Multi-criteria Decision Making Methods On Quasi-linear Fuzzy Number

There are lots of fuzzy multi-criteria decision making (FMCDM) problems in social and economic life and multi-criteria decision making based on fuzzy numbers is an important branch of them. Compared to the traditional fuzzy sets, fuzzy numbers can portray fuzzy information better. So far, researches on multi-criteria decision making methods based on fuzzy numbers have made great progress, but along them there appeared some new questions, one of which is all kinds of different types of fuzzy numbers make it very difficult to uniform the decision-making information. In addition, for the kind of multi-criteria decision making problems the criteria value of which is a mixture of various types of fuzzy numbers or a mixture of fuzzy numbers with linguistic information, there still exist some limitations. Quasi-linear fuzzy numbers can represent basic types of fuzzy numbers uniformly and it also has advantage in describing fuzzy information given in the form of linguistic terms, which makes the researches on the multi-criteria decision making methods based on quasi-linear fuzzy numbers become very prerequisite.On the basis of summarizing and analyzing achievements of the previous studies, this paper riches and improves the current multi-criteria decision making theories based on fuzzy numbers. By introducing quasi-linear fuzzy numbers into MCDM problems and studying the quasi-linear fuzzy MCDM method in depth, it mainly makes the following achievements:(1) Arithmetic rules and calculation method of quasi-linear fuzzy numbers are analyzed in detail and the quasi-linear fuzzy weighted arithmetic averaging (QLWAA) operator is proposed, laying the foundation of the further research. The comparison method of quasi-linear fuzzy numbers is proposed with some examples followed to demonstrate its validity and rationality. Expected value of quasi-linear fuzzy numbers is defined and considering the fact the relative points of quasi-linear fuzzy numbers with greater membership degree should be assigned greater weights the concept of possibilistic expected value is presented. For the MCDM problems with complete weight information, the QLWAA operator and the expected value are combined to solve it. Simultaneously, for the MCDM problems where the criteria weights are completely unknown, the weights are determined by solving the optimization model which maximizing deviations between all alternatives. Thus the MCDM model is established where the criteria values are quasi-linear fuzzy numbers with completely unknown weights based on expected value and COPRAS method respectively.(2) The quasi-linear fuzzy MCDM problems with incomplete information of criteria weights are studied. Some measurement indexes of quasi-linear fuzzy numbers such as distance, closeness, gravity and area are defined. For determining the optimal weights two programming models are established, based on the idea minimizing the closeness to absolute optimal solution and the idea maximizing the gravity index of criteria values in forms of quasi-linear fuzzy numbers respectively. Further making use of TOPSIS method as well as the gravity and area indexes, two models are established to solve quasi-linear fuzzy MCDM problems with incomplete weights information.(3) For SMEs credit rating problem with mixed decision information, the relative decision making method is proposed based on quasi-linear fuzzy numbers. When dealing with the qualitative criteria, quasi-linear fuzzy number is able to assign several adjacent linguistic grades to the evaluation criteria with its membership degree, which can reflect the confidence degree and hesitation of the decision maker and overcome the drawbacks of previous reviews which always evaluate the criteria with single linguistic grade. For the quantitative criteria in SMEs credit evaluation, the financial conditions, a method is proposed to convert them into quasi-linear fuzzy numbers based on the linguistic grades. Thus, the issue of SMEs credit rating is transformed the MCDM problem based on quasi-linear fuzzy numbers, which can be solved which the previous proposed decision making methods. Finally the SMEs credit rating method is verified through numerical examples.