Multiple Hierarchically Structured Criteria in ARAS Method Under Fuzzy Environment

Introduction

The fuzzy logic exhibits the ambiguities in human thoughts. As a matter of fact, Bellman and Zadeh (1970) were the first to introduce the fuzzy logic in the MCDA field to handle the vagueness of human judgments. They declare: ‘’Fuzzy goals and fuzzy constraints can be defined precisely as fuzzy sets in the space of alternatives. A fuzzy decision, then, may be viewed as an intersection of the given goals and constraints. A maximizing decision is defined as a point in the space of alternatives at which the membership function of a fuzzy decision attains its maximum value’’. In fact, the root of the fuzzy logic belongs to the Greek philosophy (Korner, 1967). The Fuzzy Multi-Criteria Decision Making (FMCDM) is defined as a decision theory resulting from a fusion between MCDM and Fuzzy Set Theory (FST), that deals with incomplete and imprecise knowledge and information. Since knowledge can be expressed in a natural way by adopting fuzzy sets, many decision problems can be significantly simplified. In this context, the fuzzy set theory has been promoted in a variety of disciplines such as management science, computer science, decision theory, artificial intelligence. Therefore, the fuzzy set theory gave birth to a new family of methods to cope with problems unsolvable by standard MCDM techniques and henceforth obtaining more concrete results. In this context, we developed a new fuzzy hierarchical MCDM method called fuzzy ARAS-H that extends the ARAS-H method in a context of fuzzy environment to cope with the vagueness of human judgments. To facilitate the task for the DM, we ask him to provide linguistic variables which will be defuzzified through the application of the F-ARAS-H. The advantages of the proposed method are to enhance the transparency in the decision making process and to rank alternatives evaluated on hierarchically structured criteria in the presence of imprecise data. The choice of the ARAS (Zavadskas and Turskis 2010) method is justified by the fact that it is easy to use by DMs since it requires only, as data, the decision matrix in which the alternatives are evaluated according to criteria.

The paper is divided into five sections. In section 2, a state of the art survey will be established. In section 3, the different steps of the fuzzy ARAS-H method will be explained. In section 4, an empirical study on green supplier selection problem will be presented to discuss the feasibility of the proposed model. In section 5, a conclusion with our main perspectives will be emphasized.