ORIGINAL_ARTICLE
On planned time replacement of series-parallel system
This paper investigate some characteristics of the age replacement model with minimal repair, of series-parallel system with non-uniform failure rates and are subjected to two different types of failures, which are Type I and Type II failures. The six units of the system formed three subsystems, which are subsystems A, B and C. Subsystem A is having three parallel units, subsystem B is having a single unit and subsystem C is having two parallel units. We constructed age replacement model with minimal repair that will determine the optimal replacement time of the series-parallel system. Furthermore, we also considered some modifications of the age replacement model with minimal repair constructed. Finally, some numerical examples are given to illustrate the characteristics of the age replacement models with minimal repair constructed. From the results obtained, it was observed that the optimal replacement time of the system when the three units of A are in parallel is higher than when the three units of A are in series. It was also observed that, the optimal replacement time obtained from the standard age replacement model is higher than the optimal replacement time obtained from standard age replacement model with minimal repair.
http://aotp.fabad-ihe.ac.ir/article_117919_ebaaee48f773332dfaecb6cf6e27facb.pdf
2020-10-01
1
13
10.22121/aotp.2020.240152.1033
optimal
Repair
Replacement
rate
System
time
Tijjani A
Waziri
tijjaniw@gmail.com
1
School of Continuing Education, Bayero University Kano, Nigeria
AUTHOR
Ibrahim
Yusuf
iyusuf.mth@buk.edu.ng
2
Department of Mathematical Sciences, Bayero University, Kano, Nigeria
LEAD_AUTHOR
Abdullahi
Sanusi
asanusi.sce@buk.edu.ng
3
School of Continuing Education, Bayero University, Kano, Nigeria
AUTHOR
Aven, T., & Castro, I. T. (2008). A minimal repair replacement model with two types of failure and a safety constraint. European Journal of Operational Research, 188(2), 506-515.
1
Chauhan, S. K., & Malik, S. C. (2016). Reliability evaluation of series-parallel and parallel-series systems for arbitrary values of the parameters. International Journal of Statistics and Reliability Engineering, 3(1), 10-19.
2
Chen, M., Zhao, X., & Nakagawa, T. (2019). Replacement policies with general models. Annals of Operations Research, 277(1), 47-61.
3
Chen, T. (2007). Obtaining the optimal cache document replacement policy for the caching system of an EC website. European Journal of Operational Research, 181(2), 828-841.
4
Chien, Y. H., & Sheu, S. H. (2006). Extended optimal age-replacement policy with minimal repair of a system subject to shocks. European Journal of Operational Research, 174(1), 169-181.
5
Coria, V. H., Maximov, S., Rivas-Dávalos, F., Melchor, C. L., & Guardado, J. L. (2015). Analytical method for optimization of maintenance policy based on available system failure data. Reliability Engineering & System Safety, 135, 55-63.
6
Fallahnezhad, M. S., & Najafian, E. (2017). A model of preventive maintenance for parallel, series, and single-item replacement systems based on statistical analysis. Communications in Statistics-Simulation and Computation, 46(7), 5846-5859.
7
Jain, M., & Gupta, R. (2013). Optimal replacement policy for a repairable system with multiple vacations and imperfect fault coverage. Computers & Industrial Engineering, 66(4), 710-719.
8
Khatab, A., Aghezzaf, E. H., Diallo, C., & Djelloul, I. (2017). Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations. International Journal of Production Research, 55(10), 3008-3024.
9
Ling, X., Wei, Y., & Li, P. (2019). On optimal heterogeneous components grouping in series-parallel and parallel-series systems. Probability in the Engineering and Informational Sciences, 33(4), 564-578.
10
Malki, Z. Ait, D. A., Ouali, M. S., 2015. Age replacement policies for two-component systems with stochastic dependence. Journal of Quality in Maintenance Engineering. 20(3), 346-357.
11
Mannai, N., & Gasmi, S. (2018). Optimal design of k-out-of-n system under first and last replacement in reliability theory. Operational Research, 1-16.
