Study On Approaches To Interval-Valued Intuitionistic Fuzzy Multiple Attribute Decision Making With Incomplete Information

Multiple attribute decision making(MADM) may be characterised as a process of choosing or selecting 'sufficiently good' altemative(s) or course(s) of action,from a set of altematives,to attain a goal.It should be noted,however,that much decision making involves uncertainty,and for difficult problems,conventional(nonfuzzy) methods are usually expensive and depend on mathematical approximations(e.g. linearization of nonlinear problems),which may lead to poor performance.Hence, one of the most important aspects for a useful decision aid is to provide the ability to handle imprecise and vague information.Under such circumstances,fuzzy sets often outperform conventional MADM methods.Fuzzy multiple attribute decision making (FMADM) is defined by Bellman and Zadeh as a decision process in which the goals and/or the constraints are fuzzy in nature.From the data structure,Interval-valued intuitionistic fuzzy numbers,each of which is characterized by the interval degree of membership and the interval degree of non-membership of an element,are very useful means to depict the decision information in the process of decision making.The aim of the paper is to investigate the multiple attribute decision making problems with interval-valued intuitionistic fuzzy information,in which the information about attribute weights is partially known or completely unknown,and the attribute values provided by the decision makers is expressed as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number.(1) Several optimization models are presented to generate optimal weights for attributes,and the corresponding decision-making methods have also been developed.Feasibility and effectiveness of the proposed methods are illustrated with an example of investment decision problem. (2) The score matrix of the interval-valued intuitionistic fuzzy decision matrix is constructed by the score function.Several optimization models are established to generate optimal weights for attributes.A procedure based on the interval-valued intuitionistic fuzzy weighted arithmetic averaging(IIFWAA) operator is developed to solve the multi-attribute interval-valued intuitionistic fuzzy decision making problems. Finally,a global supplier selection example is used to illustrate the developed procedure.(3) Interval-valued intuitionistic preference relations are a powerful means to expressing a decision maker's uncertainty and hesitation about its preference over weights in the process of generating the weights for attributes.First define the notion of consistent interval-valued intuitionistic preference relations.Goal programming models are established for generating priority interval weights based on interval-valued intuitionistic preference relations,and.the corresponding decision-making methods have also been proposed.Two illustrative numerical examples are furnished to demonstrate how to apply the approach.(4) Based on the two proposted methods in text and the other two methods which had been in existence, Analysis and solve the same interval-valued intuitionistic fuzzy decisoin making question,and explain the similarities and differences of the results.Finally, demonstrate three practicality methods about aggregating the order of the projects.