Ratio Mathematica Volume 45, 2023 Application of Analytic Hierarchy Process in Engineering Education M. Tirumala Devi1 Sameena Afreen2 V. Shyam Prasad3 Abdul Majeed4 G. Mahender Reddy5 Abstract Analytic Hierarchy Process (AHP) provides a mathematical technique to formulate a problem as a hierarchical structure and believes in an amalgamation of quantitative and qualitative criteria. It is this uniqueness of AHP that makes it one of the important inclusive systems, considered to make decisions with multiple criteria. This paper focuses on conducting Analytic Hierarchy Process, based on the data collected from several Engineering colleges in the state of Telangana. This paper aims to understand the reasons for removing the staple Engineering streams such as Mechanical engineering, Production engineering, Electronics and Instrumentation engineering and introducing new and contemporary streams such as Artificial Intelligence and Data Science, Artificial Intelligence and Machine Learning and Internet of Things. The World Economic Forum’s latest “Future of Jobs” report highlights the impact of ‘double disruption’ of Automation, followed by COVID-19. The report indicates that while 85 million jobs will be displaced, 47% of core skills will change by 2025. The topic thus is of immense value since it looks closely at the paradigm shift mentioned above and its further consequences. The result of the present study would be helpful to indicate the exact rankings of the programming and non-programming branches in the engineering field and thus would be instrumental in gauging learners’ inclination towards studying specific branches. This paper aims to analyze the growing demand of programming branches over traditional, non-programming branches. Keywords: Analytic Hierarchy Process, Pair-wise comparison, Priority vector. AMS Mathematical Classification: 03D55, 93A136 1 Department of Mathematics, Kakatiya University, Warangal, TS, India. Email: oramdevi@yahoo.com, ORCID ID: https://orcid.org/0000-0002-4162-0084. 2 Department of Mathematics, Kakatiya University, Warangal, TS, India. Email: afreensama82@gmail.com. 3 Guru Nanak Institutions Technical Campus, Hyderabad, Telangana, India. mail:shyamnow4u@gmail.com, https://orcid.org/0000-0002-7966-1682. 4 Muffakham Jah college of Engineering & Technology, Hyderabad, Telangana, India. Email: abdulmajeed.maths@mjcollege.ac.in. ORCID ID: https://orcid.org/0000-0002-0286-0042. 5 Guru Nanak Institutions Technical Campus, Hyderabad, Telangana, India. Email: mahender1563@yahoo.co.in, https://orcid.org/0000-0002-1387-0131 267 mailto:oramdevi@yahoo.com https://orcid.org/0000-0002-4162-0084 mailto:afreensama82@gmail.com mailto:shyamnow4u@gmail.com https://orcid.org/0000-0002-7966-1682 mailto:abdulmajeed.maths@mjcollege.ac.in https://orcid.org/0000-0002-0286-0042 mailto:mahender1563@yahoo.co.in https://orcid.org/0000-0002-1387-0131 M. Tirumala Devi et al. 1. Introduction The process of choosing the optimal alternative among all potential options is classified as decision-making, however in practice, attaining an optimized result can be difficult because decision-makers are frequently challenged with diverse decision-making problems [1]. Multi-criteria decision-making (MCDM) is one of the most significant fields of decision theory, and it is used to find the optimum solution out of all the possibilities [4]. MCDM has been improved by the development of several approaches, including: Analytic Hierarchy Process (AHP) (Saaty 1980)[8]; Techniques for determining superiority and inferiority [10]; Simos’ technique of ranking [6]; multi- attribute utility theory (MAUT) [3]; elimination and selection in accordance with reality [7]; For enrichment evaluations, a preference ranking organization method is used [2]; and selecting based on benefits [9]. These MCDM techniques are commonly used to help solve real-world decision-making difficulties. Saaty's (1980) AHP is a popular MCDM method that has gotten a lot of attention in the industry, including education and management. Earlier many researchers have done a good amount of work on decision making [5]. Students with