An Integrated Model for Evaluation of Big Data Interactive Systems Under Uncertainty

— The study aimed to propose a judgment - based evaluation model for usability evaluating of big data interactive system s. Human judgment is associated with uncertainty and gray information. We used the fuzzy technique for integration, summarization, and distance calculation of quality value judgment. The proposed model is an integrated fuzzy Multi Factors Evaluation (MFE) model based on experts’ judgments in HCI, ISPD, and AMLMs. We provided a Fuzzy Inference System (FIS) for scoring usability evaluation metrics in different big data interactive system s. A multi - model big data interactive system is implemented for experimental testing of the model. The achieved results from the proposed model and experimental tests are compared using statistical correlation tests. The results show the ability of the proposed model for usability evaluation of big data interactive systems without the need for conducting empirical tests. It is concluded that applying a dataset in a neuro - FIS and training system cause to produce more than a hundred effective rules. The findings indicate that the proposed model can be applied for big data interactive system evaluation, informative evaluation, and complex empirical tests. Future studies may improve the FIS with the integration of artificial neural networks.


INTRODUCTION
he COVID-19 scenario has led to a significant exp ansion in u sing interactive system s. Therefore, evalu ating and com paring big d ata interactive system s has received m ore and m ore attention from researchers. The m ost popu lar w ay for u sability evalu ation in big d ata interactive system s is cond u cting em pirical tests. H ow ever, som etim es the em pirical test is very tou gh and expensive d u e to secu ring sp ace, d eveloping the tests, hiring p articipants, etc. Moreover, in prototype testing, w e cannot ap ply em pirical testing. Evalu ating big d ata interactive system s is extensively investigated in H um an-Com pu ter Interaction (H CI) in interd isciplinary field s. It is an activity that exam ines the d egree to w hich an interactive system satisfies u ser goals and expectations [1]. Variou s stu d ies consid er evalu ating interactive system s.  proposed a netw ork d ata envelopm ent analysis m od el to m easu re the interactive relationship betw een system com ponents [2]. Their m od el evalu ates a parallel system w ith tw o interactive com ponents in only tw o centralized and non -centralized m od es. This m od el specifically evalu ates netw orks w ith interactive com ponents. H ow ever, d eveloping a m u lti-m od e system for evalu ation is a proper m ethod for com p aring all of the interactive system s, w hich w e ad opt from this stu d y. Benson & Pow ell (2015) prop ose an interview protocol to im prove investigative interview in g of child ren in training interactive system s [3]. Variou s stu d ies em pirically evalu ate the u sability of H CI interactive system s throu gh System Usability Scale [4], u sability heu ristics [5], or m u ltiple criteria [6]; [7]; [8]; [9]. While the typ e of interactive system is not consid ered to select proper criteria for evalu ation. For m obile applications, ed u cational system s, and agricu ltu re system s, they u sed the sam e heu ristics or scales w ith the sam e level of im portance for all criteria. The basic view in evalu ating interactive system s is em piricism [10]. Thu s, these kind s of evalu ations of T interactive system s are d om inant. Em pirical evalu ations pay to the u ser's need s, and it requ ires car efu l planning in m ethod selection. An em pirical evalu ation is essential to attend to the u sers' behavior and their interaction w ith the system . There are several m etho d s in em pirical evalu ation [3]; [11]; [12] as w ell as in books w ith m ore specific fram ing abou t the em pirical u sability evalu ation and the u ser experience [1]. These m ethod s inclu d e observation, interview, focu s grou ps, u ser testing, field tes ting, field stu d ies, qu estionnaires, su rveys, d iary stu d ies, and em pirical u sability testing. Exper im ental u sability testing is a su m m ative assessm ent that often occu rs late in the d esign phase. It is tw o types of evalu ations, inclu d ing form ative and su m m ative. Form at ive evalu ation focu ses on u sability problem s, and su m m ative evalu ation evalu ates the effectiveness of the final d esign [13]. So, d evelopers are looking at m ethod s that can be u sed earlier w hen only an im m atu re d esign is available [10]. The em pirical u sability testing shou ld provid e objective d ata that is d ifficu lt and exp ensive. It costs m oney and tim e to set u p and execu te a good em pirical stu d y. Costs revolve arou nd secu ring sp ace, the d evelopm ent tim e of the tests, hiring particip ants, etc. [14]. Therefore, w e only focu s on the formative evalu ating the interactive system s. Form ative evalu ations focu s on id entifying u sability pro blem s throu gh a red esign. Som e of the m ost com m on expert -based u sability assessm ent m ethod s inclu d e review ing gu id es based on interaction d esign gu id elines, innovative assessm ent, cognitive e nhancem ents, u sage paths, form al u sability inspections, and innovative m arches [15]. Recently, these experts-based techniqu es have becom e extend ed throu gh proposing new m od els of evalu ation fa ctors [16]; [17], new heu ristics [18]; [19], u sability evalu ation in a new generation of softw are [20]; [21], integration of expert-based techniqu es and u sing m achine learning techniqu es to pred ictive several u sability factors based on expert' opinion [22]; [55]. As w e d iscu ssed , the expert-based u sability evalu ation in the literatu re is com pletely static. To ou r best know led ge, there is not any usability evalu ation m ethod that com prehensively and d ynam ically evalu ates a big d ata interactive system w ith consid ering m u ltiple factors, u ncertainty, and experts' ju d gm ents. The past researchers u sed artificial intelligence and active learning m ethod s only for m easu ring or pred icting factors and not obtaining the effect of factors d ynam ically. For exam ple, Im el et al. (2019) proposed a system based on m achine learning techniqu es to pred icting and generating feed back in a u sability therapy assessm ent [22]. Ou r objective is to propose a new m od el to evalu ate big d ata interactive system s that covers all the need s of form ative and non-em p irical evalu ation. This m od el d ynam ically d eterm ines the effect of evalu ation factors based on the big d ata interactive system u sing a Fu zzy Inference System (FIS). Therefore, big d ata interactive system s w ill have a d ifferent and proper form u lation for their u sability evalu ation. We consid er ISO stand ard s and the m ost popu lar u sability evalu ation factors presented in the literatu re to be u sed in FIS. Finally, w e apply the fu zzy Mu ltiple Factors Evalu ation (MFE) ap proach for i) com paring tw o or m ore big d ata interactive system s or ii) evalu ating an interactive system ind ivid u ally. In fu zzy MFE and FIS, w e fu zzify hu m an opinion throu gh d esigning proper fu zzy Me mbership Fu nctions (MFs). Fu zzification of expert ju d gm ent provid es a m apping of the hu m an d ecision to crisp nu m bers [23]; [24]. We im plem ent a m u lti-mod el Big d ata interactive system s for People w ith Disabilities (ISPDs) based on fou r active m achine-learning m ethod s. This m u lti-m od el system w ill be evalu ated u sing the proposed evalu ation m od el for all fou r ap plied m achine-learning m ethod s. In this stu d y, the m ethod ology of Active Machine Learning Method s (AMLMs) evalu ation u sing the fu zzy MFE m ethod is explained in section 2. In continu e, section 3 provid es the resu lts of co nsistency, assessm ent of AMLMS effects, and evalu ating fu zzy MFE m ethod . Section 4 conclu d es the stu d y.

