A New Group Decision Making Method With Distributed Indeterminacy Form Under Neutrosophic Environment: An Introduction to Neutrosophic Social Choice Theory

Selcuk Topal,Ahmet Cevik,Florentin Smarandache

doi:10.1109/access.2020.2976872

Selcuk Topal, Ahmet Cevik + Show 1 more

Open Access

https://doi.org/10.1109/access.2020.2976872

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Abstract

We present a novel social choice theory based multi-criteria decision making method under neutrosophic environment and a new form of truth representation of neutrosophic theory called Distributed Indeterminacy Form (DIF). Our hybrid method consists of classical methods and an aggregation operator used in social choice theory. In addition to this, we also use DIF function to provide a more sensitive indeterminacy approach towards accuracy functions. We also consider reciprocal property for all individuals. This provides, as in intuitionistic fuzzy decision making theory, a consistent decision making for each individual. The solution approach presented in this paper in group decision making is treated under neutrosophic individual preference relations. These new approaches seem to be more consistent with natural human behaviour, hence should be more plausible and feasible. Moreover, the use of a similar approach to develop some deeper soft degrees of consensus is outlined. Finally, we give a Python implementation of our work in the Appendix section.

Highlights

In most cases, it is intricate for decision-makers to accurately reveal a preference when solving multi-criteria decisionmaking (MCDM) problems with imprecise, vague or incomplete information
intuitionistic fuzzy sets (IFS) have been widely used in the solution of some significant MCDM problems [4]–[6], The associate editor coordinating the review of this manuscript and approving it for publication was Alba Amato
We propose to distribute the indeterminacy on truth and falsity to be aligned with real life applications and to take into consideration such situations in which uncertainty in social choices have an effective role in truth and falsity

Summary

INTRODUCTION

It is intricate for decision-makers to accurately reveal a preference when solving multi-criteria decisionmaking (MCDM) problems with imprecise, vague or incomplete information. Under these conditions, fuzzy sets (fs) [1], where the membership degree is represented by a real number in [0, 1], are viewed as a strong mechanism method for solving MCDM problems [2], as well as reasoning approximation and pattern recognition problems. Social choice theory investigates solutions to the problem of making a collective decision on a fair and democratic ground. Knowing the fact that the consistency of these pairwise comparisons forms the main theme, such theories devise appropriate methods based on the winner of the consensus of the group or based on an ordering of the preferences with respect to a priority as a result of voting of each individual. Compared with fuzzy and intuitionistic social choice theories, our model extends the social choice theory to neutrosophic based social choice theory in solving practical decision problems and present a richer language discourse

FUNDAMENTAL DEFINITIONS

SELF COMPARISON

RECIPROCAL PROPERTY IN FUZZY THEORY

CONCLUSION

FURTHER RESEARCH DIRECTIONS