Modified Interval Arithmetic Operations onInterval Valued Neutrosophic Fuzzy Number (IVNFNS) for Solving Neutrosophic Fuzzy Unconstrained Optimization Problem (NFUOP)

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S.Shilpa Ivin Emimal, R. Irene Hepzibah , Broumi Said

Abstract

Introduction:Neutrosophic quasi-Newton techniques are utilized in many engineering applications, including control theory, electrical engineering, and mechanical engineering, for determining optimal solutions in the face of uncertainty, imprecision, and ambiguity. This paper introduced new modified arithmetic operations on interval valued Neutrosophic fuzzy numbers (IVNFNS).


Objectives: In this paper, New Arithmetic operation for  interval-valued neutrosophic fuzzy  is introduced. Some fundamental operations are also presented. The need of the interval-valued neutrosophic fuzzy matrix (IVNFM) is explained by an illustration.


Methods: The new Neutrosophic quasi-Newton techniques are optimization algorithms that integrate neutrosophic logic with the quasi-Newton method. Traditional quasi-Newton methods use a deterministic formula to approximate the Hessian matrix, but neutrosophic quasi-Newton methods use neutrosophic logic principles to correct for errors, imprecision, and ambiguity. This technique offers greater flexibility and resilience when dealing with complicated and nonlinear optimization issues, especially when the objective function's parameters are unclear, imprecise, or ambiguous.


Result: To explain the suggested technique, an exemplary numerical example is provided, as well as the Neutrosophic fuzzy output is given using MATLAB programme.


Conclusion:This paper presented how extended interval arithmetic operations and modified interval arithmetic operations can be used to solve unconstrained optimization problems. In comparison, neutrosophic fuzzy numbers. A quasi-Newtonian DFP strategy is used to solve fuzzy and unconstrained optimization problems, and the validity of the proposed approaches is confirmed through numerical examples and MATLAB program results.

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