We apologize for the inconvenience...
To ensure we keep this website safe, please can you confirm you are a human by ticking the box below.
If you are unable to complete the above request please contact us using the below link, providing a screenshot of your experience.
https://ioppublishing.org/contacts/
Intuitionistic fuzzy solid assignment problems: a software-based approach
- Original Article
- Published: 23 May 2019
- Volume 10 , pages 661–675, ( 2019 )
Cite this article
- P. Senthil Kumar ORCID: orcid.org/0000-0003-4317-1021 1
331 Accesses
42 Citations
51 Altmetric
Explore all metrics
This paper sustains a sound mathematical and computing background. In this paper, the software-based approach for solving intuitionistic fuzzy solid assignment problem (IFSAP) is presented. The IFSAP is formulated and it is solved by using Lingo 17.0 software tool. Theorems related to IFSAP is proved. The IFSAP and its crisp solid assignment problem both are solved at a time and their optimal solution is obtained. In addition, the optimal objective values of both the IFSAP and its crisp solid assignment problem (SAP) are estimated with the help of substituting the optimal solution(s) to their respective decision variables in the objective functions. Some new and important results are proposed. To illustrate the efficiency of the proposed method the numerical example is presented. The reliability of the proposed results are verified by using the numerical example. Strengths and weakness of the paper is mentioned. The novelty of the analysis is given into a coherent, concise, and meaningful manner of analysis. Social issue (real-life problem) is converted into a mathematical model and it is solved by the proposed method. At the end, the advantages of the proposed algorithm is explained.
This is a preview of subscription content, log in via an institution to check access.
Access this article
Subscribe and save.
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
Price includes VAT (Russian Federation)
Instant access to the full article PDF.
Rent this article via DeepDyve
Institutional subscriptions
Similar content being viewed by others
A Distinct Method for Solving Fuzzy Assignment Problems Using Generalized Quadrilateral Fuzzy Numbers
Linear Programming with Interval Type-2 Fuzzy Constraints
Solving fully fuzzy multi-objective linear programming problem using nearest interval approximation of fuzzy number and interval programming.
Abhishekh, Nishad AK (2018) A novel ranking approach to solving fully LR-intuitionistic fuzzy transportation problems. New Math Nat Comput 15(01):95–112. https://doi.org/10.1142/s1793005719500066
Article MathSciNet Google Scholar
Aggarwal S, Gupta C (2017) Sensitive analysis in intuitionistic fuzzy solid transportation problem. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-016-0292-8
Article Google Scholar
Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86(3):299–306. https://doi.org/10.1016/S0165-0114(96)00009-7
Article MATH MathSciNet Google Scholar
Anuradha D (2015) On solving fuzzy solid assignment problems. Int Res J Eng Technol 2(5):322–325
Google Scholar
Anuradha D, Pandian P (2012) A new method for finding an optimal solution to solid assignment problems. Int J Eng Res Appl 2(3):1614–1618
Atanassov K (1983) Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci.—Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian)
Atanassov KT (1999) Intuitionistic fuzzy sets: theory and applications. Physica-Verlag, Heidelberg
Book Google Scholar
Burillo P, Bustince H, Mohedano V (1994) Some definitions of intuitionistic fuzzy number-first properties. In: Proceedings of the first workshop on fuzzy based expert system, Sofia, Bulgaria, pp 53–55
Dinagar DS, Palanivel K (2009) The transportation problem in fuzzy environment. Int J Algorithms Comput Math 2(3):65–71
MATH Google Scholar
Faudzi S, Abdul-Rahman S, Abd Rahman R (2018) An assignment problem and its application in education domain: a review and potential path. Adv Oper Res 2018:Article ID 8958393. https://doi.org/10.1155/2018/8958393
Gotmare AD, Khot PG (2016) Solution of a fuzzy assignment problem by using Branch-and-Bound technique with application of linguistic variable. Int J Comput Technol 15(4):6649–6653
Habib M (2018) Handbook of research on investigations in artificial life research and development. IGI Global, Hershey, pp 1–501. https://doi.org/10.4018/978-1-5225-5396-0
Hossen MA, Akther A (2017) Divide row minima and subtract column minima technique for solving assignment problems. Int J Adv Res 5(12):1323–1329. https://doi.org/10.21474/IJAR01/6089