12
Mohammadi, M., Mortazavi, S. M., & Karbasian, M. (2018). Developing a method for reliability allocation of series-parallel systems by considering common cause failure. International Journal of Industrial Engineering & Production Research, 29(2).
13
Mustafa, A. (2017). Improving the Reliability of a Series-Parallel System Using Modified Weibull Distribution. In International Mathematical Forum (Vol. 12, No. 6, pp. 257-269).
14
Nakagawa, T. 2005. Maintenance Theory of Reliability. Springer-Verlag, London Limited.
15
Ouali, M. S., Yacout, S., 2003. Optional preventive replacement policy for two-component System. Journal of Decision Systems 12(1), 11-20.
16
Okamura, H., & Dohi, T. (2017). Moment-based approach for some age-based replacement problems. Journal of Industrial and Production Engineering, 34(8), 558-567.
17
Peng, R., Zhai, Q., Xing, L., & Yang, J. (2016). Reliability analysis and optimal structure of series-parallel phased-mission systems subject to fault-level coverage. Iie Transactions, 48(8), 736-746.
18
Pham, H., 2003. Handbook of Engineering. Springer-Verlag, London Limited.
19
Sandve, K., & Aven, T. (1999). Cost optimal replacement of monotone, repairable systems. European Journal of Operational Research, 116(2), 235-248.
20
Sharma, G. C., Kumar, A., & Jain, M. (2002). Maintenance Cost Analysis for Replacement Model with Perfect Minimal Repair. International Journal of Engineering, 15(2), 161-168.
21
Shen, J., Hu, J., & Ye, Z. S. (2020). Optimal switching policy for warm standby systems subjected to standby failure mode. IISE Transactions, 1-13.
22
Sibai, F. N. (2014). Modelling and output power evaluation of series-parallel photovoltaic modules. International Journal of Advanced Computer Science and Applications (IJACSA), 5(1).
23
Wang, J., Ye, J., & Wang, L. (2019). Extended age maintenance models and its optimization for series and parallel systems. Annals of Operations Research, 1-23.
24
Wang, L., Chu, J., & Mao, W. (2008). A condition-based order-replacement policy for a single-unit system. Applied mathematical modelling, 32(11), 2274-2289.
25
Wang, W., Zhao, F., & Peng, R. (2014). A preventive maintenance model with a two-level inspection policy based on a three-stage failure process. Reliability Engineering & System Safety, 121, 207-220.
26
Waziri, T. A., Yakasai, B. M., & Yusuf, I. (2019). On some discounted replacement models of a series system. Life Cycle Reliability and Safety Engineering, 1-11.
27
Xie, L., Lundteigen, M. A., & Liu, Y. (2020). Reliability and barrier assessment of series–parallel systems subject to cascading failures. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 234(3), 455-469.
28
Xu, M., Chen, T., & Yang, X. (2012). Optimal replacement policy for safety-related multi-component multi-state systems. Reliability Engineering & System Safety, 99, 87-95.
29
Xu, Q. Z., Guo, L. M., Shi, H. P., & Wang, N. (2016). Selective maintenance problem for series–parallel system under economic dependence. Defence technology, 12(5), 388-400.
30
Yusuf, I., & Ali, U. A. (2012). Structural dependence replacement model for parallel system of two units. Nigerian Journal of Basic and Applied Sciences, 20(4), 324-326.
31
Yusuf, I., Sani, B and Yusuf, B. (2019). Profit analysis of a series-parallel system under partial and complete failures, Journal of Applied Sciences, 19(6),565-574.
32
Zhao, X., Cai, J., Mizutani, S., & Nakagawa, T. (2020). Preventive replacement policies with time of operations, mission durations, minimal repairs and maintenance triggering approaches. Journal of Manufacturing Systems. Online. https://doi.org/10.1016/j.jmsy.2020.04.003.
33
Zhao, X., Mizutani, S., Chen, M., & Nakagawa, T. (2020). Preventive replacement policies for parallel systems with deviation costs between replacement and failure. Annals of Operations Research, 1-19.