technological capabilities will have excellent work possibilities in the post-COVID global economic landscape. According to the World Economic Forum, 92 per cent of firms are speeding up their digitalization efforts, with more than 90 per cent using technology such as artificial intelligence, big data analytics, and cloud computing. Students who graduate with specialized technical skills will have access to desirable job possibilities in fields such as IT, cloud services, and healthcare. It is observed that, many Engineering colleges have dropped the non-programming branches such as Mechanical Engineering, Production Engineering, Electronics & Instrumentation Engineering etc. and these are being replaced by Computer Science Engineering-Emerging Technology courses such as Artificial Intelligence & Data Science, Artificial Intelligence & Machine Learning, Internet of Things & Cyber Security etc. The authors of the paper are motivated by this scenario to present a paper on this topic. This paper tries to prove that, Emerging Technology courses are providing more employability skills required by the students in the current scenario. With this goal, variables were selected and study was done to observe the results. There are not too many discussions to understand this issue with the application of AHP method. In this context, the approach towards understanding the change in terms of choices of courses among engineering students, using AHP technique is not only a novel idea but also presents a vivid picture to understand the paradigm shift. 2. The Physical Importance of all Criteria Scope of Employment (C1): The Emerging Technology courses have a wide scope of employability in many sectors like telecommunication, transportation, corporate sector, medical etc. These graduates progress more quickly in terms of developing the necessary abilities to obtain and 6Received on July 6th, 2022. Accepted on September 15th, 2022. Published on January 30, 2023.doi: 10.23755/rm.v45i0.1025. ISSN: 1592-7415. eISSN: 2282-8214. ©The Authors. This paper is published under the CC-BY licence agreement 268 Application of Analytic Hierarchy Process in Engineering Education manage a job, resulting in better chances. However, while having such abilities increases these graduates’ chances of finding work, it does not guarantee it [3]. Subject- specific knowledge and abilities are essential for work. Other talents, undoubtedly, play an important role in the lives of students, assisting them in obtaining not just a job, but also a profession of their choice. Acquiring the right skills not only ensures sustenance but also promotes growth in the employment sector. Subject-related skills are those that students gain throughout their degree program, whereas transferable skills are those that people learn on the job and may be used to other occupations inside or outside of their organization, allowing them to go further in their careers [5]. Because information technology has such a strong influence on today's global marketplaces, this study focuses mostly on IT workers. IT firms are constantly developing and adopting new technology. Employers also seek talented candidates that can adapt to today's fast-paced work environment and are eager to learn new skills. While working to improve employability, the International Labor Organization emphasized fast globalization, new working environments, and technological advancement. This will necessitate investing in their workforce's skill development and training. The Indian economy has been moving toward digitalization since 2015, necessitating a highly qualified and capable workforce. Through numerous open online learning platforms such as MOOCS, SWAYAM, and others, where at least 350 online courses enable students to virtually attend courses taught by the best faculty, many jobs will be created in the future. Right Employability Skills (C2): Computer Science and Technology is more of an applied computer science than a completely theoretical discipline. It focuses on addressing user needs in an organizational and societal environment by performing the following tasks: Selection, creation, application, integration, and administration of computing technologies. As a result, computer graduates must have particular abilities and knowledge in order to obtain relevant positions at work; they must be able to anticipate changes in the field of technology and express the value of the same to an individual or organization. Every year, the software sector employs roughly 10 million people. In the $124–130 billion market, it contributes 67 percent. For the fiscal year 2016-17, it grew at a rate of 12- 14 percent. Because the software business is growing, it generates strong cash flows and a high return on equity. Nonetheless, rather than adding new staff, numerous IT organizations are deploying automation to improve digitalization. Employability skills are a continuous practice that can be included into the curriculum as well as the unpredictable work environment of an organization. This emphasizes the need of having the appropriate employment skills. Higher pay package (C3): Computer Science Engineering is a field that is in high demand in the industry. As a result, obtaining a professional degree or certification in Computer Science will make one a valued asset to a company, especially in the IT area. Furthermore, the pay packages in these companies are fairly high. Wide career options and career stability (C4): According to data from popular study destinations, 269 M. Tirumala Devi et al. ➢ Computer and Information Technology (IT) occupations are expected to expand by 12% in the United States by 2028, according to the Bureau of Labor Statistics. ➢ By 2023, the number of Software and Application Programmers in Australia is predicted to increase from 121,300 to 146,800. ➢ Immigration.ca reports that “Qualified Software Engineers are being hired by Canadian employers as quickly as they become available.” Freedom to work from anywhere (C5): Computer science and information technology have an impact on everything from scientific research to health development, transportation, banking, and communications, among other things. Microwave ovens, refrigerators, and door locks are now all connected to our Wi-Fi networks. Applications in all the Fields (C6): Artificial intelligence applications have advanced tremendously in recent years. Its applications can be found in virtually every industry. Artificial Intelligence Applications in E-Commerce ➢ Personalized Purchasing ➢ Assistants with Artificial Intelligence ➢ Preventing Fraud Applications of Artificial Intelligence in Education ➢ Educators will benefit from automated administrative tasks ➢ Creating Intelligent Content ➢ Virtual Assistants ➢ Personalized Education Applications of Artificial Intelligence in Lifestyle ➢ Vehicles that drive themselves ➢ Filters for Spam ➢ Recognition of faces ➢ System of Recommendation Navigation, robotics, human resources, healthcare, agriculture, gaming, automobiles, social media, marketing, chat bots, finance, and many more fields have been transformed by AI applications. 3. Significance of each Alternative Artificial Intelligence & Data Science (AI&DS) (A1): The Artificial Intelligence and Data Science Program teaches students how to do intelligent data analysis, which is a critical component in many real-world applications. Data science has evolved as one of the most high-growth, dynamic, and rewarding occupations in technology during the last 10 years. This course intends to teach not only essential technologies like artificial intelligence, data mining, and data modeling, but also advanced topics like machine learning and big data analytics. Students will gain cross-disciplinary skills in fields such as statistics, computer science, machine learning, and logic, as well as data scientists, and will have 270 Application of Analytic Hierarchy Process in Engineering Education career opportunities in healthcare, business, e-commerce, social networking companies, climatology, biotechnology, genetics, and other important fields by the end of this course. Students will learn statistical, mathematical reasoning, machine learning, knowledge discovery, and visualization abilities