Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees |
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| Affiliation: | 1. College of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China;2. School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China;3. Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China;1. INSERM CIC 1410, Centre Hospitalier Universitaire de la Réunion, 97448 Saint Pierre, Réunion, France;2. UM 134 PIMIT (CNRS 9192, INSERM U1187, IRD 249, Université de la Réunion), Cyclotron Réunion Océan Indien, Sainte Clotilde, Réunion, France;3. Oswaldo Cruz University Hospital, Recife, Brazil;4. University of Pernambuco, Recife, Brazil;5. Federal University of Pernambuco, Recife, Brazil;6. UMRS Pathologie et Virologie Moléculaire (INSERM U944, CNRS 7212, Université Paris Diderot, Sorbonne Paris Cité), Institut Universitaire d''Hématologie, Hôpital Saint-Louis, Paris, France;7. PROTECT, INSERM, Université Paris Diderot, Sorbonne Paris Cité, Paris, France;8. Centre for the Developing Brain, Department of Division of Imaging Sciences and Biomedical Engineering, King''s College London, King''s Health Partners, St Thomas'' Hospital, London, UK;1. Delft University of Technology, Delft, The Netherlands;2. California Institute of Technology, Pasadena, CA, United States;1. School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China;2. Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan;3. School of Business, Central South University, Changsha 410083, China |
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| Abstract: | As an important component of group decision making, the hybrid multi-criteria group decision making (MCGDM) is very complex and interesting in real applications. The purpose of this paper is to develop a novel interval-valued intuitionistic fuzzy (IVIF) mathematical programming method for hybrid MCGDM considering alternative comparisons with hesitancy degrees. The subjective preference relations between alternatives given by each decision maker (DM) are formulated as an IVIF set (IVIFS). The IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers (TrFNs), linguistic variables, intervals and real numbers are used to represent the multiple types of criteria values. The information of criteria weights is incomplete. The IVIFS-type consistency and inconsistency indices are defined through considering the fuzzy positive and negative ideal solutions simultaneously. To determine the criteria weights, we construct a novel bi-objective IVIF mathematical programming of minimizing the inconsistency index and meanwhile maximizing the consistency index, which is solved by the technically developed linear goal programming approach. The individual ranking order of alternatives furnished by each DM is subsequently obtained according to the comprehensive relative closeness degrees of alternatives to the fuzzy positive ideal solution. The collective ranking order of alternatives is derived through establishing a new multi-objective assignment model. A real example of critical infrastructure evaluation is provided to demonstrate the applicability and effectiveness of this method. |
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| Keywords: | Multi-criteria group decision making Fuzzy mathematical programming Interval-valued intuitionistic fuzzy set Linear Programming Technique for Multidimensional Analysis of Preference Critical infrastructure evaluation |
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