34
Zhu, Z., Xiang, Y., & Coit, D. (2018, June). Redundancy Allocation for Serial-Parallel System Considering Heterogeneity of Components. In International Manufacturing Science and Engineering Conference (Vol. 51371, p. V003T02A049). American Society of Mechanical Engineers.
35
ORIGINAL_ARTICLE
Strong algebrability of C^* algebras
In this paper, we introduce the concept strong algebrability of certain C^* algebras generated by finite generators. In fact, using Gelfand theorem, we identify the members of the C^* algebra generated by one element, with the continuous functions on its spectrum, and use some recent result for strong algebrability for functions spaces. Moreover, we introduce the new concept unitable elements in unital C^* algebras, and then we express our main result for this kind of elements. In fact, the C^* subalgebra generated by a non unitable element in a C^* algebra is strongly c algebrable. As the last result in this paper, we show 2^c strong algebrability of direct sums of C^* algebras, using non unitable elements of them.
http://aotp.fabad-ihe.ac.ir/article_118918_8ae966989526ff6db6c69d6850e3bd53.pdf
2020-10-01
15
24
10.22121/aotp.2020.230247.1029
C^* algebras
Subalgebra
Strong algebrability
Javad
Sharafi
javadsharafi@grad.kashanu.ac.ir
1
University of Imam Ali
LEAD_AUTHOR
Aizpuru, A., Pérez-Eslava, C., & García-Pacheco, F. J. (2008). Lineability and coneability of discontinuous functions on R. Publicationes Mathematicae, 72(1-2), 129-139.
1
Aron, R. M., & Seoane-Sepúlveda, J. B. (2007). Algebrability of the set of everywhere surjective functions on $mathbb {C} $. Bulletin of the Belgian Mathematical Society-Simon Stevin, 14(1), 25-31.
2
Aron, R. M., Pérez García, D., & Seoane-Sepúlveda, J. B. (2006). Algebrability of the set of non-convergent Fourier series. Studia Mathematica, 175(1), 83-90.
3
Aron, R., Gurariy, V., & Seoane, J. (2005). Lineability and spaceability of sets of functions on ℝ. Proceedings of the American Mathematical Society, 133(3), 795-803.
4
Balcerzak, M., Bartoszewicz, A., & Filipczak, M. (2013). Nonseparable spaceability and strong algebrability of sets of continuous singular functions. Journal of Mathematical Analysis and Applications, 407(2), 263-269.
5
Banakh, T., Bartoszewicz, A., Glab, S., & Szymonik, E. (2012). Algebraic and topological properties of some sets in $ l_1$. arXiv preprint arXiv:1208.3058.
6
Bartoszewicz, A., & Głab, S. (2013). Strong algebrability of sets of sequences and functions. Proceedings of the American Mathematical Society, 141(3), 827-835.
7
Bartoszewicz, A., Bienias, M., & Gła̧b, S. (2012). Independent Bernstein sets and algebraic constructions. Journal of Mathematical Analysis and Applications, 393(1), 138-143.
8
Bartoszewicz, A., Gła, S., & Paszkiewicz, A. (2013). Large free linear algebras of real and complex functions. Linear Algebra and Its Applications, 438(9), 3689-3701.
9
Bartoszewicz, A., Głab, S., Pellegrino, D., & Seoane-Sepúlveda, J. B. (2013). Algebrability, non-linear properties, and special functions. Proceedings of the American Mathematical Society, 3391-3402.
10
ORIGINAL_ARTICLE
Mathematical modeling of Imam Ali ibn Abi Ṭālib’s war strategies with the Khawārij of Nahrawān using game theory
Today, with the advancement of sciences in various fields, mathematics is being optimally used in all sciences, mathematics is therefore widely used in other sciences, and Islamic and military sciences are no exception, and mathematics can be used to design various offensive and defensive operations in battlefields and solve battlefield equations in order to gain absolute or relative superiority over the enemy as in the game theory of war, the application of mathematics can be clearly seen. This practical research, conducted through a library method, has modeled the challenges between the two armies of Imam ʿAlī ibn Abī Ṭālib (AS) and a group called the Māriqīn or Khawārij in the battle of Nahrawān using Game Theory and analyzed each army’s strategies against each other, and finally explore the war utility to find the strategic equilibrium point between them. Therefore, we calculate the utility function for the set of strategies of each of the two armies including the army of Amir al-Mu’minin, ʿAlī ibn Abī Ṭālib (AS) and the Khawārij of Nahrawān and analyze it.
http://aotp.fabad-ihe.ac.ir/article_118919_d07ace017c78b1fc61cb24fb77d1b61a.pdf
2020-10-01
25
36
10.22121/aotp.2020.231886.1030
Strategies
Mathematical Modeling
game theory
Battle of Nahrawān
Ali Nghi
Lezgi
a.lezgi@yahoo.com
1
University of Imam Ali
LEAD_AUTHOR
Reza
Faghih Zadeh
faghihr8@gmail.com
2
University of Imam Ali
AUTHOR
Ahmad ibn Abi Ya'qub,)1358( AH. Jacob's History. Beirut Publications.
1
Akramizadeh et al. (1398). H.S. Strategic Gam Theory with an Islamic Approach with Emphasis on the Early Islamic Battles. AJA Strategic Studies Center.
2
Azghandi, Sayyid Alireza, )1394( H.S. War and Peace (Considering Contemporary Military and Strategic Issues), Eighth Edition, Qom.
3
Balādhurī, Ahmad ibn Yaḥyā, )1996( AD. Jamal Min Ansab al-Ashraf, Research: Soheil Zakar and Riyadh Zarkeli, Dar al-fekar, Beirut.
4
Dīnawarī, Ahmad ibn Dawood, )1330( H.S. Al-Akhbar al-Tawal, Cairo, Maṭba’at Al-Sa’adah.
5
Ebadizadeh, Hojjatollah, )1397( H.S. Mathematical Simulation of Interactions and Strategies of the Islamic Republic of Iran and Saudi Arabia Using Game Theory, Scientific Research Journal of Strategic Knowledge Interdisciplinary Studies. Higher National Defense University.
6
Ibn A'tham, )1411 (AH. Al-Futūḥ, Beirut, Dar al-Nadwah.
7
Ibn Qutaybah Dīnawarī, 1380 H.S. al-Imāma wal-Siyāsa (History of the Caliphs), translated by Sayyid Naser Tabataba'i, Tehran, Phoenix.
8
Lezgi, Ali Naghi et al., )1398( H.S. Mathematical Simulation of Gossip Propagation with a Defensive Approach by Looking at Verses and Narratives, Scientific Research Journal of Strategic Knowledge Interdisciplinary Studies, No. 34.
9
Mas’udi, Murawwij al-Dhahab, nd. Translated by Abolghasem Payandeh, Scientific and Cultural Publications. Tehran.
10
Nahj al-Balāghah.
11
Nasr ibn Muzāḥim, )1382( H.S. Battle of Siffin, by the efforts of Abdul Salam Muhammad Aaron, Cairo.
12
Roshandel, Jalil, )1373( H.S. Military Strategy, Journal of Law Faculty and Political Sciences, University of Tehran. No. 31.
13
Ṭabarī, Muhammad ibn Jarīr, )1967( AD. Tarikh al-Umam wa al-Muluk, Research: Muhammad Abulfazl Ibrahim, Dar al-Turāth, Beirut.
14
The Holy Quran.
15
ORIGINAL_ARTICLE
Assessment of probability distributions of groundwater quality data in Gwale area, north-western Nigeria
Groundwater quality plays an important role in human, animal, and plant health. Measurements of water quality are random variables that need a probabilistic model. The interest in fitting probability distribution in modeling water quality data remains strong in hydrology and engineering. This paper has been designed to find the best fitting probability distribution of calcium concentration of groundwater collected from 28 sampling sites in Gwale area, Kano state, Northwestern Nigeria. The parameter estimates for the groundwater data are analyzed using gamma, logistic, lognormal, normal, and Weibull distributions. The statistics measure such as the Akaike information criterion (AIC), Bayesian information criterion, log-likelihood, and Kolmogorov-Smirnov (K-S) test are computed to compare the fitted distributions. The most suitable distribution has been selected using these statistics measures. The result indicates that the logistic distribution with the highest log-likelihood value, and the smallest AIC and BIC values were found to fit the calcium concentration of groundwater data than other competing distributions. This research describes the use of probability distribution in modeling groundwater quality data and could be used to describe groundwater quality data in any other location.
