Fuzzy Dynamic Programming Problem for Single Additive Constraint with Additively Separable Return by Means of Trapezoidal Membership Functions

Fuzzy Dynamic Programming Problem for Single Additive Constraint with Additively Separable Return by Means of Trapezoidal Membership Functions

Palanivel Kaliyaperumal (School of Advanced Sciences, VIT University, India)
DOI: 10.4018/978-1-5225-1008-6.ch008
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Abstract

Dynamic Programming Problem (DPP) is a multivariable optimization problem is decomposed into a series of stages, optimization being done at each stage with respect to one variable only. DP stands a suitable quantitative study procedure that can be used to explain various optimization problems. It deals through reasonably large as well as complex problems; in addition, it involves creating a sequence of interconnected decisions. The technique offers an efficient procedure for defining optimal arrangement of decisions. Throughout this chapter, solving procedure completely deliberate about as Fuzzy Dynamic Programming Problem for single additive constraint with additively separable return with the support of trapezoidal membership functions and its arithmetic operations. Solving procedure has been applied from the approach of Fuzzy Dynamic Programming Problem (FDPP). The fuzzified version of the problem has been stated with the support of a numerical example for both linear and nonlinear fuzzy optimal solutions and it is associated to showing that the proposed procedure offers an efficient tool for handling the dynamic programming problem instead of classical procedures. As a final point the optimal solution with in the form of fuzzy numbers and justified its solution with in the description of trapezoidal fuzzy membership functions.
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2. Preliminaries

L.A. Zadeh advanced the fuzzy theory in 1965. The theory proposes a mathematical technique for dealing with imprecise concepts and issues that have several potential solutions. The conception of fuzzy mathematical programming on a general level was initially projected by (Tanaka et al., 1974) within the frame work of fuzzy decision of Bellmann and Zadeh (1970). Now it tends to present some necessary definitions are:

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