as part of this program. Artificial Intelligence & Machine Learning (AI&ML) (A2): The student under B.Tech Artificial Intelligence and Machine Learning is required to write the code of the said machine. This code in essence works as a guiding instruction for the machine, where it can perform tasks with less human intervention. Internet of Things/Cyber Security (IOT/CS)(A3): B.Tech CSE (IoT& Cyber Security including Block chain Technology), undergraduate program familiarizes students with the functional and operational aspects of IoT, Cyber Security and Block chain Technology. Cyber security is a specialist topic of Information Technology (IT) that is considered a sub-discipline of Computer Science. Students will gain the information and abilities needed to safeguard computer operating systems, networks, and data from cyber-attacks in Cyber Security courses. Because of the rising occurrence of cybercrime, cyber security as a profession has evolved over time. Any industry that transacts online or handles sensitive data requires a Cyber Security expert to protect its data from such criminals. Because cyberspace is a global platform that anybody may access from anywhere in the world, the scope of cyber security is equally distributed. Cyber security is a lucrative and rapidly expanding subject that focuses on safeguarding businesses from digital threats and keeping their data and networks secure. Experts in cyber security identify flaws, offer software and hardware programs to limit risks, and create rules and processes to ensure security. The demand for qualified cyber security specialists is expected to expand as more firms transfer their activities online and cyber- attacks become more common, particularly in healthcare and financial institutions. Information security analysts, for example, are expected to expand by 40% between 2020 and 2038, according to the Bureau of Labor Statistics. Mechanical Engineering (Mech) (A4): Students in this program will learn how to become Mechanical Engineers. The goal of this curriculum is to prepare students to use mechanical engineering principles in the design, manufacture, and maintenance of mechanical systems. Production Engineering (PE) (A5): Production engineering is a branch of engineering that is closely related to mechanical engineering. Production engineers are educated to increase the efficiency and effectiveness of manufacturing and service industries. Manufacturing technology, which is a branch of mechanical engineering, is combined with management science in production engineering. A production engineer works in a variety of industries, dealing with engineering methods and management difficulties relating to manufacturing. Electronics and Instrumentation Engineering (A6): Electronics and Instrumentation Engineering is a program combining motor skills and academic skills which carve out a career in various fields of electronics, measurement, and complex process understanding. 271 M. Tirumala Devi et al. 4. Methodology The AHP technique is broken down into the following steps. I) Choosing criteria and structuring a decision-making problem II) Prioritization of criteria using pair wise comparison III) On each criterion, compare options in pairs IV) Calculating a relative score for each option 4.1 Prioritization Methods: There are a few methods for determining alternate priorities, like as i) Geometric Mean Method, ii) Additive Normalization Method, iii) Stochastic Vector Method are available to find the priorities of alternatives. The Geometric Mean Method (GMM) is employed in this paper. 4.1.1 Geometric Mean Method (GMM): The weights for the criteria or alternatives are determined using this procedure. The alternate pair-wise comparison matrix is shown in Table 1. Here 𝐾1,𝐾2,…. . ,𝐾𝑛 represents the alternatives which are to be ranked and 𝑘11,𝑘12,…. . ,𝑘𝑛𝑛 represents expert opinions. The Geometric Mean Method, which is used to calculate the priority weight vectors, is described below. 𝐾1 𝐾2 ……… 𝐾𝑛 𝐾1 𝑘11 𝑘12 ……… 𝑘1𝑛 𝐾2 𝑘21 𝑘22 ……… 𝑘2𝑛 . . . . . . . . . . . . . . . 