http://aotp.fabad-ihe.ac.ir/article_116559_63bee7ef443b3fb56baed43fd9e5691f.pdf
2020-10-29
37
46
10.22121/aotp.2020.243381.1039
probability distribution
Groundwater
Calcium concentration
Logistic distribution
Log-likelihood
Vijay
Singh
singh_vijayvir@yahoo.com
1
Department of Mathematics Yusuf Maitama Sule University, Kano, Nigeria. Formally Northwest University, Kano, Nigeria
LEAD_AUTHOR
Ahamad
Suleman
ahmadabubakkar31@gmail.com
2
Department of Statistics Kano University, of Science & Technology, Wudil, Kano, Nigeria
AUTHOR
Auwalu
Ibrahim
aiamaigora@gmail.com
3
Department of Statistics Kano University, of Science& Technology, Wudil, Kano, Nigeria
AUTHOR
Usman
Abdullahi
usiyamma@gmail.com
4
Department of Statistics Kano University, of Science& Technology, Wudil, Kano, Nigeria
AUTHOR
Suleiman
Suleiman
suleimanabubakarsuleiman@gmail.com
5
Kano State Ministry of Water Resources, Nigeria
AUTHOR
Bala, A. E., Eduvie, O. M., & Byami, J. (2011). Borehole depth and regolith aquifer hydraulic characteristics of bedrock types in Kano area, Northern Nigeria. African Journal of Environmental Science and Technology, 5(3), 228-237.
1
Chen, G., & Balakrishnan, N. (1995). A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27(2), 154-161.
2
Hahn Gerrald, J., & Shapiro Samuel, S. (1967). Statistical models in engineering. John Willey & Sons. Inc. New York.–London–Sydney, 395.
3
Kishore, K. (2011). Das, Bhanita Das, Bhupen K. Baruah. and Abani K. Misra, Development of New Probability Model with Application in Drinking Water Quality Data. Adv. Appl. Sci. Res, 2(4), 306-313.
4
la Cecilia, D., Porta, G. M., Tang, F. H., Riva, M., & Maggi, F. (2020). Probabilistic indicators for soil and groundwater contamination risk assessment. Ecological Indicators, 115, 106424.
5
Lee, J. Y., Cheon, J. Y., Lee, K. K., Lee, S. Y., & Lee, M. H. (2001). Statistical evaluation of geochemical parameter distribution in a ground water system contaminated with petroleum hydrocarbons. Journal of environmental quality, 30(5), 1548-1563.
6
Loucks, D. P., & Van Beek, E. (2017). An Introduction to Probability, Statistics, and Uncertainty. In Water Resource Systems Planning and Management (pp. 213-300). Springer, Cham.
7
Machekposhti, K. H., & Sedghi, H. (2019). Determination of the Best Fit Probability Distribution for Annual Rainfall in Karkheh River at Iran. International Journal of Environmental and Ecological Engineering, 13(2), 69-75.
8
Maryam, G., Kaveh, O.A., Saed, E., and Vijay, P.S. (2018). Analyzing the groundwater quality parameters using frequency analysis. American Journal of Engineering and Applied Sciences, 11(2), 482-490, doi.org/10.3844/ajeassp.2018.482.490.
9
Mohammed, I. (1984). Hydraulic properties of the Basement Complex and Chad Formation aquifers of Kano State based on test-pumping of selected boreholes. Unpublished M. Sc. thesis Department of Geology, Ahmadu Bello University, Zaria.
10
Nwaiwu, E. N., & Bitrus, A. (2005). Fitting probability distributions to component water quality data from a treatment plant. Global Journal of Environmental Sciences, 4(2), 151-154.
