Research article Topical Sections

Using multi-attribute decision-making technique for the selection of agribots via newly defined fuzzy sets

  • Received: 14 February 2025 Revised: 25 March 2025 Accepted: 10 April 2025 Published: 27 May 2025
  • MSC : 90B50

  • Reference parameter mapping (passing arguments by reference) is a technique where the reference (like to find physical meaning, memory address) of a parameter is passed to a function or procedure, rather than a copy of the parameter's value. This approach enables changes made to the parameter within the function to affect the original data. In decision-making systems, reference parameter mapping (passing arguments by reference) offers several key advantages that enhance flexibility, consistency, and efficiency. This is especially useful in scenarios where decisions are based on shared data, complex interactions, and iterative updates. In this paper, a new class of fuzzy set was introduced that is known as the (q1,q2)-rung Diophantine fuzzy set, where q1 and q2 are reference parameter mappings. Most of the classical and new generalized fuzzy sets are exceptional classes of (q1,q2)-rung Diophantine fuzzy set ((q1,q2)-RDFS) like intuitionistic fuzzy set (IFS), Pythagorean fuzzy Sets (PyFSs) and q-rung Orthopair fuzzy sets (q-ROFSs), linear Diophantine fuzzy sets (LDFS), and so on. It is commonly seen in multi-criteria decision-making (MCDM) scenarios that the presence of imprecise information and ambiguity in the decision maker's judgment affects the resolution technique. Fuzzy models that are now in use are unable to effectively manage these uncertainties to provide an appropriate balance during the decision-making process. Using control (reference) parameter mappings, (q1,q2)-RDFSs are potent fuzzy model that can handle these challenging problems. Two more novel ideas are presented in this work: (q1,q2)-rung Diophantine fuzzy averaging and geometric aggregation operators with newly defined score and accuracy functions. An agricultural field robot MCDM framework was proposed, incorporating (q1,q2)-rung Diophantine fuzzy averaging and geometric aggregation operators. This strategy's efficacy and adaptability in addressing real-world issues were demonstrated by its application to get more benefits. This study has a lot of potential to handle difficult socioeconomic issues and offer vital information to academic, government, and analysts searching for fresh approaches in a variety of fields.

    Citation: Muhammad Bilal Khan, Dragan Pamucar, Mohamed Abdelwahed, Nurnadiah Zamri, Loredana Ciurdariu. Using multi-attribute decision-making technique for the selection of agribots via newly defined fuzzy sets[J]. AIMS Mathematics, 2025, 10(5): 12168-12204. doi: 10.3934/math.2025552

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  • Reference parameter mapping (passing arguments by reference) is a technique where the reference (like to find physical meaning, memory address) of a parameter is passed to a function or procedure, rather than a copy of the parameter's value. This approach enables changes made to the parameter within the function to affect the original data. In decision-making systems, reference parameter mapping (passing arguments by reference) offers several key advantages that enhance flexibility, consistency, and efficiency. This is especially useful in scenarios where decisions are based on shared data, complex interactions, and iterative updates. In this paper, a new class of fuzzy set was introduced that is known as the (q1,q2)-rung Diophantine fuzzy set, where q1 and q2 are reference parameter mappings. Most of the classical and new generalized fuzzy sets are exceptional classes of (q1,q2)-rung Diophantine fuzzy set ((q1,q2)-RDFS) like intuitionistic fuzzy set (IFS), Pythagorean fuzzy Sets (PyFSs) and q-rung Orthopair fuzzy sets (q-ROFSs), linear Diophantine fuzzy sets (LDFS), and so on. It is commonly seen in multi-criteria decision-making (MCDM) scenarios that the presence of imprecise information and ambiguity in the decision maker's judgment affects the resolution technique. Fuzzy models that are now in use are unable to effectively manage these uncertainties to provide an appropriate balance during the decision-making process. Using control (reference) parameter mappings, (q1,q2)-RDFSs are potent fuzzy model that can handle these challenging problems. Two more novel ideas are presented in this work: (q1,q2)-rung Diophantine fuzzy averaging and geometric aggregation operators with newly defined score and accuracy functions. An agricultural field robot MCDM framework was proposed, incorporating (q1,q2)-rung Diophantine fuzzy averaging and geometric aggregation operators. This strategy's efficacy and adaptability in addressing real-world issues were demonstrated by its application to get more benefits. This study has a lot of potential to handle difficult socioeconomic issues and offer vital information to academic, government, and analysts searching for fresh approaches in a variety of fields.



