Abstract: In this paper we first considered a maximum likelihood estimation of trip distribution problem and next use primal-dual geometric programming method the said trip distribution problem converted into an entropy maximization trip distribution problem. Here the generalized cost function is assumed in different form, and then the said formulation is equivalent to single or multi-objective entropy maximization trip distribution problem. We use fuzzy mathematical programming method to show this equivalent problem formulation. The present article we use the concept of multi-objective trip distribution problem.

There are different university offering different types of courses over several years, and the biggest issue with that is how to get information to make course more effective. Association rule mining can be used to evaluate the course effectiveness and helps to look for in regards to changes in performance of the course. For Example there is a course offering different topics. We can say that the topics having full attendance are totally effective and carry no hesitation information. While there are some topics which are almost fully attendant carry some hesitation information. This hesitation information is valuable and can be used to make the course more effective and interesting. We use vague association rule to render that hesitation information and develop an algorithm to mine the hesitation information. Our experiments on real datasets verify that our algorithm to mine the Vague Association Rule is efficient. Compared with the traditional Association Rule mined from transactional databases, the Vague Association Rule mined from the AHpair databases are more specific and are able to capture richer information.