Multi-objective linear fractional inventory model with possibility and necessity constraints under generalised intuitionistic fuzzy set environment

Totan Garai; Harish Garg

Multi-objective linear fractional inventory model with possibility and necessity constraints under generalised intuitionistic fuzzy set environment

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Author(s): Totan Garai¹ and Harish Garg²
- Affiliations: 1: Department of Mathematics , Silda Chandra Sekhar College , Jhargram-721515, West Bengal , India ;
  2: School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University , Patiala-147004, Punjab , India
Source: Volume 4, Issue 3, September 2019, p. 175 – 181
DOI: 10.1049/trit.2019.0030 , Online ISSN 2468-2322

This is an open access article published by the IET, Chinese Association for Artificial Intelligence and Chongqing University of Technology under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)

Received 02/05/2019, Accepted 10/07/2019, Revised 26/06/2019, Published 19/07/2019

This study presented a multi-objective linear fractional inventory (LFI) problem with generalised intuitionistic fuzzy numbers. In modelling, the authors have assumed the ambiances where generalised trapezoidal intuitionistic fuzzy numbers (GTIFNs) used to handle the uncertain information in the data. Then, the given multi-objective generalised intuitionistic fuzzy LFI model was transformed into its equivalent deterministic linear fractional programming problem by employing the possibility and necessity measures. Finally, the applicability of the model is demonstrated with a numerical example and the sensitivity analysis under several parameters is investigated to explore the study.