    The human brain is highly complex. Replication of its functions through laboratory tests and computer models is not always feasible. The use of animals in neuroscience research provides a model similar in complexity to the human brain and is necessary to further research advances. Non-human primates (NHPs) are extensively used as animal models for scientific research. An NHP brain has many similarities to a human brain in regards to size, connectivity, functional areas, and aging processes, making it an ideal research model. NHPs can be trained to perform tasks that allow researchers to evaluate cognition and behavior. Specifically in neurophysiological studies, NHPs are trained on cognitive tasks prior to collecting neurophysiological data. A well-trained animal is necessary to obtain sufficient experimental results. Therefore, optimizing the training method is fundamental to successful research involving NHPs.

    However, training procedures are likely far from being optimized. Various experiments require physically restraining the NHP during training or collecting data, both for the nature of the data itself and for the safety of the personnel involved. The primate chair is a common restraint device that, with the right modifications, is suitable for a wide array of scientific experiments. However, the animal is required to maintain a fixed position in the chair throughout the training and its ability to move is reduced. Providing a more comfortable training environment ultimately reduces stress, potentially improving the animal's well-being, the speed of training, and the animal's performance. Here we present the details of a system to train animals in their home cage instead of the classic chair-restraint training.

    Training primates without chair-restraint has been used for a variety of species including chimpanzees, baboons, and gorillas [1,2,3,4,5,6,7], and also for bonnet macaques, marmosets, pigtail macaques, tufted capuchin monkeys, squirrel monkeys, lion-tailed macaques, long-tailed macaques, and mouse lemurs [2,3,4,8,9,10,11,12,13,14,15,16,17]. Several groups have also trained rhesus macaques without chair restraining the animal [13,18,19,20,21,22,23,24,25,26,27,28,29,30]. Most of these groups have provided a computer-based interactive environment interface where animals are individually or even group housed [2,3,4,5,6,7,10,11,12,13,14,15,16,17,19,21,23,24,25,26,27,28,29,30,31,32,33,34,35,36]. Overall, in-cage touch screen training has been useful to many experiments, such as those conducted by Srihasam et al. [37]. Similar to the training methods which used rhesus macaques, focusing on behavior and cognition using a touch screen within the animal's own home cage [25,26,27,28], we have designed, built and successfully utilized a fully portable cage-mountable system to train NHPs and here we describe the technical specifications, construction, and operation of the system. This system has the potential to ease and expedite the behavioral training of NHPs on a variety of tasks by allowing the animal greater control over when and how long it chooses to work, being less disruptive to the monkey's social interactions, and presumably eliminating some of the stress found in chair training. Moreover, we present data collected during the behavioral training on a visual memory and change detection task, demonstrating the feasibility of this approach for training on cognitive tasks.

    The protocols for all experimental and behavioral procedures were approved by the Montana State University Institutional Animal Care and Use Committee. The in-cage training system described here was designed for training rhesus macaques, but may be utilized to train and test various species of NHPs (Figure 1). This system makes home cage training possible for all NHPs with a design allowing the system to be portable and mountable on the NHP's cage. Additionally, the training system is designed to be safe, robust, and suitable for animal operation in-cage.

    Figure 1.  Detailed schematic of the in-cage training system.

    The system includes four components: (1) local control unit, (2) remote control unit, (3) animal interface, and (4) reward delivery system (Figure 1).

    (1) Local Control Unit: includes a desktop computer controlling the behavioral paradigm using two software. The minimum requirements for the desktop computer included an INTEL Pentium or Core i2 Processor, 2 GB of memory (DDR3 RAM), and 2 VGA ports for display. The system also included a line print terminal (LPT) also known as a parallel port to trigger the pump for reward delivery, 1 serial port to control the pump, and 1 RJ-45 port. The minimum hardware requirements for building or purchasing the desktop computer for the local control unit are listed in Table 1. The local control unit was located within the animal research facility but outside of the room housing the rhesus macaques. The graphical representation of the training behavioral paradigm was sent from the local control unit to the animal interface inside the subject's home cage (Figure 2).

