A Novel Method Based on the Fuzzy Entropy Measure to Optimize the Fuzziness in Trapezoidal Strong Fuzzy Partitions

Abstract

Analyzing the uncertainty of outcomes based on estimates of the data’s membership degrees to fuzzy sets is essential for making decisions. These fuzzy sets are often designated by experts as strong fuzzy partitions of the data domain with trapezoidal fuzzy numbers. Some indices of the fuzzy set’s fuzziness provide an assessment of the degree of uncertainty of the results. It is feasible to bring the fuzzy sets’ fuzziness below a tolerable level by suitably redefining the strong fuzzy partition. Significant differences in the original fuzzy partition, however, result in disparities concerning the decision maker’s approximative reasoning and the interpretability of the results. In light of this, we provide in this study a technique applied to trapezoidal strong fuzzy partitions that, while not appreciably altering the original fuzzy partition, reduces the fuzziness of its fuzzy sets. The fuzziness of the fuzzy sets is assessed using the De Luca and Termini fuzzy entropy. An iterative process is then executed, with the aim of modifying the cores of the trapezoidal fuzzy partitions to decrease their fuzziness. This technique is tested on datasets containing average daily temperatures measured in various cities. The findings demonstrate that this approach strikes a great balance between the goal of lessening the fuzziness of the fuzzy sets and the goal of not appreciably altering the original fuzzy partition.

Keywords

• fuzzy entropy
• fuzziness
• trapezoidal fuzzy number
• strong fuzzy partition