In this research, Quantum-mechanical calculations were performed at the HF method with the 6-31+G*basis set and at the B3LYP method with the 6-31+G* basis set in the gas phase and five solvents such as water, DMSO, methanol, ethanol and dichloromethane at six temperatures. According to these theoretical results of IR, we extracted thermo chemical parameters such as enthalpy (∆H Kcal/mol), Gibbs...

In the rough set theory with every decision rule two conditional probabilities, called certainty and co erage factors, are associated. These two factors are closely related with the lower and the upper approximation of a set, basic notions of rough set theory. It is shown that these two factors satisfy the Bayes’ theorem. The Bayes’ theorem in our case simply shows some relationship in the data...

Rough set theory offers new perspective on Bayes’ theorem. The look on Bayes’ theorem offered by rough set theory reveals that any data set (decision table) satisfies the total probability theorem and Bayes’ theorem. These properties can be used directly to draw conclusions from objective data without referring to subjective prior knowledge and its revision if new evidence is available. Thus, t...

The ohjective of this article is to suggest the application of fuzzy set theory to issues in scale development in marketing by conceptualizing response categories of a scale as fuzzy sets. Respondents' natural responses to scales are argued to have degrees of membership in more than one response category when a response scale does not match natural responses. In contrast to traditional scales, ...

Intuitionistic fuzzy information aggregation plays an important part in Atanassov’s intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and further develop some new ...

Since the seminal paper of fuzzy set theory by Zadeh in 1965, many extensions have been proposed to overcome the difficulty for assigning the membership degrees. In recent years, a new extension, the hesitant fuzzy sets, has attracted a lot of interest due to its usefulness to handle those problems in which it is difficult to provide accurately a single membership value; since for hesitant sets...

E-service evaluation is a complex problem in which many qualitative attributes must be considered. These kinds of attributes make the evaluation process hard and vague. Cost–benefit analyses applied to various areas are usually based on the data under certainty or risk. In case of uncertain, vague, and/or linguistic data, the fuzzy set theory can be used to handle the analysis. In this article,...