Literature Review on Vague Set Theory in Different Domains

Problem of decision making is a crucial task in every business. This decision making job is found very difficult when it is depends on the imprecise and vague environment, which is frequent in recent years. Vague sets are an extension of Fuzzy sets. In the fuzzy sets, each object is assigned a single value in the interval [0,1] reflecting its grade of membership. This single value does not allow a separation of evidence for membership and evidence against membership. Gau et al. proposed the notion of vague sets, where each object is characterized by two different membership functions: a true membership function and a false membership function. This kind of reasoning is also called interval membership, as opposed to point membership in the context of fuzzy sets. In this paper, reviews the related works on the decision making by using vague sets in different fields

An approach to automatic learning assessment based on the computational theory of perceptions

E-learning systems output a huge quantity of data on a learning process. However, it takes a lot of specialist human resources to manually process these data and generate an assessment report. Additionally, for formative assessment, the report should state the attainment level of the learning goals defined by the instructor. This paper describes the use of the granular linguistic model of a phenomenon (GLMP) to model the assessment of the learning process and implement the automated generation of an assessment report. GLMP is based on fuzzy logic and the computational theory of perceptions. This technique is useful for implementing complex assessment criteria using inference systems based on linguistic rules. Apart from the grade, the model also generates a detailed natural language progress report on the achieved proficiency level, based exclusively on the objective data gathered from correct and incorrect responses. This is illustrated by applying the model to the assessment of Dijkstra’s algorithm learning using a visual simulation-based graph algorithm learning environment, called GRAPH

Multi-stage mixed rule learning approach for advancing performance of rule-based classification

Rule learning is a special type of machine learning approaches, and its key advantage is the generation of interpretable models, which provides a transparent process of showing how an input is mapped to an output. Traditional rule learning algorithms are typically based on Boolean logic for inducing rule antecedents, which are very effective for training models on data sets that involve discrete attributes only. When continuous attributes are present in a data set, traditional rule learning approaches need to employ crisp intervals. However, in reality, problems usually show shades of grey, which motivated the development of fuzzy rule learning approaches by employing fuzzy intervals for handling continuous attributes. While a data set contains a large portion of discrete attributes or even no continuous attributes, fuzzy approaches cannot be used to learn rules effectively, leading to a drop in the performance. In this paper, a multi-stage approach of mixed rule learning is proposed, which involves strategic combination of both traditional and fuzzy approaches to handle effectively various types of attributes. We compare our proposed approach with existing algorithms of rule learning. Our experimental results show that our proposed approach leads to significant advances in the performance compared with the existing algorithms

An IVIF-ELECTRE outranking method for multiple criteria decision-making with interval-valued intuitionistic fuzzy sets

The method of ELimination Et Choix Traduisant la REalité (ELimination and Choice Expressing Reality, ELECTRE) is a well-known and widely used outranking method for handling decision-making problems. The purpose of this paper is to develop an interval-valued intuitionistic fuzzy ELECTRE (IVIF-ELECTRE) method and apply it to multiple criteria decision analysis (MCDA) involving the multiple criteria evaluation/selection of alternatives. Using interval-valued intuitionistic fuzzy (IVIF) sets with an inclusion comparison approach, concordance and discordance sets are identified for each pair of alternatives. Next, concordance and discordance indices are determined using an aggregate importance weight score function and a generalised distance measurement between weighted evaluative ratings, respectively. Based on the concordance and discordance dominance matrices, two IVIF-ELECTRE ranking procedures are developed for the partial and complete ranking of the alternatives. The feasibility and applicability of the proposed methods are illustrated with a multiple criteria decision-making problem of watershed site selection. A comparative analysis of other MCDA methods is conducted to demonstrate the advantages of the proposed IVIF-ELECTRE methods. Finally, an empirical study of job choices is implemented to validate the effectiveness of the current methods in the real world. First published online: 17 Sep 201

Heuristic target class selection for advancing performance of coverage-based rule learning

Rule learning is a popular branch of machine learning, which can provide accurate and interpretable classification results. In general, two main strategies of rule learning are referred to as 'divide and conquer' and 'separate and con-quer'. Decision tree generation that follows the former strategy has a serious drawback, which is known as the replicated sub-tree problem, resulting from the constraint that all branches of a decision tree must have one or more common attributes. The above problem is likely to result in high computational complexity and the risk of overfitting, which leads to the necessity to develop rule learning algorithms (e.g., Prism) that follow the separate and conquer strategy. The replicated sub-tree problem can be effectively solved using the Prism algorithm , but the trained models are still complex due to the need of training an independent rule set for each selected target class. In order to reduce the risk of overfitting and the model complexity, we propose in this paper a variant of the Prism algorithm referred to as PrismCTC. The experimental results show that the PrismCTC algorithm leads to advances in classification performance and reduction of model complexity, in comparison with the C4.5 and Prism algorithms

Type-2 Fuzzy Logic based Systems for Adaptive Learning and Teaching within Intelligent E-Learning Environments