Hu K-J (2017) Fuzzy goal programming technique for solving flexible assignment problem in PCB assembly line. J Inf Optim Sci 38(3–4):423–442. https://doi.org/10.1080/02522667.2016.1187922
Hussain RJ, Kumar PS (2012a) Algorithmic approach for solving intuitionistic fuzzy transportation problem. Appl Math Sci 6:3981–3989
MATH MathSciNet Google Scholar
Hussain RJ, Kumar PS (2012b) The transportation problem in an intuitionistic fuzzy environment. Int J Math Res 4:411–420
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), vol 1. Coimbatore Institute of Technology, pp 819–825
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. https://doi.org/10.12988/ijcms.2013.13056
Jinshuai Y, Jin L, Yi W, Tong W, Zhanqiang L (2017) Optimization of weapon-target assignment problem by intuitionistic fuzzy genetic algorithm. In: MATEC Web of conferences, vol 128, p 02004. EDP Sciences. https://doi.org/10.1051/matecconf/201712802004
Kadhem D (2017) Heuristic solution approaches to the solid assignment problem (Doctoral dissertation, University of Essex)
Khalifa HA, Al-Shabi M (2018) An interactive approach for solving fuzzy multi-objective assignment problems. J Adv Math Comput Sci 28(6):1–12. https://doi.org/10.9734/JAMCS/2018/44339
Kuhn HW (1955) The Hungarian method for the assignment problem. Naval Res Logist Q 2(1–2):83–97. https://doi.org/10.1002/nav.3800020109
Kumar PS (2016a) PSK method for solving type-1 and type-3 fuzzy transportation problems. Int J Fuzzy Syst Appl 5(4):121–146. https://doi.org/10.4018/IJFSA.2016100106
Kumar PS (2016b) A simple method for solving type-2 and type-4 fuzzy transportation problems. Int J Fuzzy Logic Intell Syst 16(4):225–237. https://doi.org/10.5391/IJFIS.2016.16.4.225
Kumar PS (2017a) PSK method for solving type-1 and type-3 fuzzy transportation problems. In: Fuzzy systems: concepts, methodologies, tools, and applications. IGI Global, Hershey, pp 367–392. https://doi.org/10.4018/978-1-5225-1908-9.ch017
Kumar PS (2017b) Algorithmic approach for solving allocation problems under intuitionistic fuzzy environment, PhD thesis, Jamal Mohamed College, affiliated to the Bharathidasan University, Tiruchirappalli, India. http://hdl.handle.net/10603/209151
Kumar PS (2018a) Search for an optimal solution to vague traffic problems using the PSK method. In: Habib M (ed) Handbook of research on investigations in artificial life research and development. IGI Global, Hershey, pp 219–257. https://doi.org/10.4018/978-1-5225-5396-0.ch011
Chapter Google Scholar
Kumar PS (2018b) A note on ‘a new approach for solving intuitionistic fuzzy transportation problem of type-2’. Int J Logist Syst Manag 29(1):102–129. https://econpapers.repec.org/article/idsijlsma/v_3a29_3ay_3a2018_3ai_3a1_3ap_3a102-129.htm
Kumar PS (2018c) Linear programming approach for solving balanced and unbalanced intuitionistic fuzzy transportation problems. Int J Oper Res Inf Syst 9(2):73–100. https://doi.org/10.4018/IJORIS.2018040104
Kumar PS (2018d) A simple and efficient algorithm for solving type-1 intuitionistic fuzzy solid transportation problems. Int J Oper Res Inf Syst 9(3):90–122. https://doi.org/10.4018/IJORIS.2018070105
Kumar PS (2018e) PSK method for solving intuitionistic fuzzy solid transportation problems. Int J Fuzzy Syst Appl 7(4):62–99. https://doi.org/10.4018/ijfsa.2018100104
Kumar PS (2019a) Integer programming approach for solving solid and intuitionistic fuzzy solid assignment problems. Int J Syst Assur Eng Manag (under review)
Kumar PS (2019b) Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set. Int J Syst Assur Eng Manag (Under review, minor revision)
Kumar PS (2019c) PSK method for solving mixed and type-4 intuitionistic fuzzy solid transportation problems. Int J Oper Res Inf Syst 10(2):20–53. https://doi.org/10.4018/IJORIS.2019040102
Kumar PS (2019d) Software-based approach for solving intuitionistic fuzzy solid transportation problems. Int J Appl Manag Sci (under review)
Kumar PS (2019e) Discovery of a new kind of type-2 fuzzy and type-2 intuitionistic fuzzy transportation problems and identification of its optimal solutions. Int J Oper Res Inf Syst (under review)
Kumar PS (2019f) Linear programming method for solving solid and intuitionistic fuzzy solid transportation problems. Int J Syst Assur Eng Manag (under review)
Kumar PS (2019g) Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem. Int J Oper Res (article in press)
Kumar PS (2019h) Using the PSK method discovery of a solution to uncertain transportation problems and determination of the solution to the special case of type-2 fuzzy transportation problems. Complex & Intelligent Systems (under review)
