No abstract

Well-foundedness is related to an important property of rewriting systems, namely termination. A well-known technique to prove well-foundedness on term orderings is Kruskal's theorem, which implies that a monotonic term ordering over a finite signature satisfying the subterm property is well-founded. However, it does not seem to work for a number of terminating term rewriting systems. In this paper, it is shown that a term ordering possessing subterm property and decomposability (in place of monotonicity) does yield a simpler proof of well-foundedness for terminating term rewriting systems than the techniques depending on Kruskal's theorem.

In this work, we used fuzzy inference system to forecast rice production covering the period 2021-2030 in Jigawa state, Nigeria. This is done by designing a fuzzy inference system using MATLAB. The system consists of two input functions and a single output function. Each function has its membership functions from which 49 inference rules of the system were formed. Three variables were considered in the course of this research. The variables are rainfall, land and rice production. Furthermore, linguistic variables were defined on each input. A rule based system was then formed which is defuzzified and a crisp value is obtained as the forecasted value. The result of this research shows that in 2022, 177950ha is required with 873mm of rainfall to produce 1070000TN of rice. Similarly, prediction is made of the required area, rainfall and rice yield up to 2030 in Jigawa state.

In this paper, a mathematical model is proposed to handle project scheduling problem under vagueness. This is done by assuming the durations of activities to be imprecise and represented by trapezoidal fuzzy numbers. In particular, the paper aimed to model patients flow process in imprecise or vague circumstances using critical path analysis. Furthermore, the research discusses utilization of fuzzy critical path method in conjunction with fuzzy program evaluation and review technique to determine the duration required for the treatment of patients in emergency ward of Aminu Kano teaching hospital. The activities considered are those affecting patients flow during treatments in the emergency ward and the related project network is drawn. The reason for incorporating fuzzy logic in this research comes from the fact that fuzzy numbers are more reliable in dealing with ambiguous processes such as witnessed in the emergency ward of a hospital. The choice of emergency department for this work is because it is a major access point where from the beginning patients are given treatments for a wide range of sicknesses and injuries. These sicknesses and injuries may be deadly and requires prompt attention. Therefore, any delay in patient treatment in the emergency ward may result in undesired consequences and losses of lives. Findings through the application of fuzzy CPM and fuzzy PERT enabled the determination of the critical path, slack times and patients’ treatment expected completion time. The entire idea is to reduce unnecessary delay, eliminate unnecessary activities at the same time increase the quality of treatment of patients in the hospital

In this paper, fuzzy critical path method and fuzzy program evaluation and review technique are used to calculate the earliest project completion time for constructing a hydroelectric power plant project. Fuzzy trapezoidal numbers are used to estimate the activity time and determine the range of pessimistic to optimistic variation of time. Furthermore, the minimum and maximum times of project completion duration were calculated by using arithmetic operations and ranking of fuzzy trapezoidal numbers. These hybrid methods are able to deal with the limitations associated with classical critical path method and program evaluation and review technique. The fuzzy techniques were applied to network activities in a manner similar to the classical methods for optimizing the project completion duration, thereby minimizing the cost of the project. Analysis was carried out to determine the critical path through the use of fuzzy critical path method. The fuzzy program evaluation and review technique was also used to determine the probability of completing the project at a scheduled time. These two methods were then compared and the most probable scenarios were analyzed. Finally, it was concluded that fuzzy program evaluation and review technique is better than fuzzy critical path method and more efficient in terms of early project completion time.