    Table 1.  Minimum requirements of the in-cage training system.
    Part Name Minimum Requirement
    CPU INTEL Pentium or i3
    RAM 2 GB DDR3
    Graphics card 1 GB with 2 VGA port
    Ports and interfaces Includes 1 parallel port, 1 VGA port, 1 serial port, and 1 RJ-45
    Touchscreen monitor ELO 1739L open-frame touchscreen LCD monitor, 43.18 cm, 1280 × 1024
    USB cable USB 2.0 A to B cable
    Speaker Logitech plug & play 10 watt
    Pump NE-4500 double OEM syringe pump
    Camera Day/night D-link IP camera
    Cage mounting frame 30.5 × 37.15 cm
    Listed are the various parts of the in-cage training system and the minimum requirement for each part.

     | Show Table
    DownLoad: CSV
    Figure 2.  Photos of the in-cage training system.

    We employed the Presentation software (Neurobehavioral Systems, Inc., Berkeley, CA) for the working memory task and Matlab Psychophysics Toolbox (The MathWorks, Inc., Natick, MA) for the change detection task to control the stimulus presentation, behavioral data acquisition and reward delivery. The various programming scripts used for the working memory task and change detection task are available upon request. Both toolboxes are available to download online and they are widely used in psychological and neurophysiological experiments.

    (2) Animal Interface: includes a touchscreen monitor, a mounting frame, a speaker for auditory feedback, and a lever. The minimum requirements for the animal interface include an ELO 1739L open-frame touchscreen LCD monitor 17 inch with a 1280 × 1024 resolution (Elo Touch Solutions, Inc., Milpitas, CA), and a USB 2.0 A to B cable. The minimum requirements for the electrical and mechanical parts of the animal interface are listed in Table 1. The monitor is 4.90 × 36.80 × 30.48 cm in size, embedded in a mounting frame of 30.5 × 37.15 cm in size, which was designed to snugly fit the side panel of the primate's cage. The frame stayed on the cage during the week and was removed once a week for cleaning. The frame was light enough (approximately 16 kilograms) for a single person to easily mount and remove it. The frame was designed in a way that the animal did not need to reach outside the cage to access the monitor. The designed frame fitting the Primate Products cages is commercially available upon request. Tasks were designed in a way that required a specific touch answer from the animal in response to a visual stimulus. The touch position was recorded by the local control unit. In the attention task, a lever response was also used in addition to a touch response and these data were also recorded by the local control unit. The local control unit could then send feedback based on the animal's performance via a speaker. We used a speaker as part of the animal interface as well as a juice delivery pump as a reward system.

    (3) Reward System: includes a syringe pump managed by the local control unit. When the trial was correct, the local control unit triggered the reward system via a TTL pulse through a parallel port. Once the pump was triggered, it delivered a user defined juice amount to the subject. The reward system allowed the reward duration or the number of rewards to be set via the SyringePumpPro application (New Era Pump Systems, Inc., Farmingdale, NY) in the local control unit. We used a NE-4500 double OEM syringe pump. As mentioned above, in addition to the juice reward the animal could receive auditory feedback. Figure 2 shows the local control unit, animal interface, and the reward system; the minimum requirements for the monitoring and reward system are listed in Table 1.

    (4) Remote Control Unit: includes a camera and a remote desktop computer. We used a night vision capable D-Link IP-camera (D-Link Systems, Inc, Fountain Valley, CA) to screen the subject's activity during the experiment. The camera was accessible over the internet to the remote control unit. This arrangement provided the possibility of monitoring the entire system remotely when the experimenter was not physically present in the animals' vivarium. The remote control unit could also remotely manage the experiment by accessing the local control unit. The subject's screen, the reward settings, and the behavioral paradigm could all be monitored and manipulated via the remote control unit.

