Shortest path (SP) optimization problems arise in a wide range of applications such as telecommunications and transportation industries. The main purpose of these problems is to find a path between two predetermined nodes within a network as cheaply or quickly as possible. Conventional SP problems generally assume that the arc weights are defined by crisp variables, though imprecise data have been lately incorporated into the analysis. The present study formulates the SP problem in a directed interval-valued triangular fuzzy network. The resulting interval-valued fuzzy SP (IVFSP) problem is converted into a multi objective linear programming (MOLP) problem. Then, a lexicographic optimization structure is used to obtain the efficient solution of the resulting MOLP problem. The optimization process confirms that the optimum interval-valued fuzzy shortest path weight preserves the form of an interval-valued triangular fuzzy number. The applicability of the proposed approach is illustrated through an example dealing with wireless sensor networks.
BaykasoģluA. and SubulanK., A direct solution approach based on constrained fuzzy arithmetic and metaheuristic for fuzzy transportation problems, Soft Computing23(5) (2019), 1667–1698.
2.
BaykasoģluA., SubulanK., DudaklN., TuranM., ÇelikE., ÜlkerO., Development of a Web-Based Decision Support System for Strategic and Tactical Sustainable Fleet Management Problems in Intermodal Transportation Networks. In: Paksoy T., Weber GW., Huber S. (eds) Lean and Green Supply Chain Management, International Series in Operations Research & Management Science273 (2019). Springer, Cham.
3.
RaniD., GulatiT.R. and KumarA., A method for unbalanced transportation problems in fuzzy environment, Sadhana39 (2014), 573–581.
4.
WangL., GaoZ. and YangL., Criteria for the a priori shortest path generation in uncertain time-varying transportation networks, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems23(06) (2015), 807–827.
5.
BiswasS.S., BashirA. and DojaM.N., An algorithm for extracting intuitionistic fuzzy shortest path in a graph, Applied Computational Intelligence and Soft Computing1 (2013), 1–5.
6.
EbrahimnejadA., KarimnejadZ. and AlrezaamiriH., Particle swarm optimization algorithm for solving shortest path problems with mixed fuzzy arc weights, International Journal of Applied Decision Sciences8(2) (2015), 203–222.
7.
EbrahimnejadA., TavanaM. and AlrezaamiriH., A novel artificial bee colony algorithm for shortest path problems with fuzzy arc weights, Measurement93 (2016), 48–56.
8.
EbrahimnejadA., A method for solving linear programming with interval-valued trapezoidal fuzzy variables, RAIRO - Operations Research22(3) (2018), 955–979.
9.
KumarG., BajajR.K. and GandotraN., Algorithm for shortest path problem in a network with interval–valued intuitionistic trapezoidal fuzzy number, Procedia Computer Science70 (2015), 123–129.
10.
MoazeniM., Fuzzy shortest path problem with finite fuzzy quantities, Applied Mathematics and Computation183 (2016), 160–169.
11.
MotameniH. and EbrahimnejadA., Constraint shortest path problem in a network with intuitionistic fuzzy arc weights. In: Medina J., Ojeda-Aciego M., Verdegay J., Perfilieva I., Bouchon-Meunier B., Yager R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2018, Communications in Computer and Information Science855 (2018). Springer, Cham.
12.
NiroomandS., MahmoodiradA., HeydariA., KardaniF. and Hadi-VenchehA., An extension principle based solution approach for shortest path problem with fuzzy arc lengths, Operational Research17(2) (2017), 395–411.
13.
YangY., YanD. and ZhaoJ., Optimal path selection approach for fuzzy reliable shortest path problem, Journal of Intelligent & Fuzzy Systems32(1) (2017), 197–205.
14.
Abbaszadeh SoriA., EbrahimnejadA. and MotameniH., The fuzzy inference approach to solve multi-objective constrained shortest path problem, Journal of Intelligent & Fuzzy Systems, Pre-press: 1–10 (2020).
