Decision Trees with Soft Numbers

In this paper we develop the foundation of a new theory for decision trees based on new modeling of phenomena with soft numbers. Soft numbers represent the theory of soft logic that addresses the need to combine real processes and cognitive ones in the same framework. At the same time soft logic develops a new concept of modeling and dealing with uncertainty: the uncertainty of time and space. It is a language that can talk in two reference frames, and also suggest a way to combine them. In the classical probability, in continuous random variables there is no distinguishing between the probability involving strict inequality and non-strict inequality. Moreover, a probability involves equality collapse to zero, without distinguishing among the values that we would like that the random variable will have for comparison. This work presents Soft Probability, by incorporating of Soft Numbers into probability theory. Soft Numbers are set of new numbers that are linear combinations of multiples of ”ones” and multiples of ”zeros”. In this work, we develop a probability involving equality as a ”soft zero” multiple of a probability density function (PDF). We also extend this notion of soft probabilities to the classical definitions of Complements, Unions, Intersections and Conditional probabilities, and also to the expectation, variance and entropy of a continuous random variable, condition being in a union of disjoint intervals and a discrete set of numbers. This extension provides information regarding to a continuous random variable being within discrete set of numbers, such that its probability does not collapse completely to zero. When we developed the notion of soft entropy, we found potentially another soft axis, multiples of 0log(0), that motivates to explore the properties of those new numbers and applications. We extend the notion of soft entropy into the definition of Cross Entropy and Kullback–Leibler-Divergence (KLD), and we found that a soft KLD is a soft number, that does not have a multiple of 0log(0). Based on a soft KLD, we defined a soft mutual information, that can be used as a splitting criteria in decision trees with data set of continuous random variables, consist of single samples and intervals.

Knowledge Verification Method Based on Artificial Intelligence-based Knowledge Graph Construction

The knowledge graph connects real-world entities and concepts through their relationships, connects all different types of information to obtain a relationship network, and can analyze “relationship” issues. Creating a knowledge graph is a continuous process, and it needs to continuously learn new knowledge and update existing knowledge in the library as time and events change. However, since the accuracy of the updated new knowledge cannot be guaranteed, the new knowledge must be verified. This paper aims to study the knowledge verification method based on artificial intelligence-based knowledge graph construction. Based on the analysis of the knowledge graph construction process, the knowledge graph construction method and the knowledge verification method, knowledge verification is realized by constructing a probabilistic soft logic model. The experimental results show that the recall rate, F1 value, and AUC value of the candidate knowledge set are verified by the knowledge verification model proposed in this paper. Therefore, it can be inferred that the knowledge verification model proposed in this paper is effective.

Work continuity constraints in repetitive project scheduling considering soft logic

PurposeRepetitive projects play an important role in the construction industry. A crucial point in scheduling this type of project lies in enabling timely movement of crews from unit to unit so as to minimize the adverse effect of work interruptions on both time and cost. This paper aims to examine a repetitive scheduling problem with work continuity constraints, involving a tradeoff among project duration, work interruptions and total project cost (TPC). To enhance flexibility and practicability, multi-crew execution is considered and the logic relation between units is allowed to be changed arbitrarily. That is, soft logic is considered.Design/methodology/approachThis paper proposes a multi-objective mixed-integer linear programming model with the capability of yielding the optimal tradeoff among three conflicting objectives. An efficient version of the e-constraint algorithm is customized to solve the model. This model is validated based on two case studies involving a small-scale and a practical-scale project, and the influence of using soft logic on project duration and total cost is analyzed via computational experiments.FindingsUsing soft logic provides more flexibility in minimizing project duration, work interruptions and TPC, especial for non-typical projects with a high percentage of non-typical activities.Research limitations/implicationsThe main limitation of the proposed model fails to consider the learning-forgetting phenomenon, which provides space for future research.Practical implicationsThis study assists practitioners in determining the “most preferred” schedule once additional information is provided.Originality/valueThis paper presents a new soft logic-based mathematical programming model to schedule repetitive projects with the goal of optimizing three conflicting objectives simultaneously.