    The in-cage training system was designed to allow the subject to have his own self-paced engagement with the task. The animal was in the same room with other monkeys but was separated into his own home cage for training. While training the subject, the system was turned on in the morning and remained on throughout the day, then turned off in the evening. This allowed the subject to have control over when and how long to work throughout the day and to take breaks on his own time. The subject worked five days a week, with two vacation days per week. Throughout the work days the subject's access to water was limited to the juice he earned performing the task. If the animal chose not to work he would receive water instead of juice at the end of the day. This water restriction helped enhance the animal's motivation to perform the task, however, later during the training phase, the animal usually preferred performing the task and receiving juice, even in the presence of full water access. We tested the system by training a rhesus monkey in two behavioral paradigms:

    Delayed Match to Sample (DMS) Task: DMS is an object working memory task. In this task the animal has to remember an object throughout a delay and choose the same object among multiple distractors after the delay period (Figure 3). The DMS task can be a time consuming and challenging task for NHPs. We broke down the DMS task into several steps to train the rhesus macaque in his home cage. In the first stage of training we focused on encouraging the subject to touch the touchscreen monitor. A sample image that encompassed the entire screen was presented as the target area and by touching anywhere on the screen, the subject earned a 4 mL juice reward per correct trial. After the subject's performance was consistently 85% correct, the image was shrunk by approximately 20%. This process was continued until the sample image size was reduced to one square inch on the touchscreen. To verify that the subject was looking at the sample image and not just the center of the screen, the second stage of training involved moving the sample image to a new screen location for each new trial. Throughout all trials until this point, the same image was used each day for each trial, with the goal of keeping all experimental factors consistent except for the specific behavioral task. After the subject was proficient with the moving sample image, the match to sample task was introduced. This third stage of training consisted of an initially presented sample image which the subject touched, followed by two target images; one of the target images was the same as the initial sample image and the other target image was a distracter image. To perform a correct trial, the subject had to select the target image that matched the initial sample image. To discourage the subject from being impatient and randomly touching the screen, and to encourage the subject to focus on deliberately touching the target, preferably with only one finger, a punishment was introduced in which an incorrect trial resulted in a three second inter-trial pause. After the subject mastered the match to sample stage, a delay was introduced between the presentation of the sample image and the two target images. The delay started at 100 ms and eventually escalated to a 2 second delay. After learning how to maintain the object information throughout a 2 second delay, new images were introduced to teach the subject how to generalize the DMS rule. After proficiency with a certain pair of images (performance rate 85%) a new pair of images was used. The subject became familiar with approximately 39 different images, generalizing the DMS rule. The training process was completed after 100 training sessions.

    Figure 3.  Delayed match-to-sample task.

    Change Detection Task: We used the same in-cage system to also train the animal with a change detection task (Figure 4). In this task the animal monitors a visual stimulus to detect a temporary contrast change. Again, the change detection task was broken down into several steps to train the rhesus macaque in his home cage. The first stage involved the subject learning how to press the lever. The subject had to press down the lever for a set amount of time in order to receive a juice reward. It occurred naturally by introducing a new object (the lever) to the curious animal's environment. After the subject learned how to sufficiently depress the lever, a visual target was introduced (a red dot) and the subject had to depress the lever and touch the target while keeping the lever pressed. After the target was touched, a visual stimulus (Gabor grating) would appear onscreen. The animal had to hold the lever for the duration of the stimulus. The stimulus duration was then gradually increased. Once the subject learned how to keep the lever pressed while maintaining its focus to detect when the stimulus turns off, then the "blink detection" part was added. In blink trials the stimulus would turn off and the subject would release the lever and receive the juice but then the stimulus would reappear. We gradually reduced the blink time to 100 ms and the subject had to release the lever quickly after the stimulus change in order to receive a juice reward. The quick release of the lever was the key to trace whether the animal was detecting the change. Once the subject was able to detect a changing Gabor, we gradually introduced variability in the location of the stimulus and the time of the change. To ensure that the subject was validly responding to the change, a no change condition was added to the task. For the no change trial, the subject had to press the lever, touch the target on the monitor, and keep the lever depressed for the duration of a non-changing stimulus in order to receive a juice reward. The ultimate goal was to detect a "contrast change". Therefore, once the animal was trained on detecting a 100 ms blink (100% change in contrast), then the duration of stimulus change (100 ms) was kept constant and the animal was gradually trained to detect smaller and smaller changes in the stimulus contrast.

