# Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 3, Issue 1, April 2019, Pages: 21-32

## Assignment problem with neutrosophic costs and its solution methodology

Tuhin Bera1* and Nirmal Kumar Mahapatra2

1Department of Mathematics, Boror S. S. High School, Bagnan, Howrah-711312, WB, India.
2Department of Mathematics, Panskura Banamali College, Panskura RS-721152, WB, India.

### Abstract

In this study, a single valued neutrosophic number has been presented in a new direction so that a decision maker has a scope of flexibility to choose different numbers in their study. Its structural characteristics are also studied here. Then this kind of number has been converted into a numeric value by means of a parameter (whose value is pre-assigned) to practice in real fields and using this, a ranking function is defined to compare two or more single valued neutrosophic numbers. In continuation, an assignment problem and its solution methodology have been developed in neutrosophic environment. Two real problems are solved to demonstrate the proposed method.

### Keywords

Neutrosophic set, Single valued neutrosophic number, Ranking function, Assignment problem.

### Reference

1. Abbasbandy S, Asady B. Ranking of fuzzy numbers by sign distance. Information Sciences, 2006; 176: 2405-2416.

2. Atanassov K. Intuitionistic fuzzy sets. Fuzzy sets and systems, 1986; 20(1): 87-96.

3. Bera T, Mahapatra NK. (α; β; γ)-cut of neutrosophic soft set and it’s application to neutrosophic soft groups. Asian Journal of Math. and Compt. Research, 2016; 12(3): 160-178.

4. Chen MS. On a fuzzy assignment problem. Tamkang J., 1985; 22: 407-411.

5. Deli I, Subas Y. A ranking method of single valued neutrosophic numbers and its application to multi-attribute decision making problems. Int. J. Mach. Learn. and Cyber., (February, 2016), DOI 10.1007/s13042-016-0505-3.

6. Li DF. A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems. Comput. Math. Appl., 2010; 60: 1557-1570.

7. Lin CJ, Wen UP. A labeling algorithm for the fuzzy assignment problem. Fuzzy sets and systems, 2004; 142: 373-391.

8. Maleki HR. Ranking function and their application to fuzzy linear programming. Far East J. Math. Sci., 2002; 4: 283-301.

9. Mukherjee S, Basu K. Application of fuzzy ranking method for solving assignment problems with fuzzy costs. Int. J. of Computational and App. Math., 2010; 5(3): 359-368.

10. Rao PPB, Shankar NR. Ranking fuzzy numbers with an area method using circumferance of centroid. Fuzzy Information and Engineering, 2013; 1: 3-18.

11. Smarandache F. Neutrosophy, neutrosophic probability, set and logic. Amer. Res. Press, Rehoboth, USA. http://fs.gallup.unm.edu/eBook-neutrosophics4.pdf (fourth version), 1998; pp. 105.

12. Smarandache F. Neutrosophic set, A generalisation of the intuitionistic fuzzy sets. Inter. J. Pure Appl. Math., 2005; 24: 287-297.

13. Wang H, Zhang Y, Sunderraman R and Smarandache F. Single valued neutrosophic sets. Fuzzy Sets, Rough Sets and Multivalued Operations and Applications, 2011; 3(1): 33-39.

14. Yao JS, Wu K. Ranking of fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and System, 2000; 16: 275-288.

15. Zadeh LA. Fuzzy sets. Information and control, 1965; 8: 338-353.