RELATED WORKS
Based on ou r objective, the stu d y is lim ited to form ative evalu ation of interactive system s, d ynam ically, and based on m u ltiple factors, expert ju d gm ents, and u ncertainty. In this section, w e d iscu ss the m ost related online pu blished w orks in 1970-2020 and , present the d ifference betw een associated w orks and the cu rrent stu d y. Usability evalu ation is a m u lti-criteria d ecision -m aking problem that in volves m u ltiple fu zzy factors. The MFE m ethod s ad d ress the u ncertainty and u ser preferences also can be ap plied for form ative u sability evalu ation. Fu zzy d istance calcu lation and p airw ise com parison are the m ost pop ular m ethod s u sed in fu zzy MFE. These m ethod s are u sed to cond u ct the u sability evalu ation of d ifferent system s [25]; [26]; [27]; [28]. Ram anayaka, Chen & Shi (2019) have ap plied MCDM m ethod s, for the w eighting of u sability factors to reveal the level of each factors' contribu tion to the u sabilit y ind ex of library w ebsites [28]. Chang and Dillon (2006) for the first tim e, u sed fu zzy set theory in u sability evalu a-tion [29]; [30].. They d efined six d im ensions for u sability evalu ation as System feed back, Consistency, Error prevention, Perform ance/ efficiency, User like/ d islike, and Error recovery. Chang and Dillon (2006) evalu ated their FIS in several d ifferent u ser interfaces [29]. Ku m ar, Tad ayoni, & Sorensen (2015) d efined five fu zzy u sability attribu tes as navigation, presentation, learnability, cu s tom izing, and task su p port [31]. H u d d y et al. (2019) su ggest a consolid ated , hierarchical u sability m od el w ith a d etailed taxonom y for specifying and id entifying the qu ality com ponents and m easu ring u sability [32]. The stu d ies as m entioned earlier solve th e u ncertainty of qu ality com ponents and ad d ress the u ser preferences in u sability evalu ations. They have prop osed FISs for a d ynam ic u sability evalu ation. This FIS is provid ed for ge neral evalu ation [29]; [30]; [32] or a specific application [31]. In these stu d ies, the evalu ation m etrics are the inpu t of FIS, and the ou tpu t is the score of u sability. Therefore, in provid ed FIS, w hen the fu zzy valu e of evalu ation m etrics changes, the system gives a new score for u sability. H ow ever, in this stu d y, w hen the interactive system changes, the system generates a new form u la for u sability evalu ation. In the new form u la, the effect of u sability factors (variables coefficient) takes a new valu e. The proposed FIS pr ovid es the effect of evalu ation m etrics (ou tpu ts of FIS) based on types of big d ata interactive system s (inpu ts of FIS).

