Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees

•Formulate multiple types of attribute values and heterogeneous MADM problems.•Propose mathematical programming method with IVIFSs from multiobjective programming.•Approach to handle with incomplete information and fuzziness of alternative comparisons. Considering the hesitancy degrees on pair-wise...

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Vydané v:	Information sciences Ročník 325; s. 484 - 503
Hlavní autori:	Wan, Shu-Ping, Li, Deng-Feng
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 20.12.2015
Predmet:	Construction Decision making Fuzzy Fuzzy logic Fuzzy mathematical programming Fuzzy set theory Green supply chain Interval-valued intuitionistic fuzzy set Linear Programming Technique for Multidimensional Analysis of Preference Mathematical analysis Mathematical models Mathematical programming Multiattribute decision-making Interval-valued intuitionistic fuzzy set Multiattribute decision-making Linear Programming Technique for Multidimensional Analysis of Preference Fuzzy mathematical programming Green supply chain
ISSN:	0020-0255, 1872-6291
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Abstract	•Formulate multiple types of attribute values and heterogeneous MADM problems.•Propose mathematical programming method with IVIFSs from multiobjective programming.•Approach to handle with incomplete information and fuzziness of alternative comparisons. Considering the hesitancy degrees on pair-wise comparisons of alternatives as interval-valued intuitionistic fuzzy (IVIF) sets (IVIFSs), we develop a new fuzzy mathematical programming method for solving heterogeneous multiattribute decision-making problems based on the Linear Programming Technique for Multidimensional Analysis of Preference. In this method, IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers, linguistic variables, intervals and real numbers are used to represent multiple types of attribute values and the attribute weights are not completely known. The preference relations between alternatives given by decision maker are expressed with IVIFSs of ordered pairs of alternatives. The consistency and inconsistency indices are defined as IVIFSs on the basis of comparisons of alternatives with IVIF truth degrees. The attribute weights and fuzzy ideal solution (FIS) are estimated through constructing a fuzzy mathematical programming model, which is solved by the technically developed method of IVIF mathematical programming. Hereby the distances of alternatives to the FIS are computed to rank the alternatives. Some generalization and discussion on the constructed IVIF mathematical programming model are also presented. A green supplier selection example is provided to illustrate the effectiveness of the proposed model and method. The comparison analyses verify the superiorities of the proposed method.
AbstractList	Considering the hesitancy degrees on pair-wise comparisons of alternatives as interval-valued intuitionistic fuzzy (IVIF) sets (IVIFSs), we develop a new fuzzy mathematical programming method for solving heterogeneous multiattribute decision-making problems based on the Linear Programming Technique for Multidimensional Analysis of Preference. In this method, IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers, linguistic variables, intervals and real numbers are used to represent multiple types of attribute values and the attribute weights are not completely known. The preference relations between alternatives given by decision maker are expressed with IVIFSs of ordered pairs of alternatives. The consistency and inconsistency indices are defined as IVIFSs on the basis of comparisons of alternatives with IVIF truth degrees. The attribute weights and fuzzy ideal solution (FIS) are estimated through constructing a fuzzy mathematical programming model, which is solved by the technically developed method of IVIF mathematical programming. Hereby the distances of alternatives to the FIS are computed to rank the alternatives. Some generalization and discussion on the constructed IVIF mathematical programming model are also presented. A green supplier selection example is provided to illustrate the effectiveness of the proposed model and method. The comparison analyses verify the superiorities of the proposed method. •Formulate multiple types of attribute values and heterogeneous MADM problems.•Propose mathematical programming method with IVIFSs from multiobjective programming.•Approach to handle with incomplete information and fuzziness of alternative comparisons. Considering the hesitancy degrees on pair-wise comparisons of alternatives as interval-valued intuitionistic fuzzy (IVIF) sets (IVIFSs), we develop a new fuzzy mathematical programming method for solving heterogeneous multiattribute decision-making problems based on the Linear Programming Technique for Multidimensional Analysis of Preference. In this method, IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers, linguistic variables, intervals and real numbers are used to represent multiple types of attribute values and the attribute weights are not completely known. The preference relations between alternatives given by decision maker are expressed with IVIFSs of ordered pairs of alternatives. The consistency and inconsistency indices are defined as IVIFSs on the basis of comparisons of alternatives with IVIF truth degrees. The attribute weights and fuzzy ideal solution (FIS) are estimated through constructing a fuzzy mathematical programming model, which is solved by the technically developed method of IVIF mathematical programming. Hereby the distances of alternatives to the FIS are computed to rank the alternatives. Some generalization and discussion on the constructed IVIF mathematical programming model are also presented. A green supplier selection example is provided to illustrate the effectiveness of the proposed model and method. The comparison analyses verify the superiorities of the proposed method.
Author	Li, Deng-Feng Wan, Shu-Ping
Author_xml	– sequence: 1 givenname: Shu-Ping surname: Wan fullname: Wan, Shu-Ping organization: School of Economics and Management, Fuzhou University, Fuzhou, Fujian 350108, China – sequence: 2 givenname: Deng-Feng surname: Li fullname: Li, Deng-Feng email: lidengfeng@fzu.edu.cn, lidengfeng65@hotmail.com organization: School of Economics and Management, Fuzhou University, Fuzhou, Fujian 350108, China
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Keywords	Interval-valued intuitionistic fuzzy set Multiattribute decision-making Linear Programming Technique for Multidimensional Analysis of Preference Fuzzy mathematical programming Green supply chain
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Snippet	•Formulate multiple types of attribute values and heterogeneous MADM problems.•Propose mathematical programming method with IVIFSs from multiobjective... Considering the hesitancy degrees on pair-wise comparisons of alternatives as interval-valued intuitionistic fuzzy (IVIF) sets (IVIFSs), we develop a new fuzzy...
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SubjectTerms	Construction Decision making Fuzzy Fuzzy logic Fuzzy mathematical programming Fuzzy set theory Green supply chain Interval-valued intuitionistic fuzzy set Linear Programming Technique for Multidimensional Analysis of Preference Mathematical analysis Mathematical models Mathematical programming Multiattribute decision-making
Title	Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees
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