The suggestion in this paper tackles the uncertainty of choosing the best analysis and selection of high-quality gemstones based on multiple specific criteria of quantitative and qualitative nature. In this paper, we use the fuzzy analytic hierarchy process (F-AHP) in order to make the right decision to know the quality of the gemstone. This method is based on an effective algorithm through comparisons between the characteristics of the stones and their weight. F-AHP applies in this work to select one criterion from five criteria (specific gravity, color, clarity, cleavage, and Hardness). From the outcome, we note the hat standard of gem size is not always the best standard as seen by some researchers, and we found that small-sizzled stones are sometimes better effective and more flexible than others. Through this study, we note that the method helps reduce bias in decision-making, and method the comparisons are converted into numerical values that are processed and compared within with hierarchy that is related to the fuzzy logic with the property of uncertainty. All computations are applied by MATLAB language.

This paper dealt with one of the spatial interpolation methods in the geostatistics field. The purpose of this research is to get the parameters of unbiased estimators based on regionalized random variables in spatial statistics. In this paper, we used universal kriging with the fuzzy inference system by the Mamdani technique. the objective of this work is to estimate the parameters of covariance functions relying on spatial real for the depth of groundwater in Mosul city, Iraq. The data adopted contains (100) real data with locations representing the depth. From the results we show the best model with the constructs of weights, we illustrate the performance of universal kriging is the best when corresponding with the fuzzy system. In conclusion, the improvement of any method of spatial interpolation or fuzzy system does not depend on more statistical structures but depends on the efficiency of the method which satisfies the conditions of weights and minimum variance errors. All programming is applied by Matlab language.