    Figure 4.  The change detection task consisted of change and no-change trials.

    Training the object working memory task took about 100 training sessions. The training goal for the animal is to be able to generalize the rule to a novel object. Figure 5A shows the animal's ability to maintain object information throughout a delay period for two different objects early in training (day 17). At the start of the training session, the animal chose object A more often than object B regardless of which object was the sample. This bias decreased over the course of the training session and the animal gradually improved his performance for object B. This performance improvement showed the animal's ability to learn new objects. The animal's ability to generalize the rule is shown in Figure 5B. Later during the training (day 34), a new pair of objects were introduced and the animal was capable of maintaining both objects in his working memory from the start of the session.

    Figure 5.  Early in training, a novel image results in low performance while later in training, a novel image results in immediate high performance.

    Training was completed for the change detection task after 43 training sessions. The goal for the animal is to report the change by releasing the lever in response to a change in the visual stimulus. Figure 6A shows the animal's release time relative to the stimulus change early in training (day 16). At this point, the animal's release time did not closely match the stimulus change time, indicating that the animal had not yet mastered the task. Figure 6B shows the animal's performance later in training. The animal's release time more reliably followed the stimulus change time, showing that the animal was following the task rule. Figure 6C illustrates the animal's overall performance for an early vs. late day of training, showing a performance improvement as the training progressed.

    Figure 6.  Early in training, release time is not dependent on the time of the stimulus change, and performance remains unchanged during a single training session, whereas later in training, release time reflects time of change and performance improves over a single training session.

    The change detection task measures the animal's sensitivity to changes in a sensory signal (visual stimulus blink). After the animal was trained to detect a blink for the duration of 100 ms, we reduced the total signal change by keeping the blink duration constant and varying the magnitude of the luminance change. The animal performed well for the 100% contrast change condition (stimulus completely disappeared). To cover the dynamic range of the animal's performance the contrast change varied between 5%-65%. Figure 7A shows that the animal's performance depended on the contrast change, indicating that the animal was following the visual signal. The animal's performance gradually improved over time (Figure 7B), showing that the training stages enabled the animal to learn the task.

    Figure 7.  Performance depends on the % contrast change.

    It is imperative to provide a low stress environment to enhance learning [38]. The ability to train NHPs in their own home cage could potentially expedite training and improve the animal's quality of life. Here we described the system we designed and used to successfully train an NHP on a change detection and a working memory task. We observed that the animal's motivation to perform these tasks was drastically higher compared to our previous experience of training other animals on similar tasks using a primate chair. This heightened motivation was also associated with faster training and higher performance. Moreover, once the animal was more familiar with the task they chose to perform the task even without water restriction. Rhesus monkeys are highly intelligent animals and a huge part of their daily care is providing them with sufficient mental activity and enrichment. Moving the training to the animal's cage not only expedited the training, it provided a great repertoire of behavioral enrichment throughout the day available at the animal's discretion.

    The main impediment to exclusively using in-cage training is the need to track the eye position in most visual tasks. Eye tracking systems usually require the head to be stationary. Other groups have successfully used face masks to restrict the animal's head movement, potentially enabling tracking of their eye movements in their home cage [39,40,41,42,43,44]. Training the animal to use a face mask while performing behavioral tasks could drastically change the set of behavioral paradigms that these animals can learn in their home cage. If successful, this addition of eye tracking to this system could move most of the behavioral training to the animal's home cage. Ultimately once wireless electrophysiological recording devices are improved, recording the animal's behavioral and neural responses in more natural environments will be possible.

    The work was supported by MSU start-up fund, Whitehall 2014-5-18, NIH R01EY026924, and NSF1439221 and 1632738 grants to BN.

    All authors declare no conflicts of interest in this paper.



