A new expert system for learning management systems evaluation based on neutrosophic sets

There has been a sudden increase in the usage of Learning Management Systems applications to support learner's learning process in higher education. Many studies in learning management system evaluation are implemented under complete information, while the real environment has uncertainty aspects. As these systems were described by development organizations with uncertainty terms such as vague, imprecise, ambiguity and inconsistent, that is why traditional evaluation methods may not be effective. This paper suggests neutrosophic logic as a better option to simulate human thinking than fuzzy logic because unlike fuzzy logic, it is able to handle indeterminacy of information which expresses the percentage of unknown parameters. As previous studies suggested neutrosophic decision maker and neutrosophic expert systems as future work in ecommerce and e‐learning applications, this paper presents neutrosphic expert system for learning management systems evaluation. Information for building and validating the neutrosophic expert system is collected from five experts using surveys, and then analysis is done by using Fuzzytech 5.54d software. Finally, the comparison between fuzzy expert system and neutrosophic expert system results show that the neutrosophic logic is capable of representing uncertainty in human thinking for evaluating Learning Management Systems.


| INTRODUCTION
Learning Management Systems (LMSs) are software applications that assist instructors and learners with course management. The use of these applications has been increasing in higher education system as it is a useful tool that support universities in spreading educational resources to the learners in (Chung et al., 2013;Aggarwal et al., 2012). System quality is a wide concept that is associated with system performance and user interface (Almarashdeh et al., 2010). Former studies showed that system quality is an important determinant of user satisfaction and perceived usefulness (Lwoga, 2014). It can be defined as the usability, availability, response time, stability, reliability and suitability of the system (Almarashdeh et al., 2010). Previous researches (Yigit et al., 2014;Dubey et al., 2012) proposed multi-criteria decision making and fuzzy logic approach for LMSs software evaluation which requires availability of complete information. Multi-criteria decision making cannot handle uncertainty, whereas fuzzy logic presents a poor representation of uncertain data as it expresses the true membership degree in a value between 0 and 1. Fuzzy sets do not express the degree of false membership, and they have no solution when experts have a hesitancy to define membership. This problem demands new approaches based on many valued logic models that deals with uncertainty (Vern & Dubey, 2013). (Smarandache, 1999) proposed a new approach called neutrosophic logic as an extension of fuzzy logic. Neutrosophy comes from Latin "neuter", which means neutral and Greek "Sophia", which means skill or wisdom. It means knowledge of neutral thought.
Neutrosophic logic is a better option to simulate human thinking than fuzzy logic because unlike fuzzy logic, it is able to handle indeterminacy of information which expresses the percentage of unknown parameters (Ansari et al., 2013;Raheja & Dhadich, 2013;Aggarwal et al., 2010a). Expert systems and decision support systems tend to rely not only on true value, but also on false membership. So current systems which are dedicated to simulate human brain are constrained with strict conditions, whereas, neutrosophic logic holds its chance to simulate human thinking and to be utilized for real world problems (Aggarwal et al., 2010a). In neutrosophic logic, the sum of components is not necessarily 1 as in fuzzy logic, but any number between −0 and 3; therefore, neutrosophic logic is able to deal with contradictions

| Usability
Usability is a significant factor that evaluates system quality software.
Usability is an essential quality attribute of interactive software systems that deals with the continuous use of LMS application (Jain et al., 2012). Usability of LMS is directly related to the interactions between users and the system. LMSs are different from other systems as their focus is on how the user can interact to learn through them (Nagpal et al., 2013). There are many models that define usability quality attributes or factors that affect usability (Senol & Gecili, 2014).
• Efficiency: This dimension deals with the user understanding of the software. It indicates whether the system can achieve the users' objectives. The most common measures of efficiency taken by usability researchers are: number of goals/task not achieved, time taken for task completion, unproductive period, and percentage of task not completed.
• Error tolerance: It refers to the number of failures and easy error recovery. The most common measures of error tolerance are: number of times the user couldn't continue the task, number of actions taken that do not solve the problem, time spent on one error recovery, and number of times the user has to restart the application.
• Learnability: The dimension deal with the user ability to understand and learn software in an appropriate time frame.
• Memorability: The possibility of the user to remember basic functions of software even after some period of time.
• User Satisfaction: The software should be easy to use. If the four mentioned requirements are not achieved, user satisfaction is difficult to meet (Bhatnagar et al., 2012).

