aid of triangular intuitionistic fuzzy numbers. In: Proceedings in international conference on mathematical modeling and applied soft computing (MMASC-2012), Coimbatore Institute of Tech- nology, Coimbatore, pp 819–825, 2012 Hussain RJ, Kumar PS (2013) An optimal more-for-less solution of mixed constraints intuitionistic fuzzy transportation problems. Int J Contemp Math Sci 8:565–576 Kumar PS, Hussain RJ (2014a) A method for finding an optimal solution of an assignment problem under mixed intuitionistic fuzzy environment. In: Proceedings in international conference on mathematical sciences (ICMS-2014) Elsevier, Chennai, pp 417–421, 2014 Kumar PS, Hussain RJ (2014b) A systematic approach for solving mixed intuitionistic fuzzy transportation problems. Int J Pure Appl Math 92:181–190 Mohideen SI, Kumar PS (2010) A comparative study on transpor- tation problem in fuzzy environment. Int J Math Res 2:151–158 Pandian P, Natarajan G (2010) A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems. Appl Math Sci 4:79–90 Singh SK, Yadav SP (2014) Efficient approach for solving type-1 intuitionistic fuzzy transportation problem. Int J Syst Assur Eng Manag. doi:10.1007/s13198-014-0274-x Taha HA (2008) Operations research: an introduction, 8th edn. Pearson Education India, Gurgaon Varghese A, Kuriakose S (2012) Centroid of an intuitionistic fuzzy number. Notes Intuit Fuzzy Sets 18:19–24 Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353 Int J Syst Assur Eng Manag 123 Author's personal copy