    [1] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
    [2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 doi: 10.1016/S0165-0114(86)80034-3
    [3] W.-R. Zhang, Bipolar fuzzy sets and relations: a computational frame work for cognitive modeling and multi agent decision analysis, The First International Joint Conference of the North American Fuzzy Information Processing Society Biannual Conference, San Antonio, TX, USA, 1994,305–309.https://doi.org/10.1109/IJCF.1994.375115
    [4] J. J. Chen, S. G. Li, S. Q. Ma, X. P Wang, m-Polar fuzzy sets: An extension of bipolar fuzzy sets, Sci. World J., 2014 (2014), 416530. https://doi.org/10.1155/2014/416530 doi: 10.1155/2014/416530
    [5] F. Smarandache, A unifying field in logics: neutrosophic logic, Philosophy: American Research Press, 1999.
    [6] R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE T. Fuzzy Syst., 22 (2014), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989 doi: 10.1109/TFUZZ.2013.2278989
    [7] R. R. Yager, Generalized orthopair fuzzy sets, IEEE T. Fuzzy Syst., 25 (2017), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005 doi: 10.1109/TFUZZ.2016.2604005
    [8] M. R. Seikh, U. Mandal, Multiple attribute group decision making based on quasirung orthopair fuzzy sets: Application to electric vehicle charging station site selection problem, Eng. Appl. Artif. Intel., 115 (2022), 105299.https://doi.org/10.1016/j.engappai.2022.1052
    [9] M. R. Seikh, U. Mandal, Multiple attribute decision-making based on (3,4)-quasirung fuzzy sets, Granul. Comput., 7 (2022), 965–978. https://doi.org/10.1007/s41066-021-00308-9 doi: 10.1007/s41066-021-00308-9
    [10] M. R. Seikh, U. Mandal, q-Rung orthopair fuzzy Frank aggregation operators and its application in multiple attribute decision-making with unknown attribute weights, Granul. Comput., 7 (2022), 709–730. https://doi.org/10.1007/s41066-021-00290-2 doi: 10.1007/s41066-021-00290-2
    [11] M. R. Seikh, U. Mandal, q-Rung orthopair fuzzy Archimedean aggregation operators: application in the site selection for software operating units, Symmetry, 15 (2023), 1680. https://doi.org/10.3390/sym15091680 doi: 10.3390/sym15091680
    [12] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, T. Mahmood, Spherical fuzzy sets and their applications in multi-attribute decision making problems, J. Intell. Fuzzy Syst., 36 (2019), 2829–2844. https://doi.org/10.3233/JIFS-172009 doi: 10.3233/JIFS-172009
    [13] T. Mahmood, K. Ullah, Q. Khan, N. Jan, An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets, Neural Comput. & Applic., 31 (2019), 7041–7053. https://doi.org/10.1007/s00521-018-3521-2 doi: 10.1007/s00521-018-3521-2
    [14] T. Mahmood, I. Haleemzai, Z. Ali, D. Pamucar, D. Marinkovic, Power muirhead mean operators for interval-valued linear diophantine fuzzy sets and their application in decision-making strategies, Mathematics, 10 (2021), 70. https://doi.org/10.3390/math10010070 doi: 10.3390/math10010070
    [15] T. Mahmood, A novel approach towards bipolar soft sets and their applications, J. Math., 2020 (2020), 4690808. https://doi.org/10.1155/2020/4690808 doi: 10.1155/2020/4690808
    [16] M. Riaz, M. R. Hashmi, Linear diophantine fuzzy set and its applications towards multi-attribute decision-making problems, J. Intell. Fuzzy Syst., 37 (2019), 5417–5439.
    [17] M. Z. Hanif, N. Yaqoob, M. Riaz, M. Aslam, Linear diophantine fuzzy graphs with new decision-making approach, AIMS Mathematics, 7 (2022), 14532–14556. https://doi.org/10.3934/math.2022801 doi: 10.3934/math.2022801
