Solution of a Triangular Intuitionistic Fuzzy Optimal Subdivision Problem - A Novel Approach

Abstract

Introduction: Dynamic Programming is the mathematical technique of optimizing a series of connected decisions over a given amount of time. The process of making decisions in many real-world scenarios involves choosing a set of plans from a wide range of possible combinations in unclear circumstances.

Objectives: In this article, a novel approach is developed to solve a triangular intuitionistic fuzzy optimal subdivision problem in which a positive quantity which is to be partitioned is taken as triangular intuitionistic fuzzy number.

Methods: The mathematical induction technique is applied in the process of obtaining the optimal solution with fuzzy approach. The unique characteristics of the proposed approach is that the fuzziness and ambiguity in optimal subdivision models is eradicated by applying the technique of fuzzy dynamic programming.

Results: A new approach has been proposed in this paper for solving fuzzy optimal subdivision problem in which the positive quantity which is to be divided into ‘n’ factors is taken as trapezoidal fuzzy number. The solution is obtained by the method of Mathematical Induction. The optimal solution is obtained by using the fuzzy recursive equations.

Conclusions: Many real-world problems involve sequential or multistage decision making. Sometimes, the parameters may not be known precisely due to some uncontrollable factors. If the obtained results are crisp values then it might lose some helpful information. Fuzzy Dynamic Programming is a powerful optimization procedure that is particularly applicable to many complex problems requiring a sequence of interrelated decisions in a fuzzy environment and hence it has wide range of applications in the future