References

1. 1)
  - [22]. Iskandar, M.G.: ‘A possibility programming approach for stochastic fuzzy multi-objective linear fractional programs’, Comput. Math. Appl., 2004, 48, pp. 1603–1609 (doi: 10.1016/j.camwa.2004.04.035).
2. 2)
  - [24]. Dutta, D., Kumar, P.: ‘Application of fuzzy goal programming approach to multi-objective linear fractional inventory model’, Int. J. Syst. Sci., 2015, 46, pp. 2269–2278 (doi: 10.1080/00207721.2013.860639).
3. 3)
  - [5]. Zadeh, L.A.: ‘Fuzzy sets as a basis for a theory of possibility’, Fuzzy Sets Syst., 1978, 1, pp. 3–28 (doi: 10.1016/0165-0114(78)90029-5).
4. 4)
  - 24. Liu, B., Liu, Y.K.: ‘Expected value of fuzzy variable and fuzzy expected value models’, IEEE Trans. Fuzzy Syst., 2002, 10, (4), pp. 445–450 (doi: 10.1109/TFUZZ.2002.800692).
5. 5)
  - [26]. Ali, I., Gupta, S., Ahmed, A.: ‘Multi-objective linear fractional inventory problem under intuitionistic fuzzy environment’, Int. J. Syst. Assur. Eng. Manage., 2018, 10, pp. 173–189 (doi: 10.1007/s13198-018-0738-5).
6. 6)
  - [8]. Klir, J.G.: ‘On fuzzy set interpretation of possibility theory’, Fuzzy Sets Syst., 1992, 108, pp. 263–273 (doi: 10.1016/S0165-0114(97)00371-0).
7. 7)
  - [25]. Garg, H.: ‘Fuzzy inventory models for deteriorating items under different types of lead-time distributions’, in Kahraman, C., , Çevik Onar, S. (Eds.): ‘Intelligent systems in project planning’, 2015, vol. 87, pp. 247–274, doi: 101007/978-3-319-17906-3_11.
8. 8)
  - [3]. Xu, Z.S., Yager, R.R.: ‘Some geometric aggregation operators based on intuitionistic fuzzy sets’, Int. J. Gen. Syst., 2006, 35, pp. 417–433 (doi: 10.1080/03081070600574353).
9. 9)
  - [29]. Garg, H.: ‘A hybrid PSO-GA algorithm for constrained optimization problems’, Appl. Math. Comput., 2016, 274, pp. 292–305.
10. 10)
  - [15]. Roy, K.T., Maiti, M.: ‘Multi-objective inventory models of deteriorating items with some constraints in a fuzzy environment’, Comput. Oper. Res., 1998, 25, pp. 1085–1095 (doi: 10.1016/S0305-0548(98)00029-X).
11. 11)
  - [11]. Heilpern, S.: ‘The expected value of a fuzzy number’, Fuzzy Sets Syst., 1992, 47, pp. 81–86 (doi: 10.1016/0165-0114(92)90062-9).
12. 12)
  - [16]. Garg, H., Rani, M., Sharma, S.P., et al: ‘Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment’, Expert Syst. Appl., 2014, 41, pp. 3157–3167 (doi: 10.1016/j.eswa.2013.11.014).
13. 13)
  - [7]. Yager, R.R.: ‘On the specificity of a possibility distribution’, Fuzzy Sets Syst., 1992, 50, pp. 279–292 (doi: 10.1016/0165-0114(92)90226-T).
14. 14)
  - [13]. Garai, T., Chakraborty, D., Roy, T.K.: ‘Possibility mean, variance and covariance of generalized intuitionistic fuzzy numbers and its application to multi-item inventory model with inventory level dependent demand’, J. Intell. Fuzzy Syst., 2018a, 35, pp. 1021–1036 (doi: 10.3233/JIFS-17298).
15. 15)
  - [18]. Jafariana, E., Razmi, J., Baki, M.F.: ‘A flexible programming approach based on intuitionistic fuzzy optimization and geometric programming for solving multi-objective nonlinear programming problems’, Expert Syst. with Appl., 2018, 93, pp. 245–256 (doi: 10.1016/j.eswa.2017.10.030).
16. 16)
  - 21. Zadeh, L.A.: ‘Fuzzy sets’, Inf. Control, 1965, 8, (3), pp. 338–353 (doi: 10.1016/S0019-9958(65)90241-X).
17. 17)
  - [30]. Garg, H.: ‘A hybrid GSA-GA algorithm for constrained optimization problems’, Inf. Sci., 2019, 478, pp. 499–523 (doi: 10.1016/j.ins.2018.11.041).
18. 18)
  - [19]. Garai, T., Chakraborty, D., Roy, T.K.: ‘A multi-item multi-objective inventory model in exponential fuzzy environment using chance-operator techniques’, J. Anal., 2019, 3, pp. 1–27.
19. 19)
  - [4]. Garai, T., Chakraborty, D., Roy, T.K.: ‘Possibility necessity credibility measures on generalized intuitionistic fuzzy number and its applications to multi-product manufacturing system’, Granular Comput., 2017, 2, pp. 1–15 (doi: 10.1007/s41066-016-0022-5).
20. 20)
  - [20]. Dutta, D., Tiwari, R.N., Rao, J.R.: ‘Effect of tolerance in fuzzy linear fractional programming’, Fuzzy Sets Syst., 1993, 55, pp. 133–142 (doi: 10.1016/0165-0114(93)90126-3).
21. 21)
  - [2]. Atanassov, T.K.: ‘Intuitionistic fuzzy sets’, Fuzzy Sets Syst., 1986, 20, pp. 87–96 (doi: 10.1016/S0165-0114(86)80034-3).
22. 22)
  - [17]. Rani, D., Gulati, T.R., Garg, H.: ‘Multi-objective non-linear programming problem in intuitionistic fuzzy environment: optimistic and pessimistic viewpoint’, Expert Syst. with Appl., 2016, 64, pp. 228–238 (doi: 10.1016/j.eswa.2016.07.034).
23. 23)
  - [21]. Dutta, D., Tiwari, R.N., Rao, J.R.: ‘Fuzzy approaches for multiple criteria linear fractional optimization: a comment’, Fuzzy Sets Syst., 1994, 54, pp. 347–349 (doi: 10.1016/0165-0114(93)90381-Q).
24. 24)
  - [23]. Sadjadi, S.J., Aryanezhad, M.B., Sarfaraj, A.: ‘A fuzzy approach to solve a multi-objective linear fractional inventory model’, J. Ind. Eng. Intell., 2005, 1, pp. 43–47.
25. 25)
  - [27]. Garai, T., Chakraborty, D., Roy, T.K.: ‘A multi-item periodic review probabilistic fuzzy inventory model with possibility and necessity constraints’, Int. J. Bus. Forecast. Mark. Intell., 2016, 2, pp. 175–189.
26. 26)
  - [14]. Garai, T., Chakraborty, D., Roy, T.K.: ‘A multi-objective multi-item inventory model with both stock-dependent demand rate and holding cost rate under fuzzy rough environment’, Granular Comput., 2018, 3, pp. 1–18 (doi: 10.1007/s41066-017-0067-0).
27. 27)
  - [6]. Dubois, D., Prade, H.: ‘Possibility theory’ (Plenum Press, New-York, 1988).
28. 28)
  - [10]. Carlsson, C., Fuller, R.: ‘On possibilistic mean and variance of fuzzy number’, Fuzzy Sets Syst., 2001, 122, pp. 315–326 (doi: 10.1016/S0165-0114(00)00043-9).
29. 29)
  - [12]. Garg, H.: ‘A novel approach for analyzing the reliability of series–parallel system using credibility theory and different types of intuitionistic fuzzy numbers’, J. Braz. Soc. Mech. Sci. Eng., 2016, 38, (3), pp. 1021–1035 (doi: 10.1007/s40430-014-0284-2).
30. 30)
  - [28]. Chakraborty, D., Jana, D.K., Roy, T.K.: ‘Expected value of intuitionistic fuzzy number and its application to solve multi-objective multi-item solid transportation problem for damageable items in intuitionistic fuzzy environment’, J. Intell. Fuzzy Syst., 2016, 30, pp. 1109–1122 (doi: 10.3233/IFS-151833).

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Multi-objective linear fractional inventory model with possibility and necessity constraints under generalised intuitionistic fuzzy set environment

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