The recent years have witnessed an increased interest in e-learning platforms that incorporate adaptive learning and teaching systems that enable the creation of adaptive learning environments to suit individual student needs. The efficiency of these adaptive educational systems relies on the methodology used to accurately gather and examine information pertaining to the characteristics and needs of students and relies on the way that information is processed to form an adaptive learning context. The vast majority of existing adaptive educational systems do not learn from the users’ behaviours to create white-box models to handle the high level of uncertainty and that could be easily read and analysed by the lay user. The data generated from interactions, such as teacher–learner or learner–system interactions within asynchronous environments, provide great opportunities to realise more adaptive and intelligent e-learning platforms rather than propose prescribed pedagogy that depends on the idea of a few designers and experts. Another limitation of current adaptive educational systems is that most of the existing systems ignore gauging the students' engagements levels and mapping them to suitable delivery needs which match the students' knowledge and preferred learning styles. It is necessary to estimate the degree of students’ engagement with the course contents. Such feedback is highly important and useful for assessing the teaching quality and adjusting the teaching delivery in small and large-scale online learning platforms. Furthermore, most of the current adaptive educational systems are used within asynchronous e-learning contexts as self-paced e-learning products in which learners can study in their own time and at their own speed, totally ignorant of synchronous e-learning settings of teacher-led delivery of the learning material over a communication tool in real time. This thesis presents novel theoretical and practical architectures based on computationally lightweight T2FLSs for lifelong learning and adaptation of learners’ and teachers’ behaviours in small- and large-scale asynchronous and synchronous e-learning platforms. In small-scale asynchronous and synchronous e-learning platforms, the presented architecture augments an engagement estimate system using a noncontact, low-cost, and multiuser support 3D sensor Kinect (v2). This is able to capture reliable features including head pose direction and hybrid features of facial expression to enable convenient and robust estimation of engagement in small-scale online and onsite learning in an unconstrained and natural environment in which users are allowed to act freely and move without restrictions. We will present unique real-world experiments in large and small-scale e-learning platforms carried out by 1,916 users from King Abdul-Aziz and Essex universities in Saudi Arabia and the UK over the course of teaching Excel and PowerPoint in which the type 2 system is learnt and adapted to student and teacher behaviour. The type-2 fuzzy system will be subjected to extended and varied knowledge, engagement, needs, and a high level of uncertainty variation in e-learning environments outperforming the type 1 fuzzy system and non-adaptive version of the system by producing better performance in terms of improved learning, completion rates, and better user engagements

The Geometric Mean as a Generator of Truth-Value in Heuristic Expert Systems: An Improvement over the Fuzzy Weighted Arithmetic Mean

Many earlier expert systems that were modeled after MYCIN, the first expert system, employed truth-value factors for their rule antecedents (premises) and consequents (conclusions). These crisp truth-value factors were usually called certainty factors and attempted to provide a measure of confidence and computational capability to the analysis of rule uncertainty (Shortliffe, 1977; Kandel, 1994). However, in the literature criticism has been often expressed concerning the lack of precision a crisp truth/certainty factor value conveys (Zadeh, 1983; Turban, 1993). Zadeh (1973) and Xingui (1988) utilized the weighted fuzzy average algorithm to improve the precision of truth/certainty factor values. Kandel (1994) further extended the fuzzy weighted mean concept introducing rule confidence, priority, and conclusion weighting factors. Later, Chen (1996) further modified the fuzzy weighted mean algorithm through the factoring of independent rule premise and consequent weights, truth-values and certainty factors. All of these progressive variants of the fuzzy weighted mean enhanced perceived rule antecedent and consequent truth-value. This research investigated a modification of the fuzzy weighted algorithms of Chen and Kandel utilized in assessing heuristic expert system rule truth-value. Their algorithms were modified to demonstrate that a more statistically precise rule truth-value can be achieved by utilizing the geometric mean to aggregate rule truth-value components

Educational data mining using fuzzy sets to facilitate usability and user experience - an approach to integrate artificial intelligence and human-computer interaction

Artificial Intelligence (AI) and Human-Computer Interaction (HCI) have the common goal of enhancing effectiveness of a system and making it easier for people to use. AI accomplishes that by demonstrating intelligent behavior on a machine, whereas HCI involves the design approach required to obtain usability and user experience. This study integrates AI and HCI techniques in a real-world application complementing the aims of each field. A web based system was developed for a school board in Eastern Canada by following the user-centered approach of HCI. In the course of designing a good interface, it was found that fuzzy inference of AI was going on in users’ minds when they formed conceptual models to understand the application. The interface was evaluated by applying heuristic evaluation, cognitive walkthroughs and user feedback. It was shown that usability and user experience can be improved by employing fuzzy set techniques. Therefore, fuzzy set modeling can serve as a user centered method for HCI design. Furthermore, data gathering techniques of HCI helped to define the cognitive processes that could be replicated with the aid of fuzzy sets.Master of Science (MSc) in Computational Science

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches