New transitivity property of intuitionistic fuzzy multiplicative preference relation and its application in missing value estimation
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In the decision-making process, consistency is a crucial issue which causes wide public concern of exports. The lack of consistency in preference relations results in an inconsistent solution. In this paper, we propose a characterization of the consistency property using newly defined transitivity property for intuitionistic fuzzy multiplicative preference relations (IFMPR) together with complementing missing elements for incomplete IFMPR. In 2015 Jiang et al. worked on incomplete intuitionistic fuzzy multiplicative preference relations (incomplete IFMPRs) in which the IFMPRs split into two multiplicative preference relation (MPRs), and the missing elements were calculated by using the consistency of MPRs. Using new transitivity property of IFMPR, and we have developed two different methods to find the missing element of IFMPRs. The first method is two-step procedure method containing estimating step followed by adjusting step. In estimating step, the missing elements of incomplete IFMPRs are calculated by using a new transitive property instead of splitting IFMPRs into two multiplicative preference relations(MPRs). Sometimes the initial value may not satisfy the conditions of IFMPRs. An optimization model is developed in the second step to adjust the initial values that are solved by MATLAB optimization tool. The second proposed method is goal programming model based on new transitivity property to calculate the missing elements directly. Acceptably Consistent with complete IFMPRs is also checked. Two numerical examples are carried out to illustrate the above-said methods.
Abstract
In the decision-making process, consistency is a crucial issue which causes wide public concern of exports. The lack of consistency in preference relations results in an inconsistent solution. In this paper, we propose a characterization of the consistency property using newly defined transitivity property for intuitionistic fuzzy multiplicative preference relations (IFMPR) together with complementing missing elements for incomplete IFMPR. In 2015 Jiang et al. worked on incomplete intuitionistic fuzzy multiplicative preference relations (incomplete IFMPRs) in which the IFMPRs split into two multiplicative preference relation (MPRs), and the missing elements were calculated by using the consistency of MPRs. Using new transitivity property of IFMPR, and we have developed two different methods to find the missing element of IFMPRs. The first method is two-step procedure method containing estimating step followed by adjusting step. In estimating step, the missing elements of incomplete IFMPRs are calculated by using a new transitive property instead of splitting IFMPRs into two multiplicative preference relations(MPRs). Sometimes the initial value may not satisfy the conditions of IFMPRs. An optimization model is developed in the second step to adjust the initial values that are solved by MATLAB optimization tool. The second proposed method is goal programming model based on new transitivity property to calculate the missing elements directly. Acceptably Consistent with complete IFMPRs is also checked. Two numerical examples are carried out to illustrate the above-said methods.
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