𝐾𝑛 𝑘𝑛1 𝑘𝑛2 ……… 𝑘𝑛𝑛 Table 1: Pair-wise comparisons Obtain the geometric row means of each row as Priority vector 𝑘1 = (𝑘11 × 𝑘12 × …..× 𝑘1𝑛) 1 𝑛 Priority vector 𝑘2 = (𝑘21 × 𝑘22 × …..× 𝑘2𝑛) 1 𝑛 Priority vector 𝑘𝑛 = (𝑘𝑛1 × 𝑘𝑛2 × …..× 𝑘𝑛𝑛) 1 𝑛 The normalized vector of (𝑘1,𝑘2, …. . ,𝑘𝑛) becomes the solution vector. Table 2 describes AHP Measurement scale about the importance of Saaty’s crisp numbers. Intensity of importance Definition Explanation 1 Same importance Two elements contribute same to the property 3 Moderate importance of one over another Experience and judgment some favor one over the other 5 Essential or high Experience and judgment highly favor 272 Application of Analytic Hierarchy Process in Engineering Education importance one over another 7 Very strong importance An element is highly favored and its dominance is demonstrated in practice 9 Extreme importance One of the most possible orders of affirmation is evidence favoring one element over another. 2,4,6,8 Lying between two adjacent judgments Comprise is needed between two judgments Reciprocals Whenever activity i compared to j is assigned one of the above numbers, the activity j compared to i is assigned its reciprocal Rational Ratios occurring from forcing consistency of judgments Table 2: AHP Measurement Scale Table 3 lists the number of courses offered in selected engineering colleges. S.No Name of the college TS EAMCET CODE Number of courses Percentage 1. MuffakhamJah College of Engineering & Technology MJCT 10 15 2. CVR College of Engineering CVRH 10 15 3. Geetanjali College of Engineering and Technology GCTC 9 13 4. Guru Nanak Institute of Technology GNIT 8 12 5. Guru Nanak Institutions Technical Campus GURU 9 13 6. Methodist College of Engineering and Technology METH 6 8 7. Nalla Narasimha Reddy Educational Society Group of Institutions NNRG 8 12 8. Lords Institute of Engineering & Technology LRDS 8 12 Table 3: Number of Courses from selected Engineering Colleges Table 4 exhibits Program-wise intake in three consecutive academic years 2019-2020, 2020-2021 and 2021-2022. MJCT CSE INF ECE CIV MEC H PE EEE EIE AI& DS AI& ML IOT/ CS 2019-2020 120 120 120 120 120 60 60 60 0 0 --- 2020-2021 120 120 120 120 120 0 60 60 60 0 --- 2021-2022 120 120 120 120 120 0 60 0 60 60 --- CVRH 2019-2020 300 240 240 120 120 --- 120 60 0 0 0 2020-2021 300 240 240 60 60 --- 60 60 60 60 60 273 M. Tirumala Devi et al. 2021-2022 300 240 120 60 60 --- 60 60 120 120 60 GCTC 2019-2020 240 60 240 120 120 --- 120 --- 0 0 0 2020-2021 240 60 240 60 60 --- 60 --- 60 60 120 2021-2022 240 60 240 60 60 --- 60 --- 60 180 120 GNIT 2019-2020 180 60 120 120 120 --- 60 --- --- 0 0 2020-2021 180 60 120 120 120 --- 60 --- --- 60 60 2021-2022 180 60 120 120 120 --- 60 --- --- 60 60 GURU 2019-2020 300 60 300 180 300 --- 120 --- 0 0 0 2020-2021 300 60 300 180 300 --- 120 --- 60 60 60 2021-2022 300 60 300 180 180 --- 120 --- 60 60 60 METH 2019-2020 120 --- 120 120 120 --- 60 --- 0 --- --- 2020-2021 120 --- 120 120 60 --- 60 --- 60 --- --- 2021-2022 120 --- 120 60 60 --- 60 --- 120 --- --- NNRG 2019-2020 180 0 180 60 120 --- 60 --- 0 0 --- 2020-2021 180 60 180 60 60 --- 60 --- 0 0 --- 2021-2022 180 60 180 30 30 --- 30 --- 60 60 --- LRDS 2019-2020 180 120 120 180 180 --- 60 --- 0 0 --- 2020-2021 180 180 120 180 180 --- 60 --- 60 120 --- 2021-2022 180 180 120 180 120 --- 60 --- 60 180 --- Table 4: Program-wise intake in three consecutive academic years 5. Weight Vectors of each Criteria To find the weight vectors of each criterion Geometric Mean Method (GMM) has been applied. The data furnished below is fetched from inputs collected from the major stake holders like students, parents, alumni and employers. Table 5 to Table 10 shows the measurement of the weight vectors of Criteria 1 to 6. Table 11 displays the weight vectors of all Criteria and Table 12 presents average weights of each Alternative with respect to all Criteria. AI&DS AI&ML IOT/CS Mech PE EIE Weight Vector AI&DS 1 1/2 2 3 5 7 2.1720 AI&ML 2 1 3 4 5 7 3.0717 IOT/CS 1/2 1/3 1 2 3 5 1.3076 Mech 1/3 1/4 1/2 1 2 3 0.7937 PE 1/5 1/5 1/3 1/2 1 2 0.4869 EIE 1/7 1/7 1/5 1/3 1/2 1 0.2965 Table 5: Weights of C1 (Scope of Employment) 274 Application of Analytic