Multiple Attribute Group Decision Making Problems by Using Operator the Induced Vague Ordered Weighted Averaging (IVOWA) Appear for Vague Sets with New Developed Algorithm

There are several approaches to extend the basic multi attribute decision making techniques for the case of group decision. If the objective function is the single criterion, the constraints are the requirements on the alternatives. Depending on the form and functional description of the optimization problem like as linear, non – linear programming, discrete optimization techniques etc. But it is very important to make a decision between the cases where we have a single or multiple criteria. When a decision problem has a finite number of criteria or multiple criteria, and the number of the feasible alternatives (the one meeting requirements) is infinite, then the decision problem belongs to the field of multiple criteria optimization. Also, technique of multiple criteria optimization can be used when there are a finite number of feasible alternatives, but are given only in implicit form. In this article we focus on making problem when the number of the criteria (attribute) and alternatives is finite and the alternatives are explicitly given. And also the ordered weighted average is presented in the context of vague set theory. Vague sets can better handle vagueness and uncertainty than intuitionistic fuzzy sets. Initially the vague weighted averaging (VWA) operator was developed and based on VWA operator the vague ordered weighted averaging (VOWA) operator was introduced. Finally the induced ordered weighted averaging (IVOWA) operator was developed and MAGDM model was proposed using all the above proposed operators. The proposed model of MADGM can be utilized based on distance function by using Hausdorff Metric distance technique