METHODOLOGIES
This research has been perform ed both experim entally and analytically. We propose a m od el for evalu a ting com pu ter big d ata interactive system s based on experts' ju d gm ents. This m od el resolves to evalu ate big d ata interactive system s in conflict problem s. It is proper for situ ations that cond u cting an em pirical evalu ation of an interactive system is costly or com plicated . The prop osed m od el has three p hases (Figu re 1). In the first phase, an expert system is im plem ented to form u la u sability evalu ation for big d ata interactive system s, d ynam ically. In the second and third phases, the big d ata interactive system s evaluate or com pare accord ingly based on the generated form u la in the first phase. If a practitioner w ants to evalu ate an interactive system ind ivid u ally, they need to ap ply the second and third phases. Also, if a practitioner w ants to com p are tw o big d ata interactive system s, then they need to u se the first and third phases.

Pre-processing of Model
In the first phase, a FIS is p resented , w hich u ses the interactive system as an inpu t and prod u ces the effect of u sability criteria as an ou tpu t. We u sed the effects received in the form u la of u sability evalu ation as the new variable coefficients. Therefore, w e obtain a new form u lation of u sability evalu ation, w hich is su itable for evalu ating the sp ecified interactive system .

Classify Big data interactive systems
Types of big d ata interactive system s are d eterm ined throu gh the classification of big d ata interactive system s. In the cau se of the variety of big d ata interactive system s, w e consid er the fou r m ain H CI classifications i) hu m an contribu tion, ii) hu m an activities, iii) system objective and iv) inform ation processing. The first classification is based on the level of hu m an contribu tion. That is ad opted from Sherid an & Verplank (1978), w hich prop osed grou ps of hu m an contribu tions for big d ata interactive system s [33]. Figu re 2 show s a 10-point scale of grou ps of the hu m an contribu tion that is provid ed in an interactive system . Fig. 2 Grou ps of H u m an Contribu tion in Big d ata interactive system s In im plem entating ou r expert system , these10 levels form 10 inpu ts of the sys tem . The classification of hu m an contribu tion is one of the factors to d eterm ine interactive system type. The second classification is associated w ith u ser actions. These actions inclu d e instru ction, conversation, m anipu lation & navigation, and exploration [34]. It is im portant to note that these actions can d o together. Different m ethod s are u sed in u ser interface d evelopm ent. The first m ethod is to allow the u ser to issu e instru ctions to the sy stem w hile perform ing tasks. The second m ethod can be based on the u ser's conversation w ith the system . In the third m ethod , the u ser can m anipu late an environm ent of virtu al objects and go their ow n w ay. The fou rth m ethod is based on a stru ctu red inform ation presentation system . This system allow s u sers to learn things w ithou t having to ask specific qu estions. The third classification is based on the pu rpose of the interactive system . Usability evalu ation is d irectly affected by the pu rpose of the interactive system . An interactive learning system and an interactive m ed ical system have d ifferent u sers, and the u sers have d ifferent need s. The m ost proper system w ith a high u sability level is the system , w hich has the m axim u m m apping to u ser need s. We cond u cted a su rvey on 182 articles that is resu lted from the search in Web of Science Core Collection, in 2018-2019 w ith "interactive system " search key and in the category of com pu ter science. Com p onent factor analysis in "IBM SPSS statistics 25" is u sed to classify pu rposes of interactive system s in these articles. Finally, w e obtained six classes for pu rpose of int eractive system s and nam ed bu siness, gam es, u rban, ed u cation, m ed ical, and m ilitary (Figu re 3). The classes have d iffe rent popu larities in collected articles. For exam ple, com m erce has the m ost popu lar and the m ilitary has less p opu larity am ong interactive system s.

Fig. 3 Interactive System s Pu rposes
Interactive systems w ith the purpose of commerce personalize electronic commerce environments based on Human Factors. Today, personalization is everyw here. Interactive systems with education purposes include elearning, virtual learning, learning management, and learning services like producing data sets or exploring databases [35]. Interactive systems w ith medical purposes consist of medical decision support systems, ther apist robots, surgery robots, health information systems, and therapeutic systems in interaction with the physician, patient, or expert. The final classification is based on the level of information processing. We adopted a four-level of information processing [36] (Figure 4). In this four-level model, almost all the components of human information processing are obtained during information processing by cognitive psychologists. The performance of different levels in processing operations overlaps in time. Levels can also be coordinated in "perception-action" cycles to provide a precise serial sequence from stimulus to response.

Fig. 4 Levels of Information Processing in Interactive Systems
The first level includes the positioning and orienting of sensory receptors, sensory processing, initial preprocessing of data before complete comprehension, and selective attention. The second level involves the co nscious understanding and manipulating information processed and retrieved in w orking memory. The third level is w here decisions are made based on cognitive processing. The last level, the fourth level, involves executing a response or action consistent with the choice of decision.

Determining Usability Criteria
In this section, we focused on tw o sources of usability evaluation criteria: i) ISO standards, and ii) literature review. According to ISO 9126, the usability feature is defined as "the ability of a software product to be u nderstood, learned, used and attractive to the user when used in specific circumstances" (ISO 9126-2 2001). ISO 9241-11 defines usability as "the extent to which a product is used by specified users to achieve specified goals with specific effectiveness, efficiency, and satisfaction." The definitions of effectiveness, efficiency, and satisfa ction are similar in ISO 9241 and ISO 9126, except that ISO 9126 is softw are-based, and ISO 9241-11 is userbased. The latest revision of 9241-11 proposes eight criteria for interactive systems usability (learnability, regular use, error protection, accessibility, maintainability, effectiveness, efficiency, and satisfaction) [37]. Error protection is minimizing the possibility that users can make errors that could lead to undesirable consequen ces. In the current research, from these eight criteria, we exclude regular use, maintain ability, and satisfaction because w e are focusing on a formative evaluation. There is not a ready softw are product to use users' opinions for the informative evaluation. The usability predicts based on the expert opinion. Therefore, the regular use, maintainability, and satisfaction metrics are not measurable in this stage. In literature, researchers co nsider a w ide range of criteria for usability evaluation. We selected the high cited articles with more than 100 citations in google scholar that provided a list of usability metrics ( Figure 5). Sharp et al. (2019) is the most associated and latest work that proposes six criteria (effectiveness, efficiency, safety, utility, learnability, me morability) for usability evaluation, especially in interactive systems [34]. The system utility is directly associated with how its performance is appropriate based on the users' needs. One of the users' needs is the simplicity of using a system. Ease of learning methods is essential to use a system. Users do not like to spend a lot of time learning how to w ork the system. This problem is especially important for interactive products intended for daily usage. How ever, many users find this tedious, complex, and time-consuming. It seems that if most users are not able to spend their time learning using the system, it is necessary to create a wide range of lear ning capabilities for the system. Since we are going to conduct a formative evaluation, memorability, and safety. Sharp et al. (2019) define memorability as "w hen users return to the design after a period of not using it, how easily can they reestablish proficiency [34]." In the current study, we do not consider flexibility and security evaluation, and w e only focus on usability, so we exclude the safety factor as w ell.

Fig. 5 Usability Evaluation Metrics in High Cited Studies
In this study, we adopt the expert measurable and formative usability evaluation principles collected from standards and literature ( Figure 6). Therefore, the final usability evaluation metrics th at we select for the ou tput of the usability evaluation formula are effectiveness, efficiency, error protection, learnability, and utility. Accessibility and utility have overlap definitions so, we combine them under utility.

Implementing a Fuzzy Inference Analyzer
Usability criteria are generally in tw o groups fuzzy variables and linguistic variables. The interactive system is determined based on four criteria. There are three criteria of fuzzy variables. They include user participation, user activity, and information processing. In this study, FIS w as designed for usability evaluation using MATLAB with a fuzzy logic toolbox. In this study, we implemented a Mam dani-based FIS. This system was designed to measure the influence of the usability criteria on the whole interactive system (Figure 7). In this method, a fuzzy control strategy is used to plot the given inputs through rules, and produce an output based on these rules. The input is four classifications of big data interactive systems, and the output is five usability metrics. One of the inputs (System Aim) is not considered as a fuzzy variable because we only determine one main objective for an interactive system. However, the other three inputs and five outputs are fuzzy variables.

Fig. 7 Usability Evaluator FIS with Four Inputs and Five Outputs
The designed system is based on fuzzy MFs and if-then rules. The MFs and generated rules help to fuzzy and eliminate fuzzy variables, which is called fuzzification. In fuzzification, perform the process of converting a fuzzy output to a clear output in FIS. The input for the FIS is a fuzzy set, and the output is a single number. An MF is a curve w ith membership rates betw een 0 and 1. The MF represents a fuzzy set and is usually d enoted by μA. In the fuzzy set, for an element x of X, the value of μA is called the membership degree x. Membership degree, μA (x) determines a degree of membership of the element x in the fuzzy set. A value of 0 show s that x is not a member of the fuzzy set. A value of 1 show that x is a full member of the fuzzy set. Specifies values betw een 0 and 1 indicate the fuzzy members. Fuzzy logic has eleven internal MFs, and these fun ctions are made up of several essential functions, including linear fragment functions, Gaussian distribution function, sigmoid curves, and quadratic & cube polynomial curves. We determine the MFs for interactive system type inputs and usability metrics output according to the suitability of MF in representing fuzzy var iables [38]. Figure 8 show s the designed MFs of inputs of big data interactive systems classes. Human contribution MFs have ten trapezoidal MFs representing the ten groups of human contribution (Figure 8.a). Human activities have 4 Gaussian MFs representing instructing, conversing, manipulating/ navigating, and explo ring/ brow sing (Figure 8.b). The simplest MFs are formed using straight lines, and the simplest is a triangular MF that we used for crisp input (system purpose) (Figure 8.c). We defined four polynomial curves represen ting the information processing levels since each level includes the low er levels (Figure 8.d).

Fig. 8 Input Variables MFs
The output variables have the same MFs. A nine fuzzy scale of importance representing nine Gaussian curves was applied to determine the importance degree for each usability metric ( Figure 9). Finally, we design if-then rules in the relation betw een interactive system types, and the effect of usability metrics to predict the effect of usability metrics using fuzzy inferencing ( Figure 10).

Formulating usability evaluation
This study aimed to generate evaluation scores for all types of big data interactive systems. We proposed a fuzzy approach to creating the effect of usability metrics. We make a usability evaluation formula (Equation 1) based on the relationship between effects obtained and the final evaluation score, to calculate the final evalu ation score.
Usability is a variable that keeps the final score of usability calculated in this equation (1). Variable "i" is a counter that counts from 1 to 5 since w e have five usability metrics. Here, usability is a standard value. Arithmetic means to divide into random usability indices. Usually, based on the simulation method and the number of matrices, calculate different RIs. We adopt RI from Noble and Sanchez (1993) [39], which carried out 2500, 1000, and 5000 simulation runs. Random usability index (RI) is associated with previous usability experience of similar big data interactive systems (Table 1). If a similar system is very successful in providing usability, then the usability RI is 0.4, and if w e do not have experience in a similar case, then the RI is 1.0. Variable MI is the effect of usability metrics generated by a FIS. MI1, MI2, MI3, MI4, MI5 are the effects of effectiveness, efficiency, learnability, utility, and error protection correspondingly. Variable MV is the value of usability metrics, which is calculated through MFE methods. MV1, MV2, MV3, MV4, MV5 are the values of effectiveness, efficiency, learnability, utility, and error protection. In the second and third phases, we e xplained that how w e can obtain MV, when w e have one interactive system for evaluation, or when we have multiple big data interactive systems for comparison.

Usability Evaluating of an Interactive System
In the second phase, the following steps should be conducted for evaluating an interactive system. A distancebased multi-factor evaluation method is proposed to provide the value of metrics (MV) in the usability form ula.

Identify the Interactive System Class
This section is a typical section for phases 2 and 3. We need to determine the state of the entire interactive system in each class that is an input of the fuzzy system. For example, in an interactive system, the human contribution is at the sixth level, human activities are at the conversing level, and the purpose of the system is education. Also, the information processing contains all four steps of processing ( Figure 11).

Set Related Evaluation Formula
We need to have MI, IR, and MV for the usability formula. In the example mentioned above, the obtained effect of usability factors (MI) is the output of the fuzzy system ( Figure 12).

Fig. 12 Obtained Outputs in Sample Interactive System
When w e have, a similar implemented, and usability tested interactive system, we select the proper RI from Table 1. In the aforementioned interactive system example, we assume not existing similar case so, the IR is 1 and the usability formula is (Equation 2),

Judgment Sampling
Expert ju d gm ent is the basis of evalu ation u sability valu es (MV). In the FIS system , a lim ited nu m ber of featu res can be consid ered . In this case, system d esigners m u st be experts in im plem enting and evalu a ting big d ata interactive system s. In ou r system , a ju d gm ental sam pling strategy is u sed to perform the evalu ation. This m ethod is a non -probability sam pling m ethod in w hich the researcher selects m easu r able featu res based on existing know led ge or professional ju d gm ent. In this sam pling, the expertise of experts has priority instead of the nu m ber of experts [40]. In this stu d y, w e u se the ju d gm ent sam pling m ethod to select experts. The experts ju g the interactive system and provid e the inp u t of the fu zzy sy stem and su p ply essential d ata for the m u lti-factor evalu ation m ethod .

Assess Metrics Based on The Fuzzy Calculating Distance
The implemented FIS is only used to determine the effect of usability metrics, but the value of usability me trics for evaluating an interactive system w ill obtain through an MFE method, which is an operational research approach. MFE typically deals with evaluating a set of alternatives based on multiple criteria and experts ' judgment. Since MFE considers multiple factors for evaluation and it w orks based on decision makers' opinions, it can be used for the assessment softw are and systems w hen the empirical testing is complex. In this phase, w e determine a multi-dimension scale corresponding to our criteria. We have five dimensions because of five usability metrics. The experts selected for judgment, indicate the performance of the Where I = (10, 10, 10) and M is a fuzzy value that corresponds to linguistic variables, which are expressed by an expert for a metric.

Comparating Usability Between More Than One Interactive System
For comparing big data interactive systems w ith a different purpose, phase 2 is applicable as we run this phase separately for each interactive system and obtain usability scores. Then we look at the usability scores for comparing systems. H owever, w hen we w ant to compare big data interactive systems with the same purpose, human contribution, human activities, and information processing, we apply a pairwise comparison based MFE method for providing MVs. The usability of an interactive system w ith the same type calculates through Equation 4: For example, MV21 contains the value of the human contribution metric for interactive system 2. Also, when we have tw o big data interactive systems, then usability1 is the value of usability for interactive system one, and usability2 is the value of usability for interactive system 2.

