Search

In this paper, we propose an uncertain linguistic hybrid geometric mean (ULHGM) operator, which is based on the uncertain linguistic weighted geometric mean (ULWGM) operator and the uncertain linguistic ordered weighted geometric (ULOWG) operator proposed by Xu [Z. S. Xu, "An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations", Decision Support Systems41 (2006) 488–499] and study some desirable properties of the ULHGM operator. We have proved both ULWGM and ULOWG operators are the special case of the ULHGM operator. The ULHGM operator generalizes both the ULWGM and ULOWG operators, and reflects the importance degrees of both the given arguments and their ordered positions. Based on the ULWGM and ULHGM operators, we propose a practical method for multiple attribute group decision making with uncertain linguistic preference relations. Finally, an illustrative example demonstrates the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Point-, line- or boundary-sampled intercepts may be measured inside a particle as a measure of particle size. Each intercept is primarily characterized by three geometric properties: length, location and orientation. Circle and sphere models are used in the present study to analyze these properties. The probability distribution function, probability density function, expectation and coefficient of variation for each of the properties were presented based on geometric probability and mathematical statistics. Such presentation would be helpful for potential users of stereology to better understand the concept of intercepts and implement stereological intercept measurement for estimation of particle sizes in practice. [ABSTRACT FROM AUTHOR]