Hierarchy Process in Engineering Education AI&DS AI&ML IOT/CS Mech PE EIE Weight Vector AI&DS 1 1 2 4 3 5 2.2209 AI&ML 1 1 2 3 3 4 2.0396 IOT/CS 1/2 1/2 1 2 2 2 1.1224 Mech 1/4 1/3 1/2 1 1 2 0.6609 PE 1/3 1/3 1/2 1 1 2 0.6933 EIE 1/5 1/4 1/2 1/2 1/2 1 0.4291 Table 6: Weights of C2 (Right Employability Skills) AI&DS AI&ML IOT/CS Mech PE EIE Weight Vector AI&DS 1 1/2 3 3 3 6 2.0800 AI&ML 2 1 2 4 5 7 2.8709 IOT/CS 1/3 1/2 1 3 3 5 1.3990 Mech 1/3 1/4 1/3 1 1 2 0.6177 PE 1/3 1/5 1/3 1 1 1/2 0.4723 EIE 1/6 1/7 1/5 1/2 2 1 0.4101 Table 7: Weights of C3 (Higher pay package) AI&DS AI&ML IOT/CS Mech PE EIE Weight Vector AI&DS 1 1/2 2 4 4 7 2.1955 AI&ML 2 1 3 5 5 8 3.2598 IOT/CS 1/2 1/3 1 2 2 4 1.1775 Mech 1/4 1/5 1/2 1 1 3 0.6493 PE 1/4 1/5 1/2 1 1 1/3 0.4502 EIE 1/7 1/8 1/4 1/3 3 1 0.4057 Table 8: Weights of C4 (Wide career options and career stability) AI&DS AI&ML IOT/CS Mech PE EIE Weight Vector AI&DS 1 1 1 5 5 7 2.3650 AI&ML 1 1 1 5 5 7 2.3650 IOT/CS 1 1 1 5 5 7 2.3650 Mech 1/5 1/5 1/5 1 1 1 0.4472 PE 1/5 1/5 1/5 1 1 1 0.4472 EIE 1/7 1/7 1/7 1 1 1 0.3779 Table 9: Weights of C5 (Freedom to work from anywhere) AI&DS AI&ML IOT/CS Mech PE EIE Weight Vector AI&DS 1 1 1 5 5 7 2.3650 AI&ML 1 1 1 7 7 5 2.5014 275 M. Tirumala Devi et al. IOT/CS 1 1 1 6 6 4 2.2894 Mech 1/5 1/7 1/6 1 1 1 0.4101 PE 1/5 1/7 1/6 1 1 1 0.4101 EIE 1/7 1/5 1/4 1 1 1 0.4388 Table 10: Weights of C6 (Applications in all the fields) 𝑪𝟏 𝑪𝟐 𝑪𝟑 𝑪𝟒 𝑪𝟓 𝑪𝟔 Priority vector 𝑪𝟏 1 2 2 1 1/2 1/3 0.9346 𝑪𝟐 1/2 1 1/2 1/2 1/3 1/4 0.4673 𝑪𝟑 1/2 2 1 1/2 1/3 1/4 0.5887 𝑪𝟒 1 2 2 1 1/3 1/3 0.8735 𝑪𝟓 2 3 3 3 1 1/2 1.7320 𝑪𝟔 3 4 4 3 2 1 2.5697 Table 11: Weight Vectors of all Criteria 𝑪𝟏 𝑪𝟐 𝑪𝟑 𝑪𝟒 𝑪𝟓 𝑪𝟔 Average weight 𝑨𝟏 2.1720 2.2209 2.0800 2.1955 2.3650 2.3650 2.2307 𝑨𝟐 3.0717 2.0396 2.8709 3.2598 2.3650 2.5014 2.6506 𝑨𝟑 1.3076 1.1224 1.3990 1.1775 2.3650 2.2894 1.5351 𝑨𝟒 0.7937 0.6609 0.6177 0.6493 0.4472 0.4101 0.5813 𝑨𝟓 0.4869 0.6933 0.4723 0.4502 0.4472 0.4101 0.4859 𝑨𝟔 0.2965 0.4291 0.4101 0.4057 0.3779 0.4388 0.3898 Table 12: Average weights of each Alternative with respect to all Criteria Following are the 3-D clustered column charts representing the weights of Alternatives with respect to Criteria. Figure 1 to 6 will show the graphical representation of all the criteria i.e. criteria 1 to criteria 6. Figure 1: Weights of alternatives with respect to C1 Figure 2: Weights of alternatives with respect to C2 0 0,5 1 1,5 2 2,5 3 3,5 0 0,5 1 1,5 2 2,5 276 Application of Analytic Hierarchy Process in Engineering Education Figure 3: Weights of alternatives with respect to C3 Figure 4: Weights of alternatives with respect to C4 Figure 5: Weights of alternatives with respect to C5 Figure 6: Weights of alternatives with respect to C6 Table 13 indicates the ranking and weights of alternatives which is further graphically presented through bar chart(Figure 7). S.No Alternatives Weights Ranks 1 AI&DS 2.2307 2 2 AI&ML 2.6506 1 3 IOT/CS 1.5351 3 4 Mech 0.5813 4 5 PE 0.4859 5 6 EIE 0.3898 6 Table 13: Ranking and Weights of Alternatives 0 0,5 1 1,5 2 2,5 3 0 1 2 3 4 0 0,5 1 1,5 2 2,5 0 0,5 1 1,5 2 2,5 3 277 M. Tirumala Devi et al. Figure 7: Ranks of Alternatives 6. Conclusions According to the ranking of the Alternative weights, Artificial Intelligence & Machine Learning branch is the most important branch in the field of engineering education, followed by Artificial Intelligence & Data Science, Internet of Things, Mechanical Engineering, Production Engineering and finally Electronics and Instrumentation Engineering. The authors are of the opinion that the technological disruptions appear to be more powerful in the post-Covid scenario. This is one of the potential reasons behind the current change in the employment scenario, affecting the equilibrium of the workforce. The stakeholders as well as the government policy makers must be aware of the quick transition in the educational field and thus make judicious plans where the boom of a particular field does not create a vacuum or dearth of skilled labourers in another field especially in the core, non-programming branches of engineering education. 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