15.
HassanzadehR., MahdaviI., Mahdavi-AmiriN. and TajdinA., A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths, Mathematical and Computer Modelling57(1–2) (2013), 84–99.
16.
JamilM. and SharmaA., Reconfiguration of electrical distribution system using ACO methodology, Journal of Intelligent & Fuzzy Systems35(5) (2018), 4901–4908.
17.
ElloumiW., BakloutiN., AbrahamA. and AlimiA.M., The multi-objective hybridization of particle swarm optimization and fuzzy ant colony optimization, Journal of Intelligent & Fuzzy Systems27(1) (2014), 515–525.
18.
KeshavarzE. and KhorramE., A fuzzy shortest path with the highest reliability, Journal of Computational and Applied Mathematics230 (2009), 204–212.
19.
DouY., ZhuL. and WangH.S., Solving the fuzzy shortest path problem using multi-criteria decision method based on vague similarity measure, Applied Soft Computing12(6) (2012), 1621–1631.
20.
DengY., ChenY., ZhangY. and MahadevanS., Fuzzy Dijkstra algorithm for shortest path problem under uncertain environment, Applied Soft Computing12 (2012), 1231–1237.
21.
KungJ.-Y., ChuangT.N. and LinC.T., A new dynamic programming approach for finding the shortest path length and the corresponding shortest path in a discrete fuzzy network, Journal of Intelligent & Fuzzy Systems18(2) (2007), 117–122.
22.
YangY., YanD. and ZhaoJ., Optimal path selection approach for fuzzy reliable shortest path problem, Journal of Intelligent & Fuzzy Systems32(1) (2017), 197–205.
23.
EbrahimnejadA., VerdegayJ.L. and GargH., Signed distance ranking based approach for solving bounded interval-valued fuzzy numbers linear programming problems, International Journal of Intelligent Systems9(34) (2019), 2055–2076.
24.
DeyA., PradhanR., PalA. and PalT., A genetic algorithm for solving fuzzy shortest path problems with interval type-2 fuzzy arc lengths, Malaysian Journal of Computer Science31(4) (2018), 255–270.
25.
EnayattabrM., EbrahimnejadA., MotameniH. and GargH., A novel approach for solving all-pairs shortest path problem in an interval-valued fuzzy network, Journal of Intelligent & Fuzzy Systems37(5) (2019), 6865–6877.
26.
MukherjeeS., Dijkstra’s algorithm for solving the shortest path problem on networks under intuitionistic fuzzy environment, Journal of Mathematical Modelling and Algorithm11(4) (2012), 345–359.
27.
GeetharamaniG. and JayagowriP., Using similarity degree approach for shortest path in Intuitionistic fuzzy network, In: International Conference on Computing, Communication and Applications (ICCCA), IEEE, Dindigul, Tamilnadu, India, 2012, 1–6.
28.
EbrahimnejadA. and VerdegayJ.L., An efficient computational approach for solving type–2 intuitionistic fuzzy numbers based transportation problems, International Journal of Computational Intelligence Systems9(6) (2016), 1154–1173.
29.
ChenW., JiangX., LiX., GaoJ., XuX. and DingS., Wireless sensor network nodes correlation method in coal mine tunnel based on Bayesian decision, Measurement46 (2013), 2335–2340.
30.
FunckJ. and GühmannC., Comparison of approaches to time-synchronous sampling in wireless sensor networks, Measurement56 (2014), 203–214.
31.
GargH., A novel improved accuracy function for interval valued Pythagorean fuzzy sets and its applications in decision making process, International Journal of Intelligent Systems32(12) (2017), 1247–1260.
32.
GargH., Generalized Pythagorean fuzzy Geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process, International Journal of Intelligent Systems32(6) (2017), 597–630.
33.
GargH., A new exponential operational laws and their aggregation operators of interval-valued Pythagorean fuzzy information, International Journal of Intelligent Systems33(3) (2018), 653–683.
