Convergence of information and communication technology has brought a radical change in the way data are collected or generated for ease of multi criterion decision making. The huge data is of no use unless it provides certain information. It is very tedious to select a best option among an array of alternatives. Also, it becomes more tedious when the data contains uncertainties and objectives of evaluation vary in importance and scope. Unlocking the hidden data is of no use to gain insight into customers, markets and organizations. Therefore, processing these data for obtaining decisions is of great challenge. Based on decision theory, in the past many methods are introduced to solve multi criterion decision making problem. The limitation of these approaches is that, they consider only certain information of the weights and decision values to make decisions. Alternatively, it makes less useful when managing uncertain and vague information. In addition, an information system establishes relation between two universal sets. In such situations, multi criterion decision making is very challenging. Therefore, an effort has been made in this paper to process inconsistencies in data with the introduction of intuitionistic fuzzy rough set theory on two universal sets.

The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal set to rough set on two universal sets. In this paper, we introduce rough equality of sets on two universal sets and rough inclusion of sets employing the notion of the lower and upper approximation. Also, we establish some basic properties that refer to our knowledge about the universes.

Information technology revolution has brought a radical change in the way data are collected or generated for ease of decision making. It is generally observed that the data has not been consistently collected. The huge amount of data has no relevance unless it provides certain useful information. Only by unlocking the hidden data we can not use it to gain insight into customers, markets, and even to setup a new business. Therefore, the absence of associations in the attribute values may have information to predict the decision for our own business or to setup a new business. Based on decision theory, in the past many mathematical models such as naïve Bayes structure, human composed network structure, Bayesian network modeling etc. were developed. But, many such models have failed to include important aspects of classification. Therefore, an effort has been made to process inconsistencies in data being considered by Pawlak with the introduction of rough set theory. In this paper, we use two processes such as pre process and post process to predict the output values for the missing associations in the attribute values. In pre process we use rough computing, whereas in post process we use Bayesian classification to explore the output value for the missing associations and to get better knowledge affecting the decision making.