Identify the Big data interactive systems Class
We have multiple interactive systems with the exact class of human contribution and activities, objectives, and information processing. Therefore, w e will receive the same effect of usability metrics (MI) for these systems.

Pairwise Comparating Systems on Related Criteria Based on the Fuzzy Variables
The Pairw ise comparison matrices are constructed to compare the interactive systems for each criterion (us ability metric). The intensity of big data interactive systems in a metric corresponds using jud gment's opinions through linguistic variables (Table 2). The relative intensity of one system over another system for ranking in a usability metric is expressed using pairw ise comparisons. These comparisons construct five pairwise comparison matrices corresponding to five criteria (usability metrics). Let = [C i ] n i = 1, 2, … , n be the set of big data interactive systems. The result of the pairwise comparison is summarized in an evaluation matrix as follow s (Equation 5): Where = [cw ij ] n×n and cw ij show s the intensity of the system C i over system C j through defuzzificating fuzzy values.

Obtaining Eigenvector
We produce the eigenvector from the pairwise comparison matrices to determine the ranking of big data interactive systems in each metric. We apply squaring, summarization, and normalization operations on pairw ise comparison matrixes to obtain the eigenvector (Equations 5 & 6): 4. Repeat steps 1-3 and compare the unique vector in each iteration w ith the previous step to make the difference betw een the special vectors much smaller. The last special vector is the priority vector.
Previous mathematical studies have shown that special vector solutions are the best approach to obtain prior ity rankings from the pairw ise comparison matrix [54]. Therefore, values of big data interactive systems in each metric w ill obtain from the eigenvector ⃗⃗⃗⃗⃗ . The appropriate vector is the priority that MV represents for big data interactive systems. Each pairwise comparison matrix corresponds to one criterion. The specific vector obtained for each matrix, including the rank of the systems in a criterion, is considered.

EXPERIMENTAL EXAMPLE
The research utilizes the experiment to evaluate the proposed model. The correlation between the results of the experimental test and the proposed model, represents the efficiency of the proposed model for evaluating big data interactive systems. Researchers apply different methodologies in ASRs (Automatic Speech Recogn ition) to address various types of disabilities [41]; [42]; [43]. The AMLMS algorithms are frequently applied in these systems to recognize the speech of disabled people who suffered from dysarthria [44]; [45]; & [46]. We implement a multimodel ASR interactive system in four ways of classification data in each mode that applies one of the AMLMs. We evaluate the usability in four modes of the multi-model ASR system through i) proposed model and ii) experimental study, then the results compare w ith statistical analysis ( Figure 13). The multimodal ASR system applies for recognizing continuous speech at the sentence level. The effect of usability metrics for multimodel ASR is determined through a FIS (phase 1). Active learning methods can be divid-ed into four categories: (1) single-view, single-learner (SVSL); (2) single-view, multi-learner (SVML); (3) multiview, single-learner (MVSL); and (4) multi-view, multi-learner (MVML) [47]. Multimodel ASR is based on the AMLMs (SVSL, SVML, MVSL, and MVML) and acts like four separate big data interactive systems. Weighting the usability metrics for multimodel ASR is conducted through the third phase. Based on judgment sampling, three experts in H CI, ISPD, and AMLMs w ere recruited to compare four system modes in multiple metrics.

Fig. 13 Process of Experimental Testing
The experts' judgments are processed using Equations 2, 3, 4, 5, & 6 to obtain the usability score in four modes of the ASR system. In the experimental test, w e recruited ten participants with speech disorders as utterances.
The participants utter the sentences in different system modes then the usability metrics are measured based on system output. The correlation between the experimental results and the proposed model's results represents the efficiency of the proposed model for evaluating big data interactive systems. The hypotheses analysis is conducted to show the efficiency of the proposed model based on the obtained results in an exper imental test of methods. The study population included academics working on HCIs, ISPDs, and machine learning techniques. The selection of these individuals w as made by searching the search portal of academic researchers at http:/ / academic.research.microsoft.com/ and searching Google at http:/ / www.google.com. Finally, among the retrieved individuals, ten specialists appointed to collect data. After sending an electronic invitation to them, three experts responded positively and participated in the study. First, they briefly informed about the study background and objectives through the Skype video conference tool, and explan ations gave about the multi-criteria evaluation method. Then, these experts were asked to determine the modes together according to five criteria and compare them based on the third step or study.