Kumar PS (2020a) The PSK method for solving fully intuitionistic fuzzy assignment problems with some software tools. Theoretical and applied mathematics in international business. IGI Global, Hershey (accepted)
Kumar PS (2020b) Computationally simple and efficient method for solving real-life mixed intuitionistic fuzzy solid assignment problems. Int J Fuzzy Syst Appl (accepted)
Kumar PS (2020c) Developing a new approach to solve solid assignment problems under intuitionistic fuzzy environment. Int Journal of Fuzzy Syst Appl 9(1),Article 1 (accepted)
Kumar PS, Hussain RJ (2014a) A systematic approach for solving mixed intuitionistic fuzzy transportation problems. Int J Pure Appl Math 92:181–190. https://doi.org/10.12732/ijpam.v92i2.4
Article MATH Google Scholar
Kumar PS, Hussain RJ (2014b) 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, Sathyabama University, pp 417–421, ISBN-978-93-5107-261-4
Kumar PS, Hussain RJ (2014c) New algorithm for solving mixed intuitionistic fuzzy assignment problem. Elixir Appl Math 73:25971–25977
Kumar PS, Hussain RJ (2014d) A method for solving balanced intuitionistic fuzzy assignment problem. Int J Eng Res Appl 4(3):897–903
Kumar PS, Hussain RJ (2015) A method for solving unbalanced intuitionistic fuzzy transportation problems. Notes Inst Fuzzy Sets 21(3):54–65
Kumar PS, Hussain RJ (2016a) Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems. Int J Syst Assur Eng Manag 7(1):90–101. https://EconPapers.repec.org/RePEc:spr:ijsaem:v:7:y:2016:i:1:d:10.1007_s13198-014-0334-2 . https://doi.org/10.1007/s13198-014-0334-2
Kumar PS, Hussain RJ (2016b) A simple method for solving fully intuitionistic fuzzy real life assignment problem. Int J Oper Res Inf Syst 7(2):39–61. https://EconPapers.repec.org/RePEc:igg:joris0:v:7:y:2016:i:2:p:39-61 https://doi.org/10.4018/IJORIS.2016040103
Kumar PS, Hussain RJ (2016c) An algorithm for solving unbalanced intuitionistic fuzzy assignment problem using triangular intuitionistic fuzzy number. J Fuzzy Math 24(2):289–302
Kumar N, Shukla D (2016) Resource management through fuzzy assignment problem in cloud computing environment. In: Proceedings of the second international conference on information and communication technology for competitive strategies. ACM, p 87. https://doi.org/10.1145/2905055.2905146
Malini P, Ananthanarayanan M (2016) Solving fuzzy assignment problem using ranking of generalized trapezoidal fuzzy numbers. Indian J Sci Technol 9(20):1–4. https://doi.org/10.17485/ijst/2016/v9i20/88691
Mohideen SI, Kumar PS (2010) A comparative study on transportation problem in fuzzy environment. Int J Math Res 2:151–158
Muralidaran C, Venkateswarlu B (2017) A method for solving equally spread symmetric fuzzy assignment problems using branch and bound technique (14th ICSET-2017). IOP Conf Ser Mater Sci Eng 263(4):042123. https://doi.org/10.1088/1757-899x/263/4/042123
Nagoorgani A, Kavikumar J, Mohamed VN, Shamsidah A. N (2016) A labeling algorithm for solving intuitionistic fuzzy optimal assignment problems. In: 2016 IEEE international conference on fuzzy systems (FUZZ-IEEE). IEEE, Vancouver, BC, Canada, pp 1621–1627). https://doi.org/10.1109/fuzz-ieee.2016.7737884
Ozor PA, Chigozirim PO, Odukwe AO, Ume JI, Ozoegwu CG (2017) Application of the assignment technique to optimisation of solid waste management in Enugu region. Int J Environ Waste Manag 19(1):52–73
Pierskalla WP (1967) The tri-substitution method for the three-dimensional assignment problem. CORS J 5:71–81
Saini RK, Sangal A, Prakash O (2018) Fuzzy transportation problem with generalized triangular-trapezoidal fuzzy number. In: Soft computing: theories and applications. Springer, Singapore, pp 723–734. https://doi.org/10.1007/978-981-10-5687-1_64
Sam’an M, Surarso B, Zaki S (2018) A modified algorithm for full fuzzy transportation problem with simple additive weighting. In: 2018 International conference on information and communications technology (ICOIACT). IEEE, pp 684–688. https://doi.org/10.1109/icoiact.2018.8350745
Thakre TA, Chaudhari OK, Dhawade NR (2018) Placement of staff in LIC using fuzzy assignment problem. Int J Math Trends Technol 53(4):259–266
Varghese A, Kuriakose S (2012) Centroid of an intuitionistic fuzzy number. Notes Inst Fuzzy Sets 18:19–24
Vinoliah EM, Ganesan K (2018) Fuzzy optimal solution for a fuzzy assignment problem with octagonal fuzzy numbers. J Phys Conf Ser 1000(1):012016
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Download references
Acknowledgements
The author is grateful to anonymous referees for their constructive as well as helpful suggestions and comments to revise the paper in the present form.
