Fuzzy molecular modeling

Increased knowledge and understanding of chemistry has enabled researchers to develop materials such as polymers and composites which have superior characteristics to naturally-occurring materials. Yet, even with the most advanced equipment, we still cannot accurately model chemical properties such as lattice parameters and bond angles in simple tetragonal structures such as the chalcopyrite family of compounds. The imprecision results from the analytical techniques and imprecision in the samples and measurement process. The research in this paper presents a new method for representing lattice parameters and bond angles-through the use of fuzzy logic. Since fuzzy logic by definition is imprecise, it is a natural means to represent the imprecision of lattice parameters and bond angles. The fuzzy lattice parameters are created by collecting parameter values from literature. From the minimum, maximum and average of these parameter values, a fuzzy number is created which represents the imprecision in that parameter. Then, through the use of fuzzy arithmetic operators and recently-developed fuzzy trigonometric functions, atom locations within the unit cell and bond angles can be calculated. Using fuzzy logic in this manner benefits us by allowing the direct representation and calculation of the imprecision found in chemical compounds which arises from measurement error, structural defects, and thermal and vibrational characteristics