Multi-Model ASR System
This study has developed a multi-model ASR system in four modes; each mode applies one of the AMLMs to perform the data classification. This system as modern state of the art ASR system can act for pre -processing or feature extraction as w ell as acoustic, lexical, and language models. Some procedures have been developed for acoustic modeling, including Dynamic Time Warping (DTW), Hidden Markov Model (HMM), Vector Quantization, and Neural N etworks [48]. HMM is a model based on the dominant recognition paradigm, in which speech changes are statistically modeled. In a multimodal ASR system, neural networks are commonly used to estimate w ord probabilities. In this system, the probabilities determined using HMM eventually b ecome the most probable strings of the w ord. Figure 14 shows the general structure of the multi-model ASR system.

Fig. 14 Multi-Model ASR System
The ASR system detects several models of continuous speech at the first level (one-sentence phrases) for each participant. This system uses users' voice to detect users' speech disorders. These disorders include the pr oduction of incorrect speech sounds or improper sounds. Each participant spoke 215 sentences including a total of 1,079 w ords. Each sentence was spoken three times to minimize errors in mispronunciation in recor ding their speech. The audio is recorded in a suitable studio to reduce external no ises. The sampling rate used to record w as 16 kHz. All recorded voices were then labeled using a w ave tagging tool to show the boundary of silence and pause between the words in each sentence. The MFCC technique w as used to perform feature vector extraction operations using 25 ms frames and ten ms in the H amming window.

Participants
We recruited ten participants with speech disorders. The participants have speech problems such as difficu lties pronouncing sounds, or articulation disorders, and stuttering. Since there are two criteria (utility and Efficiency) subjective and must be rated based on participants' opinions, the participants can express their opinion in these two criteria are selected from previous studies. The demographic information of these par ticipants is given in Table 3. The participants uttered 30 sentences containing 75 words (an average of 2.5 words per sentence) in different system m od es. Then, the criteria are m easu red based on system ou tpu t.

Metrics Measurements
System u tility is m easu red su bjectively (self-reported ) and objectively (com pu ter record ed m easu res). In som e stu d ies, u sing su bjective m easu res is a w eak form of m easu rem ent [49]. Using ASR show that som e u sers' stand ard featu res in speeching are the repetition of som e w ord s, as w ell as the non -u se of som e w ord s. H ow ever, u sing a sp ecific system to cond u ct stu d ies in this area, relies on the participants in the stu d y. A m u lti-m od el ASR system d epend s on the nu m ber of tim es the system is u sed as an inpu t in term ed iary and the tasks assigned to the system [50]. Learnability is a qu antitative criterion calcu lated u sing the follow ing form u la (Equ ation 7): Where n is the nu m ber of evalu ation sam ples.
Error Protection is calcu lated throu gh three elem ents: failu re to hear or u nd erstand (E1); falsehood s pr od u ced in hearing or u nd erstand ing (E2) and clarifications requ ired to hear or u nd erstand (E3). These problem s need to solve for both u sers, and the system (Equ ation 8).
In w hich m is the nu m ber of evalu ation sam ples, and n is the vocabu lary size.
The Efficiency ind icated the ability of ASR to d eal w ith variou s inform ation attribu tes. We u tilized a list of inform ation attribu tes relevant for a broad spectru m of H CI applications that is presented by van and his colleagu es [51]. It is highly su bjective and com m only rated based on u sers' opinions. We then place each of the AMLMs for Au d ition Speech m od ality as "less," "neu tral," or "m ore" ap p ropriate to present the specific inform ation attribu te that is proposed by van Erp & Toet (2015) [51]. The am ou nt of effectiveness in the ASR system u su ally ind icates the accu racy of the tasks perform ed by the system , and this m eans the d egree of accu racy of the system in d etecting the u ser's speech. Accu racy is d eterm ined by checking the nu m ber of w ord s cau ght. The p ercentage of these w ord s is d eterm ined by the total nu m ber of w ord s. Another alternative m easu re of the ASR system 's response, especially w hen recognizing impaired speech, is the w ord error rate (WER) [50], w hich is form u lated as follow s (Equ ation 9):

RESULTS AND DISCUSSION
The resu lts of the stu d y present in three sections. The first section is abou t the relation of interactive system classes and u sability m etrics, the second section is related to fu zzy MFE resu lts, and the third section is related to hypothesis MFE resu lts.

Relation of Interactive System Classes and Usability Metrics
In

Fuzzy MFE Results
In the third phase, w e u sed MFE m ethod s for evalu ating AMLMs. This evalu ation is based on expert opinions rather than experim ents. The experts have been selected from the acad em ic board of the University of Malaya w ith experience, and know led ge in tw o scop es: i) AMLMs, and ii) ISPDs. Five evalu ation criteria as "u tility," "Efficiency," "Learnability," "Effectiveness," and "Error Protection" are d eterm ined in the first phase. The grou p experts w ere asked to com pare the ASR m od es w ith each other in the criteria (u sability m etrics). The aggregating their opinions is illu strated in Table 4. We constru cted the pairw ise com parison m atrix for each u sability m etric. We presented the resu lts ass ociated w ith u tility m etrics. Table 5 show s the com parison m atrix associated to criterion "u tility." We replaced the lingu istic variables w ith their corresp ond ing fu zzy nu m bers d eterm ined in Table 2. Table 6 show s the fu zzified com parison m atrix of u tility. Equ ation 2 has been ap plied for d efu zzificating the com p arison m atrix of u tility (Table 7). We obtained the eigenvector of the d efu zzified pairw ise com parison m atrix related to u tility. It is consi dered the MVs of ASR m od es in u tility criterion (Table 8). We u sed the sam e proced u re for obtaining the MVs in other criteria (Table 9).  Table 10. The SVML m od e has the m axim u m overall effect and , MVML has the third priority for u se in ISPDs.

