Application of Fuzzy Neutrosophic Cone in Decision Making

Abstract

Aims: This article deals with a new decision-making process under a neutrosophic fuzzy environment. First of all, we develop various types of neutrosophic set by means of neutrosophic cones. In fact, this set has been developed from the general equation of second degree in the field of classical geometry. Considering the neutrosophic components “true membership”, the “falsity membership” and the “indeterminacy” as the three variables of three-dimensional rectangular axes we develop various types of cones like structures of the traditional neutrosophic set and hence a new defuzzification method. Background: Fuzzy set has some limitations in its domain [0,1] to describe real-life decisionmaking problems. The problem of difficulties lies in the variation of lower and upper bound and also the single valued logic (membership function only) systems. In reality, three valued logics (membership function, non-membership function and indeterminacy) have been established in the name of Neutrosophic logic/sets, and two valued logics (membership and non-membership functions) have developed in the name of Intuitionistic fuzzy logic/sets. In three valued logic system, the concepts of negation are now a growing subject of any group decision making problems. However, to draw a clear estimation of a neutrosophic decision has not yet been studied by modern researchers. Objective: Various kinds of new establishments of the Neutrosophic set have been studied from the algebraic point of view, along with some polynomial structures. We have seen that; no finite geometric structures have been developed yet to qualify the real-world problems. Method: We consider the three components of a neutrosophic set as the variables of threedimensional geometry. Since, the decisions are compact and constructive, we may consider the convex neutrosophic cone for analyzing single/ multiple group decision making problems. Result: Various definitions are made over the cone- fundamentals using non-standard neutrosophic set in the domain [−1,1] × [−1,1] × [−1,1]. Then, we studied the constructions of several expressions/ functions of neutrosophic cones, such as reciprocal cone, and enveloping cone via a novel thinking process. Then using some examples, we have developed a new ranking method along with their geometric structures exclusively. Conclusion: In this changing world, the nature of decision-making behaviors is also changing rapidly. So, the need of establishing new concepts is an emerging area of research. However, more attention is required in discussing such vital issues in near future. The proposed approach may be applied to the decision-making problems of global issues also.