Fuzzy Number – A New Hypothesis and Solution of Fuzzy Equations

Makwana, Vijay C.; Soni, Vijay P.; Patel, Nayan I; Sahni, Manoj

doi:10.13189/ms.2022.100116

Cited by 1 publication

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“…Forootani et al [17] constructed a stochastic dynamic programming technique to solve the machine replacement problem. Makwana et al [18] proposed a new hypothesis and solution for fuzzy equations. As a result, the illustrious scientist Zadeh [1] proposed Fuzzy Sets, an extension of classical set theory, in the 1960 s. The fuzzy set theory and the classical set theory approach ambiguity differently.…”

Section: Introductionmentioning

confidence: 99%

A comparative analysis of the fuzzy and intuitionistic fuzzy environment for group and individual equipment replacement Models in order to achieve the optimized results

Saranya,

Murugan

2023

Int. J. Simul. Multidisci. Des. Optim.

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The main goal of this research is to compare group and individual replacement models based on fuzzy replacement theory and intuitionistic fuzzy replacement theory. The capital costs are assumed to be triangular fuzzy numbers, triangular intuitionistic fuzzy numbers, and trapezoidal intuitionistic fuzzy numbers, respectively. As a result, interpreting the direct relationship between volatility and ambiguity is critical. It is difficult to predict when specific equipment will unexpectedly fail. This problem can be solved by calculating the probability of failure distribution. Furthermore, the failure is assumed to occur only at the end of period t. In this situation, two types of replacement policies are used. The first is the Individual Replacement Policy, which states that if an item fails, it will be replaced immediately. The Group Replacement Policy states that all items must be replaced after a certain time period, with the option of replacing any item before the optimal time. The dimensions of the prosecution are fuzzy, and they are then assessed using mathematical and logical procedures. The fuzzy assessment criteria of the replacement model are provided as a set of outcomes, whereas the intuitionistic fuzzy replacement model has many advantages. A methodological technique is used to determine quality measurements in which fuzzy costs or values are kept without being merged into crisp values, allowing us to draw mathematical inferences in an uncertain setting. A comparison conceptualise is created for each fuzzy number, and in an uncertain environment, a comparison study on group and individual replacement was also conducted.

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Section: Introductionmentioning

confidence: 99%