| Reliability
There are some uncertainty factors that affect the software reliability, whereas the conventional models deal with software failures (Cao et al., 2014). Conventional software reliability models concern with attributes such as probability of failure, average time to repair, and average time between system failures. Because of uncertain data, imprecise information, and incomplete knowledge in the software reliability assessment, the fuzzy theory can be used (Georgieva & Dimov, 2011). Reliability of LMSs deals with minimum loss in case of software failure, whereas data recoverability is very important. It is defined as follows: • Fault tolerance: It is the ability of software to recover from failure.
• Maturity: It concerns software failure frequency, where increasing maturity is associated with decreasing of failure.
• Recoverability: It concerns with the ability to return back failed system to full functionality.

| Accessibility
The accessibility allows individual with or without disabilities to take full advantage of information and services offered by the system (Al & Kamoun, 2012). Accessibility in e-learning refers to a learner's ability to access e-learning resources with minimal effort (Lin, 2010). Tamara et al., in (Almarabeh et al., 2014), define accessibility as learners to access the learning to material whenever and wherever they want without losing important information. The concept of accessibility in e-learning websites concerns with the following: • Navigability: User interface and navigation must be operable. The interface cannot require interaction that a user cannot perform.
• Robustness: Content must be able to be accessed by a wide variety of users including evolving technologies.
• Understandability: Information and user interface components must be presentable to users in a perceivable way.

| NEUTROSOPHIC LOGIC AND NEUTROSOPHIC EXPERT SYSTEM
Neutrosophic logic is an extension of the fuzzy logic, all of which variable x is described by triple values x = (t, i, f) where t is the degree of true, f is the degree of false, and i is the level of indeterminacy. For example, the proposition "Tomorrow it will be raining" does not mean a fixed-valued components structure; this proposition may be 40% true, 50% indeterminate, and 45% false at a time; but a second time may change to 50% true, 49% indeterminate, and 30% false (Ansari et al., 2011). Neutrosophic decision making, and neutrosophic expert systems in e-learning are suggested as future work for neutrosophic logic applications (Wang et al., 2005). In neutrosophic logic, the membership functions of inputs of every logical variable x is described by the degree of true, the degree of false and the level of indeterminacy as shown in Figure 1.
The presented neutrosophic expert system consists of neutrosophication unit that accepts crisp input. It assigns the appropriate membership functions, neutrosophic knowledge base that maps input to output variable depending on rules that are designed by experts and deneutrosophication unit that maps neutrosophic value to crisp value having a triplet format (true, indeterminacy, false); this differs from the fuzzy expert system which assigns a true input membership value as shown in Figure 2. In which, neutrosophication unit accepts the crisp input and assigns the appropriate membership (true, indeterminacy, false). Input variables are mapped to output using the Neutrosophic rule base. The resulting Neutrosophic output is mapped to a crisp value in deneutrosophication step using defuzzification methods. Neutrosophic sets can handle indeterminate information where an expert is asked about a certain statement to give a degree that the statement is true, false, and indeterminate. Different evaluation models for e-learning quality attributes developed under the condition of complete information availability.
Real environment is characterized by imprecise knowledge, incomplete information and uncertain data, this problem leads researchers to use approaches that deals with vagueness like fuzzy logic (Popenţiu-Vlădecescu & Albeanu, 2012;Salmi et al., 2014), and to suggest neutrosophic logic that handle uncertainty for e-Learning quality evaluation (Albeanu & Vlada, 2014). Expert system simulates human expert thinking to solve a problem and take decision in a particular domain which is mainly composed of the user interface, knowledge base, and inference engine (Anuradha & Kumar, 2013). Expert system aims to represent the problem of uncertainty in knowledge to draw conclusion The Difference between Fuzzy Expert System and Neutrosophic Expert System with the same level of accuracy as would a human expert do (Kaur et al., 2013). Designing an expert system depends on personnel interaction: an expert who has knowledge and solves the problems; a knowledge engineer who encodes the expert's knowledge in inference engine and knowledge base; and a user who uses the system to get advice and information needed (Anuradha & Kumar, 2013;Tripathi, 2011).

