A Multi-Criteria Decision Making Method Based On New Definition of Belief Function in Dempster Shafer Theory

Document Type : Original Article

Authors

1 PhD student, Department of Statistics, Science and Research branch, Islamic Azad University, Tehran, Iran.

2 Professor, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.

3 Professor, School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran.

4 Assistant Professor, Department of Industrial Engineering, Robat Karim Branch, Islamic Azad University, Tehran, Iran

Abstract

Basic probability assignment or mass function is an important tool in Dempster-Shafer theory. Based on this function, belief and plausibility functions are used to present insufficient, inconsistencies or conflict information. Generally, the information source is based on expert’s opinions when the deterministic probability of any proposition may not be obtained. In this paper, a new method for solving multi-criteria decision-making is proposed based on belief functions. Three main elements are considered in the definition of the belief functions are: (1) the degree of the true belief or belief function, (2) the degree of the false belief or non-belief function (3) the degree of uncertainty for each alternative among alternatives. In the proposed method, the amount of different distance between an alternative and the ideal alternative can be measured based on the minimum and maximum operators. It may help to utilize the belief measure between the ideal alternative and each alternative to rank the alternatives with respect to measure the value and then select the desirable one. Furthermore, in the proposed method, the weighted criteria and weighted belief function are considered in the decision-making process. Finally, two illustrative examples are given to demonstrate its application effectiveness.

Keywords

References

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