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Picture Fuzzy Linear and Non-Linear Break-Even Analyses for Rent or Buy Decisions
Elif Haktanir and Cengiz Kahraman
Classical break-even analysis (BEA) is applied by considering linear or non-linear revenue and total cost functions. However, the experts’ estimations for these functions are vague and imprecise rather than exact. If the experts have insufficient data, the application of the classical BEA approach will not yield accurate results. Under these conditions, experts prefer to make predictions for parameters by using linguistic expressions. Due to the capability of fuzzy set theory to model such predictions, fuzzy BEA will be developed in this paper using one of the fuzzy sets’ extensions in the literature. Picture fuzzy sets, which are one of the most recent extensions of ordinary fuzzy sets, are employed in the development of BEA under fuzziness incorporating experts’ thoughts on the positive, neutral, and negative membership degrees of an estimation. Picture fuzzy singular and triple non-linear total cost and revenue functions are considered in the BEA model. The developed picture fuzzy BEA is applied to an excavator rent or buy decision problem.
Keywords: Picture fuzzy sets, break-even analysis, break-even point, non-linear functions, rent or buy