11
Standard Methods for the Examination of Water and wastewater, (2005): 21st edn, American Public Health Association/American Water Works Association/Water Environment Federation, Washington DC, USA.
12
Surendran, S., & Tota-Maharaj, K. (2015). Log logistic distribution to model water demand data. Procedia Engineering, 119(1), 798-802.
13
Tahir, M.H., Adnan, M.H., Cordeiro, G.M., Hamedani, G.G., Mansoor, M., and Zubair, M. (2016): “The Gumbel-Lomex Distribution: Properties and Applications." Journal of Statistical Theory and Applications. Atlantic Press, Volume 15-1, pp. 61-79.
14
ORIGINAL_ARTICLE
Geometric operators based on linguistic interval-valued intuitionistic neutrosophic fuzzy number and their application in decision making
The paper aims to give some new kinds of operational laws named as neutrality addition and scalar multiplication for the pairs of linguistic interval-valued intuitionistic neutrosophic fuzzy number. The main idea behind these operations is to include the linguistic interval-valued intuitionistic neutrosophic fuzzy number of the decision-maker and score function. We define the linguistic interval-valued intuitionistic neutrosophic fuzzy number and operational laws. We introduce the three geometric operators including, linguistic interval-valued intuitionistic neutrosophic fuzzy weighted geometric operator, linguistic interval-valued intuitionistic neutrosophic fuzzy ordered weighted geometric operator and linguistic interval-valued intuitionistic neutrosophic fuzzy weighted hybrid geometric operatorl. Finally, a multiattribute group decision-making approach based on the proposed operators is presented and investigated with numerous numerical examples.
http://aotp.fabad-ihe.ac.ir/article_116561_0190b0b2f54e3ac599d4641c0d0f1331.pdf
2020-10-29
47
71
10.22121/aotp.2020.240887.1034
Linguistic
neutrosophic set
Geometric operators, MCDM
Aliya
Fahmi
fahmialiya@yahoo.com
1
School of Mathematics, Management Department, The University of Faisalabad, Faisalabad, Pakistan
LEAD_AUTHOR
Fazli
Amin
fazliamin@hu.edu.pk
2
Department of Mathematics, Hazara University Mansehra, Pakistan
AUTHOR
Syed Bilal
Shah
syedbilalhussain060@gmail.com
3
Department of Mathematics, Hazara University Mansehra, Pakistan
AUTHOR
Smarandache, F. (1999). A unifying field in Logics: Neutrosophic Logic. In Philosophy (pp. 1-141). American Research Press.
1
Wang, H., Smarandache, F., Sunderraman, R., & Zhang, Y. Q. (2005). interval neutrosophic sets and logic: theory and applications in computing: Theory and applications in computing (Vol. 5). Infinite Study.
2
Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Infinite study.
3
Ye, J. (2014). Single valued neutrosophic cross-entropy for multicriteria decision making problems. Applied Mathematical Modelling, 38(3), 1170-1175.
4
Broumi, S., Ye, J., & Smarandache, F. (2015). An extended TOPSIS method for multiple attribute decision making based on interval neutrosophic uncertain linguistic variables. Infinite Study.
5
Ye, J. (2014). Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. Journal of Intelligent & Fuzzy Systems, 26(1), 165-172.
6
Ye, J. (2014). A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. Journal of Intelligent & Fuzzy Systems, 26(5), 2459-2466.
7
Herrera, F., & Herrera-Viedma, E. (1996). A model of consensus in group decision making under linguistic assessments. Fuzzy sets and Systems, 78(1), 73-87.
8
Herrera, F., & Herrera-Viedma, E. (2000). Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets and systems, 115(1), 67-82.
9
Xu, Z. (2006). A note on linguistic hybrid arithmetic averaging operator in multiple attribute group decision making with linguistic information. Group Decision and Negotiation, 15(6), 593-604.
10
Wang, J. Q., & Li, J. J. (2009). The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Science & Technology Information, 33(1), 8-9.
