Application of Linear Programming Model in Multiple Criteria Decision Making Under the Framework of Interval-Valued Hesitant Fuzzy Sets

Hesitant fuzzy sets (HFSs) further extended into interval-valued hesitant fuzzy sets (IVHFSs). IVHFSs comprises belonging degree in terms of intervals. The weights of the criteria are the basic key to decide the best option from the identical options. We introduce the linear programming (LP) model to compute the criteria’s the unknown weights in the present work. Furthermore, an extended TOPSIS is applied under the INVHFs circumstances. Our proposed method is beneficial to reduce the complexity of computation as compare to other existing MCDM methods. The said model is implemented in a practical example regarding the energy sector to explain the validity and strength.

[1]  V. Torra,et al.  A framework for linguistic logic programming , 2010 .

[2]  Alireza Alinezhad,et al.  Sensitivity Analysis of SAW Technique: the Impact of Changing the Decision Making Matrix Elements on the Final Ranking of Alternatives , 2014 .

[3]  Chen Wang,et al.  Correlation Coefficients of Interval‐Valued Hesitant Fuzzy Sets and Their Application Based on the Shapley Function , 2016, Int. J. Intell. Syst..

[4]  Zeshui Xu,et al.  Interval-valued hesitant preference relations and their applications to group decision making , 2013, Knowl. Based Syst..

[5]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[6]  Jurgita Antucheviciene,et al.  Solving Civil Engineering Problems by Means of Fuzzy and Stochastic MCDM Methods: Current State and Future Research , 2015 .

[7]  Tabasam Rashid,et al.  Convex hesitant fuzzy sets , 2016, J. Intell. Fuzzy Syst..

[8]  Zhi-yong Bai,et al.  Distance similarity measures for interval-valued hesitant fuzzy sets and their application in multicriteria decision making , 2013, J. Decis. Syst..

[9]  Deyu Li,et al.  An interval-valued hesitant fuzzy multigranulation rough set over two universes model for steam turbine fault diagnosis , 2017 .

[10]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[11]  Wenkai Zhang,et al.  Multiple criteria decision analysis based on Shapley fuzzy measures and interval-valued hesitant fuzzy linguistic numbers , 2017, Comput. Ind. Eng..

[12]  Ching-Lai Hwang,et al.  Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey , 1981, Lecture Notes in Economics and Mathematical Systems.

[13]  Zeshui Xu,et al.  Hesitant fuzzy information aggregation in decision making , 2011, Int. J. Approx. Reason..

[14]  Zeshui Xu,et al.  Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information , 2013, Knowl. Based Syst..

[15]  Zeshui Xu,et al.  Hesitant Fuzzy Methods for Multiple Criteria Decision Analysis , 2016, Studies in Fuzziness and Soft Computing.

[16]  Tabasam Rashid,et al.  Multiple Criteria Decision Making Based on Probabilistic Interval-Valued Hesitant Fuzzy Sets by Using LP Methodology , 2019, Discrete Dynamics in Nature and Society.