Theories And Methods Of Group Decision Making With Interval-valued Intuitionistic Fuzzy Preference Relations

With the complexity of the real decision making problems,it is difficult for individual decision maker to evaluate such problems comprehensively.Moreover,due to the numerous criteria for evaluating complex problems,it is difficult for decision makers to provide the accurate values on each criterion for alternatives.Thus,group decision making with preference relations comes into being.Considering the limitation of human being’s thinking and complexity of decision problems,decision makers often encounter something that is difficult to describe accurately.Such uncertainty is expressed as ambiguity and hesitancy.Interval-valued intuitionistic fuzzy preference relation expresses the preferences among alternatives with by interval-valued intuitionistic fuzzy values,which can describe the uncertainty of the scheme more flexibly.Thus,it is of great theoretical and practical significance to study the theory and method of group decision making with interval-valued intuitionistic fuzzy preference relations.This paper focuses on the group decision making with interval-valued intuitionistic fuzzy preference relations and proposes the corresponding group decision making methods to apply to real-world decision-making problems.The main contribution is divided into the following six aspects.(1)A ranking algorithm of intuitionistic fuzzy values is designed and applied to multi-attributes group decision making.Firstly,to overcome the limitation of intuitionistic fuzzy ranking methods,the preference degree of intuitionistic fuzzy values is defined and a new ranking algorithm is designed.Then this algorithm is employed to multi-attributes group decision making.A multi-objective programming model is constructed to obtain the attribute weights of each decision maker.The weights of decision makers are derived by maximizing the group consensus index.The collective rating values of alternatives are obtained by aggregation operators.Using the designed ranking algorithm,the ranking order of alternatives is generated.(2)The group decision making problem with interval fuzzy preference relations is addressed,which contains the consistency analysis of interval fuzzy preference relation,the derivation of the weights of decision makers and the determination ofpriority weights.Firstly,the additive consistency of interval fuzzy preference relation is analyzed and applied to construct intuitionistic fuzzy programming models to obtain the priority weights.The consensus index is defined to derive the weights of decision makers.Then a group decision making method with additive consistent interval fuzzy preference relations is proposed.Subsequently,the geometric consistency of interval fuzzy preference relation is analyzed.Considering the risk attitude of decision maker,the geometric consistency index is defined to obtain the acceptable consistent interval fuzzy preference relation.Then a fuzzy logarithm programming model is established to determine the interval priority weights.The weights of decision makers are derived by the similarities of decision makers.Then a parameter programming model is constructed to generate the group priority weights.Thus,a group decision making method with geometric consistent interval fuzzy preference relations is proposed.(3)A ranking method of interval-valued intuitionistic fuzzy values is addressed and applied to multi-attribute group decision making.Firstly,to overcome the limitations of existing ranking methods of interval-valued intuitionistic fuzzy values,the possible degree and divergence degree are defined to propose the order relation of interval-valued intuitionistic fuzzy values.In multi-attribute group decision making,to obtain the weights of decision makers,an intuitionistic fuzzy programming model is constructed.Three approaches are proposed to solve such model,including the optimistic,pessimistic and mixed approaches.The attribute weights are determined by constructing the adjusted possible distribution matrices of alternatives.The collective rating values of alternatives are obtained by aggregation operators.Using the proposed ranking method,the ranking order of alternatives is generated.Thus,an interval-valued intuitionistic fuzzy multi-attribute group decision making method is proposed.(4)Based on intuitionistic fuzzy preference relation,the group decision making with additive consistent interval-valued intuitionistic fuzzy preference relations is addressed.According to the additive consistency of intuitionistic fuzzy preference relation,the additive consistent interval-valued intuitionistic fuzzy preference relation is defined.Then some programming models are constructed to extract the mostoptimistic and pessimistic consistent intuitionistic fuzzy preference relations.Considering the risk preference of decision maker,a risk attitude based consistent intuitionistic fuzzy preference relation is obtained.Then a multi-objective programming model is constructed to derive the intuitionistic fuzzy priority weights.Subsequently,in the group decision making,the comprehensive important degrees of decision makers are obtained by the similarities of decision makers.Then by aggregating the individual interval-valued intuitionistic fuzzy preference relations,the group interval-valued intuitionistic fuzzy preference relation is obtained using comprehensive importance interval-valued intuitionistic fuzzy induced ordered weighted averaging(CI-IVIF-IOWA)operator to generate the priority weights of alternatives.Thus,a three phase method is proposed to solve the group decision making with interval-valued intuitionistic fuzzy preference relations.(5)Based on interval fuzzy preference relation,the group decision making with additive consistent interval-valued intuitionistic fuzzy preference relations is addressed.According to the additive consistency of interval fuzzy preference relation,the additive consistent interval-valued intuitionistic fuzzy preference relation is defined.A parameter programming model is constructed to derive the interval-valued intuitionistic fuzzy priority weights from two extracted interval fuzzy preference relations.In this group decision making method with interval-valued intuitionistic fuzzy preference relations,the group consensus is defined and applied to establish a mathematical programming model for deriving the weights of decision makers.Then the group interval-valued intuitionistic fuzzy preference relations is obtained to generate the interval-valued intuitionistic fuzzy priority weights,which is ranked to obtain the order of alternatives.(6)The group decision making with multiplicative consistent interval-valued intuitionistic fuzzy preference relations is addressed.The multiplicative consistency of interval-valued intuitionistic fuzzy preference relation is defined.The interval-valued intuitionistic fuzzy priority weights are determined by two single objective programming models.Especially,if the feasible domains of the two programming models are empty,two adjusted programming models are proposed to replace the original.Then the group consensus is defined and the acceptable groupconsensus is proposed.To improve the group consensus,an iteration algorithm is designed for the decision makers with unacceptable group consensus.The convergence of the iteration algorithm also proves.Then the weights of decision makers are determinated by Markov model,which is used to obtain the group interval-valued intuitionistic fuzzy preference relation.The group interval-valued intuitionistic fuzzy priority weights are obtained to generate the ranking order of alternatives.Thus,a group decision making method with multiplicative consistent interval-valued intuitionistic fuzzy preference relations is proposed.