11
Garg, H., & Kumar, K. (2019). Linguistic interval-valued atanassov intuitionistic fuzzy sets and their applications to group decision making problems. IEEE Transactions on Fuzzy Systems, 27(12), 2302-2311.
12
Garg, H. (2020). Novel neutrality aggregation operator-based multiattribute group decision-making method for single-valued neutrosophic numbers. Soft Computing, 24(14), 10327-10349.
13
Garg, H. (2020). Multiple attribute decision making based on immediate probabilities aggregation operators for single-valued and interval neutrosophic sets. Journal of Applied Mathematics and Computing, 1-35.
14
Garg, H. (2019). Linguistic single-valued neutrosophic power aggregation operators and their applications to group decision-making problems. IEEE/CAA Journal of Automatica Sinica, 7(2), 546-558.
15
Garg, H. (2019). Algorithms for possibility linguistic single-valued neutrosophic decision-making based on COPRAS and aggregation operators with new information measures. Measurement, 138, 278-290.
16
Garg, H. (2018). New logarithmic operational laws and their applications to multiattribute decision making for single-valued neutrosophic numbers. Cognitive Systems Research, 52, 931-946.
17
Harish, G. (2020). New ranking method for normal intuitionistic sets under crisp, interval environments and its applications to multiple attribute decision making process. Complex & Intelligent Systems, 6(3), 559-571.
18
Garg, H. (2020). Linguistic Interval-Valued Pythagorean Fuzzy Sets and Their Application to Multiple Attribute Group Decision-making Process. Cognitive Computation, 1-25.
19
Li, J., Niu, L. L., Chen, Q., & Wu, G. (2020). A consensus-based approach for multi-criteria decision making with probabilistic hesitant fuzzy information. Soft Computing, 1-18.
20
Mishra, A., & Kumar, A. (2020). JMD method for transforming an unbalanced fully intuitionistic fuzzy transportation problem into a balanced fully intuitionistic fuzzy transportation problem. Soft Computing, 1-16.
21
Chiao, K. P. (2020). Closed Forms of the Interval Type 2 Fuzzy Sets Additions Based on Archimedean T-norms with Application in Decision Making Aggregation. International Journal of Fuzzy Systems, 1-19.
22
Jin, F., Garg, H., Pei, L., Liu, J., & Chen, H. (2020). Multiplicative Consistency Adjustment Model and Data Envelopment Analysis-Driven Decision-Making Process with Probabilistic Hesitant Fuzzy Preference Relations. International Journal of Fuzzy Systems, 1-14.
23
Guo, X., Liu, A., Li, X., & Xiao, Y. (2020). Research on the Intelligent Fault Diagnosis of Medical Devices Based on a DEMATEL-Fuzzy Concept Lattice. International Journal of Fuzzy Systems, 1-16.
24
Suzan, V., & Yavuzer, H. (2020). A Fuzzy Dematel Method to Evaluate the Most Common Diseases in Internal Medicine. International Journal of Fuzzy Systems, 1-11.
25
Liu, L., Cao, W., Shi, B., & Tang, M. (2019). Large-Scale Green Supplier Selection Approach under a Q-Rung Interval-Valued Orthopair Fuzzy Environment. Processes, 7(9), 573.
26
Smarandache, F. (2005). Neutrosophic set-a generalization of the intuitionistic fuzzy set. International journal of pure and applied mathematics, 24(3), 287.
27
Ali, M., & Smarandache, F. (2017). Complex neutrosophic set. Neural Computing and Applications, 28(7), 1817-1834.
28
Abdel-Basset, M., Ali, M., & Atef, A. (2020). Uncertainty assessments of linear time-cost tradeoffs using neutrosophic set. Computers & Industrial Engineering, 141, 106286.
29
Khatter, K. (2020). Interval valued trapezoidal neutrosophic set: multi-attribute decision making for prioritization of non-functional requirements. Journal of Ambient Intelligence and Humanized Computing, 1-17.
30
Rashno, E., Minaei-Bidgoli, B., & Guo, Y. (2020). An effective clustering method based on data indeterminacy in neutrosophic set domain. Engineering Applications of Artificial Intelligence, 89, 103411.
31