Hypothesis Results
Throu gh statistical analysis, w e first proved that d ifferent ASR m od es have d ifferent applications. The u sability  Table 11). The resu lts of tests for su bject effects ind icate that there are significant d ifferences betw een the m od es in the overall u sability. Based on Estim ated Marginal Means (Table 12), the MVSL has better u sability than other AMLMs.  The resu lts of Post H oc Tests show that there is not a significant d ifference betw een MVSL and MVML in u sability (Table 13). Also, the classification resu lts of m ethod s show that MVML and MVSL are in the sam e grou p in term s of their effectiveness (Table 14).
The CC analysis is cond u cted to find the relation betw een the ranking of m od es prod u ced by the pr oposed m od el and the em pirical system test. The resu lts show that there is a strong and linear relation betw een them . N is the nu mber of criteria consid ered in rankings (Table 15).   (2-tailed) .000 N 5 5 **. Correlation is significant at the 0.01 level (2-tailed).

CONCLUSION
The u sability evalu ation by the big d ata interactive system s is a d ecision-m aking issu e and it has a strong influ ence on the overall im provem ent of big d ata interactive system s. In the form ative evalu ation of an interactive system or situ ations that cond u cting em pirical tests are costly, the d evelop ers need to pred ict the u sability w ithou t cond u cting em pirical tests. The u sability evalu ation of big d ata interactive system s consid ers in term s of qu alitative and qu antitative criteria. Moreover, there is no co nstant situ ation for evalu ating big d ata interactive system s, the im portance of u sability m etrics w ill change based on the interactive system . Therefore, an efficient and d ynam ic evalu ation m ethod is necessary to im prove the evalu ation process. In this stu d y, w e proposed an integrated m od el w ith three phases of evalu ation. The fu zzy m ethod is integrated w ith MFE m ethod s to increase the accu racy of evalu ation. The first phase w as the preprocessing of evalu ation. In this phase, w e d eterm ined the u sability fa ctors based on the m ost associated stand ard s and literatu re review. Fou r classifications of big d ata interactive system s are proposed based on a su rvey of 182 associated articles. We im plem ented a FIS w ith 50 fu zzies if-then ru les to prod u ce the best m etric effect for any interactive system . Tw o fu zzy MFE m ethod s are proposed for i) evalu ating an interactive system based on fu zzy d istance calcu lation to id eal solu tion and ii) com paring m u ltiple big d ata interactive system s based on the pairw ise com parison, along w ith tw o form u lations of overall u sability corresp ond ingly. To the best of ou r know led ge, an expert -based u sability evalu ation fu zzy system is a novel system w ith a d ynam ic aspect. The fu zzification scale of lingu istic variables d esign based on the experts' opinions. The proposed m od el is applied to assess the u sability of an im pl em ented m u ltim od el ASR for people w ith d isabilities. The resu lts show that the prop osed m od el has an accu rate pred iction of u sability scores for fou r m od es of the ASR system . The MVML m od e had the highest effect on u tility and learnability. H ow ever, it had the low est valu e for error protection, efficiency, and effectiveness. SVML m od e had the m axim u m valu e in Error Protection and Efficiency. The resu lts of the proposed m od el have been exam ined throu gh experim ental and hypothesis tests. The system is tes ted for p articipants w ith speech d isord ers. The criteria are m easu red sep arately in fou r m od es based on the system 's perform ance. The statistical resu lts show the im portance of AMLMs. The hypotheses analyses ind icated the high correlation betw een proposed m od el resu lts and experim ental resu lts. The ou tpu t su rfaces of the fu zzy system s allow ed u s to d eterm ine the relationship betw een interactive system types and u sability m etrics. It is conclu d ed that ap plying a d ataset in a neu ro-FIS and training system cau se to prod u ce m ore than a hu nd red effective ru les. The find ings ind icate that the proposed m od el can ap ply for interactive system evalu ation, inform ative evalu ation, and cond u ct ing com plex em pirical tests. Fu tu re stu d ies m ay im prove the FIS w ith the integration of artificial neu ral netw orks.

DECLARATIONS
 Ethics approval and consent to participate: This article d oes not contain any stu d ies w ith hu m an or anim al particip ants perform ed by any of the au thors.  Consent for pu blication: The pu blisher has the au thor's perm ission to pu blish the w ork.