    [18] A. O. Almagrabi, S. Abdullah, M. Shams, Y. D. Al-Otaibi, S. Ashraf, A new approach to q-linear Diophantine fuzzy emergency decision support system for COVID19, J. Ambient Intell. Human. Comput., 13 (2022), 1687–1713. https://doi.org/10.1007/s12652-021-03130-y doi: 10.1007/s12652-021-03130-y
    [19] H. Kamacı, Complex linear diophantine fuzzy sets and their cosine similarity measures with applications, Complex Intell. Syst., 8 (2022), 1281–1305. https://doi.org/10.1007/s40747-021-00573-w doi: 10.1007/s40747-021-00573-w
    [20] T. Mahmood, I. Haleemzai, Z. Ali, D. Pamucar, and D. Marinkovic, Power muirhead mean operators for interval-valued linear diophantine fuzzy sets and their application in decision-making strategies, Mathematics, 10 (2021), 70. https://doi.org/10.3390/math10010070 doi: 10.3390/math10010070
    [21] S. Ayub, M. Shabir, M. Riaz, M. Aslam, R. Chinram, Linear diophantine fuzzy relations and their algebraic properties with decision making, Symmetry, 13 (2021), 945. https://doi.org/10.3390/sym13060945 doi: 10.3390/sym13060945
    [22] M. Parimala, S. Jafari, M. Riaz, M. Aslam, Applying the dijkstra algorithm to solve a linear diophantine fuzzy environment, Symmetry, 13 (2021), 1616. https://doi.org/10.3390/sym13091616 doi: 10.3390/sym13091616
    [23] M. Riaz, H. M. A. Farid, Enhancing green supply chain efficiency through linear diophantine fuzzy soft-max aggregation operators, J. Ind. Intell., 1 (2023), 8–29. https://doi.org/10.56578/jii010102 doi: 10.56578/jii010102
    [24] J. J. Peng, X. G. Chen, X. K. Wang, J. Q. Wang, Q. Q. Long, L. J. Yin, Picture fuzzy decision-making theories and methodologies: a systematic review, Int. J. Syst. Sci., 54 (2023), 2663–2675. https://doi.org/10.1080/00207721.2023.2241961 doi: 10.1080/00207721.2023.2241961
    [25] A. B. Yan, Y. Chen, Z. Y. Gao, T. M. Ni, Z. F. Huang, J. Cui, et al., Fempim: A FeFET -based multifunctional processing-in-memory cell, IEEE T. Circuits-II, 71 (2024), 2299–2303. https://doi.org/10.1109/TCSII.2023.3331267 doi: 10.1109/TCSII.2023.3331267
    [26] L. R. Yin, L. Wang, S. Y. Lu, R. Y. Wang, Y. S. Yang, B. Yang, et al., Convolution-transformer for image feature extraction, CMES-Comp. Model. Eng., 141 (2024), 87–106.https://doi.org/10.32604/cmes.2024.051083
    [27] L. R. Yin, L. Wang, S. Y. Lu, R. Y. Wang, H. T. Ren, A. AlSanad, et al., AFBNet: A lightweight adaptive feature fusion module for super-resolution algorithms, CMES-Comp. Model. Eng., 140 (2024), 2315–2347.https://doi.org/10.32604/cmes.2024.050853
    [28] H. M. A. Farid, R. Kausar, M. Riaz, D. Marinkovic, M. Stankovic, Linear diophantine fuzzy fairly averaging operator for suitable biomedi cal material selection, Axioms, 11 (2022), 735. https://doi.org/10.3390/axioms11120735 doi: 10.3390/axioms11120735
    [29] M. Riaz, H. Garg, M. R. Hashmi, H. M. A. Farid, Generalized linear diophantine fuzzy choquet integral with application to the project management and risk analysis, Comput. Appl. Math., 42 (2023), 286. https://doi.org/10.1007/s40314-023-02421-8 doi: 10.1007/s40314-023-02421-8
    [30] M. Riaz, H. M. A. Farid, W. W. Wang, D. Pamucar, Interval-valuedlinear diophantine fuzzy frank aggregation operators with multi-criteria decision making, Mathematics, 10 (2022), 1811. https://doi.org/10.3390/math10111811 doi: 10.3390/math10111811
    [31] A. Revathy, V. Inthumathi, S. Krishnaprakash, M. Kishorekumar, Fermatean fuzzy normalised bonferroni mean operator in multi criteria decision making on selection of electric bike, 2023 Fifth International Conference on Electrical, Computer and Communication Technologies (ICECCT), Erode, India, 2023, 1–7.https://doi.org/10.1109/ICECCT56650.2023.10179658