| THE PROPOSED NEUTROSOPHIC EXPERT SYSTEM FOR EVALUATING LMSS QUALITY
In this section, a neutrosophic expert system is proposed to assess LMS system quality considering three main attributes: usability, accessibility, and reliability are taken to provide a value of system quality.  Neutrosophic expert system uses neutrosophic logic to map the inputs to true, false, and indeterminacy membership functions. These inputs are obtained from the questionnaire of some domain experts; their option is of degree of truth, indeterminacy, and false. In this paper, five experts (referred in the acknowledgments) help us to develop neutrosophic expert system for evaluating the LMS; experts define the membership function for inputs, knowledge base and membership of output. The researchers conducted two surveys; one for collecting the data needed to build the rules of LMS expert system evaluation, and the other one is for validating the system rules and results after building it as shown in Figures 3 and 4. In (Alshibly, 2014;Aggarwal et al., 2010b), the authors suggested to simulate neutrosophic inference system as currently no software is available for it by designing three fuzzy inference systems representing true, indeterminate, and false value, which can be executed independently of each other using MATLAB Fuzzy logic toolbox. Simulation of the proposed neutrosophic expert system has been carried out by Fuzzytech 5.54 software as there is no need to develop a new system from scratch (http://fuzzytech.com, ).
Currently, Fuzzytech does not provide with the facility of neutrosophication, so to simulate it, three fuzzy inference systems have been created with the representing true, indeterminate and false value.
Fuzzytech allows more building and connecting than fuzzy inference systems. Also, it permits the implementing of true, indeterminacy, and false memberships freely without applying fuzzy membership restrictions which is not provided in the Matlab fuzzy logic toolbox.
Algorithm of the proposed neutrosophic expert system is stated as below: Step 1. Determine the system requirements represented in inputs, rules, and outputs.
Step 2. Experts define the neutrosophic memberships of inputs variables of the system which are usability, reliability, and accessibility,  Step 3. Inputs are presented to appropriate neutrosophic sets using truth, false, and indeterminacy membership functions. This step is called as neutrosophication step.
Step 4. Neutrosophied sets are then used by the inference engine to create the rules which are stored in the neutrosophic.
Step 5. In the final step of cycle, neutrosophic sets is then converted into a single crisp value which has triple format: truth, indeterminacy and false. This is the best representative FIGURE 10 Indeterminacy System Quality Knowledge Base    Step 6. Developing and implementing the neutrosophic expert system by using inputs, rules, and output is defined earlier to show the results.
Step 7. Validating neutrosophic expert system to ensure that the output of the intelligent system is equivalent to those of human experts when the same inputs are given. Then the results of validation steps are used to determine and fix errors to improve the knowledge base.
In uncertain environments, system validation includes extensive testing to guarantee that the system provides the correct decisions like an expert in the same field. The testing only compares the system's results with that of experts expected results (Zhu et al., 2011;Gonzalez & Barr, 2000). The validation is the process of confirming that the output of the expert system is equal to those of human experts when given the same inputs (Knauf et al., 2007). Knauf (Knauf et al., 2007) and Jiri Bartos at al. (Bartoš et al., 2012;Bartos & Walek, 2013) propose methodologies for evaluating system quality under uncertainty where functional and non-functional requirements can be tested which is used in this paper. These methods involve steps which are: identification of criteria for testing that cover the domain and generating a set of questions to validate neutrosophic knowledge base; different tests are prepared that evaluates whether the system is compatible with predefined criteria, where the test does not involve subjective opinions of the tester. Then, a comparison between system responses and five experts' (the same experts who help us in creating

| Membership functions for input parameters
As illustrated in Section 2, to evaluate system quality, there are three main linguistic variables: usability, reliability, and accessibility in which three fuzzy inference systems have been created with the representation of true, indeterminate, and false values as shown in Figure 3. As discussed in Section 2, usability is affected by efficiency, learnability, memorability, error tolerance, and user satisfaction. Reliability is affected by fault tolerance, maturity, and recoverability, whereas accessibility is affected by navigability, robustness, and understandability. All these variables have different contributions

| Knowledgebase and evaluation process
In the proposed neutrosophic model, five inputs for usability are con-

| Membership and knowledge base for output
The proposed neutrosophic expert system evaluates system LMSs system quality considering three main criteria; inputs usability, reliability, and accessibility. True, indeterminacy, and false membership values for the system quality are shown in Figure 12, 13 and 14, respectively.
Therefore three inputs for system quality are considered; consisting of five terms, then each true, indeterminacy, and false system quality