Some Aggregation Operators & Information Measures for Solving Decision-Making Problems

Abstract

Multi criteria decision making (MCDM) techniques have wide applications in various ar- eas such as decision theory, operation research, management research, social psychology etc. These methods enable us to find the most optimal alternative among the available choices which are characterized by different criteria. In MCDM processes, the judgements values corresponding to alternatives may not be expressed using crisp numbers always as uncertainty is present in almost every real world system. Therefore, in order to han- dle uncertain and fuzzy situations existing in the real world, the decision-makers need to have such theories using which they could consider fuzzy data values and maintain their decision-making (DM) criteria in accordance to the particular situation. In this direction, numerous models such as fuzzy sets, intuitionistic fuzzy sets and interval-valued intu- itionistic fuzzy sets have been designed and introduced so far. Under these disciplines, a number of researchers developed various methods for dealing with DM problems. Among these techniques, aggregation operators (AOs) and information measures are the basic and efficient tools for handling DM problems. AOs reduce a set of numbers into a unique representative one. Information measures such as similarity and distance process the un- certain information by calculating the degree of similarity and discrimination respectively among input arguments. Although a number of DM techniques have been established so far under the above said models but these environments cannot handle time periodic problems and portray two dimensional information simultaneously in one set. So as to address this issue, a new model named as complex intuitionistic fuzzy set (CIFS) has been developed in 2012. CIFSs have the characteristic of portraying membership and non-membership degrees over the unit disc of the complex plane. Under this model, membership and non-membership degrees are represented in polar form in which the amplitude terms corresponding to membership (non-membership) value explicit the intensity of belongingness (not-belongingness) of the element in a set and the phase terms provide additional periodic information. The objective of this work is to develop new methodologies for handling cases which involve time periodic and two dimensional information. In order to achieve it, some information measures such as distance, similarity, correlation, entropy for processing CIFSs and various generalized AOs for aggregating dependent and independent input arguments are proposed. A number of properties of the proposed measures and operators are explored. Based on the presented measures and operators, MCDM techniques are developed for addressing such two dimensional problems which are either difficult or impossible to be solved using existing theories. The applicability of the proposed methods is demonstrated by applying them in several real life DM problems. The results of the proposed techniques are compared with several existing methods.