Author information
Authors and affiliations.
Department of Humanities and Sciences, Navodaya Institute of Technology, Bijanagera Road, P.B. No. 26, Navodaya Nagar, Raichur, Karnataka, 584103, India
P. Senthil Kumar
You can also search for this author in PubMed Google Scholar
Corresponding author
Correspondence to P. Senthil Kumar .
Additional information
Publisher's note.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Reprints and permissions
About this article
Kumar, P.S. Intuitionistic fuzzy solid assignment problems: a software-based approach. Int J Syst Assur Eng Manag 10 , 661–675 (2019). https://doi.org/10.1007/s13198-019-00794-w
Download citation
Received : 24 February 2018
Revised : 17 April 2019
Published : 23 May 2019
Issue Date : August 2019
DOI : https://doi.org/10.1007/s13198-019-00794-w
Share this article
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative
- Intuitionistic fuzzy set
- Intuitionistic fuzzy number
- Triangular intuitionistic fuzzy number
- Assignment problem
- Solid assignment problem
- Intuitionistic fuzzy solid assignment problem
- Software-based approach
- Optimal assignment
- Optimal solution
- Find a journal
- Publish with us
- Track your research
COMMENTS
The objective of fuzzy assignment problem is to find the least assignment fuzzy cost (maximum fuzzy profit) of workers with varying degree of skills to job. To attain the objective in this article ...
This paper presents optimum solution of fuzzy assignment problem by using fourier elimination method. This method is to obtain a minimum assignment cost in fuzzy environment for a fuzzy assignment problem with all parameters are triangular fuzzy numbers. Fuzzy numbers are converting in to a crisp number with the help of ranking functions.
To illustrate a fuzzy assignment problem whose elements are Heptogonal fuzzy numbers by using the proposed method taken from the paper 'Fuzzy assignment Problem Using Normalised Heptagonal Fuzzy numbers' by P. Selvam, A. Rajkumar and J. Sudha Easwari. Let us consider a fuzzy assignment problem with rows representing three jobs J 1, J 2, J 3
Keywords—Balanced fuzzy assignment problem; fuzzy number; A fuzzy numberHungarian Method I. INTRODUCTION An assignment problem (AP) has many applications in transportation, healthcare, education, and sports. Using assignment problems we minimize time, minimize cost, minimize length path route, and maximize profit.
Fuzzy assignment problems, Hexagonal Fuzzy optimal solution, Diagonal Optimal method. I. INTRODUCTION The fuzzy set theory was put forward by Zadeh [20] in the year 1965. For the past six decades researchers gave more attention to the set fuzzy theory. It may be applied in the fields like operations research, control theory, neural
Assignment problem is the biggest significant problem in decision-making. In this paper, a novel technique is planned to discover the best possible solution to a balanced fuzzy assignment problem (FAP). We derive two formulae; one is related to the odd number of...
The fuzzy assignment problems and fuzzy travelling salesman problems which can be solved by using the existing method, can also be solved by using the proposed methods. But, there exist certain fuzzy assignment problems and fuzzy travelling salesman problems which can be solved only by using the proposed methods. To illustrate the proposed ...
Keywords: Assignment problem, Fuzzy quantity, Fractional linear programming, Parallel moving method. 1. Introduction The assignment problem (AP) is a special type of a transportation problem and a linear zero-one programming problem [11]. It is a one of the well-studied
We solve a fully fuzzy assignment problem (FAP) where the costs are triangular fuzzy numbers. The FAP has gained its importance in the recent years. We have represented the fuzzy numbers in their parametric form and then solved it through ones assignment method. To the best of our knowledge, several authors have acquired the solution for a FAP ...
erally, the transportation problems and assignment prob-lems both are called optimization problems) under fuzzy environment successfully. Recently, Anuradha (2015) solved solid assignment problem under the fuzzy environment. Fuzzy set consider the membership value. But, it does not taken into account of non-membership value and hesitation index.