    [32] X. P. Yang, T. Mahmood, J. Ahmmad, Picture fuzzy soft bonferroni mean aggregation operators and their applications, Heliyon, 9 (2023), e17278. https://doi.org/10.1016/j.heliyon.2023.e17278 doi: 10.1016/j.heliyon.2023.e17278
    [33] S. Chakraborty, A. K. Saha, Novel fermatean fuzzy bonferroni mean aggregation operators for selecting optimal health care waste treatment technology, Eng. Appl. Artif. Intel., 119 (2023), 105752. https://doi.org/10.1016/j.engappai.2022.105752 doi: 10.1016/j.engappai.2022.105752
    [34] K. Jabeen, Q. Khan, K. Ullah, T. Senapati, S. Moslem, An approach to madmbased on aczel-alsina power bonferroni aggregation operators for q-rung orthopair fuzzy sets, IEEE Access, 11 (2023), 105248–105261. https://doi.org/10.1109/ACCESS.2023.3270267 doi: 10.1109/ACCESS.2023.3270267
    [35] H. M. A. Farid, M. Riaz, M. J. Khan, P. Kumam, K. Sitthithakerngkiet, Sustainable thermal power equipment supplier selection by Einstein prioritized linear Diophantine fuzzy aggregation operators, AIMS Mathematics, 7 (2022), 11201–11242. https://doi.org/10.3934/math.2022627 doi: 10.3934/math.2022627
    [36] A. Iampan, G. S. Garcıa, M. Riaz, H. M. A. Farid, R. Chinram, Linear Diophantine fuzzy Einstein aggregation operators for multicriteria decision-making problems, J. Math., 2021 (2021), 5548033. https://doi.org/10.1155/2021/5548033 doi: 10.1155/2021/5548033
    [37] H. Z. Ibrahim, I. Alshammari, (n, m)-Rung orthopair fuzzy sets with applications to multi-criteria decision making, IEEE Access, 10 (2022), 99562–99572. https://doi.org/10.1109/ACCESS.2022.3207184 doi: 10.1109/ACCESS.2022.3207184
    [38] P. Panpho, P. Yiarayong, (p, q)-Rung linear Diophantine fuzzy sets and their application in decision-making, Comp. Appl. Math., 42 (2023), 324. https://doi.org/10.1007/s40314-023-02456-x doi: 10.1007/s40314-023-02456-x
    [39] M. Riaz, H. M. A. Farid, F. Karaaslan, Linear Diophantine fuzzy aggregation operators with multi-criteria decision-making, Journal of Computational and Cognitive Engineering, 4 (2023), 24–35. https://doi.org/10.47852/bonviewJCCE3202420 doi: 10.47852/bonviewJCCE3202420
    [40] M. R. Seikh, P. Chatterjee, Identifying sustainable strategies for electronic waste management utilizing confidence-based group decision-making method in interval valued Fermatean fuzzy environment, Eng. Appl. Artif. Intel., 135 (2024), 108701. https://doi.org/10.1016/j.engappai.2024.108701 doi: 10.1016/j.engappai.2024.108701
    [41] M. R. Seikh, P. Chatterjee, Determination of best renewable energy sources in India using SWARA-ARAS in confidence level-based interval-valued Fermatean fuzzy environment, Appl. Soft Comput., 155 (2024), 111495. https://doi.org/10.1016/j.asoc.2024.111495 doi: 10.1016/j.asoc.2024.111495
    [42] M. B. Khan, A. M. Deaconu, J. Tayyebi, D. E. Spridon, Diamond intuitionistic fuzzy sets and their applications, IEEE Access, 12 (2024), 176171–176183. https://doi.org/10.1109/ACCESS.2024.3502202 doi: 10.1109/ACCESS.2024.3502202
    [43] Y. M. Zhang, Multi‐slicing strategy for the three‐dimensional discontinuity layout optimization (3D DLO), Int. J. Numer. Anal. Met., 41 (2017), 488–507. https://doi.org/10.1002/nag.2566 doi: 10.1002/nag.2566
    [44] Y. M. Zhang, X. Y. Zhuang, A softening-healing law for self-healing quasi-brittle materials: analyzing with strong discontinuity embedded approach, Eng. Fract. Mech., 192 (2018), 290–306. https://doi.org/10.1016/j.engfracmech.2017.12.018 doi: 10.1016/j.engfracmech.2017.12.018
    [45] Y. M. Zhang, X. Y. Zhuang, Cracking elements: A self-propagating strong discontinuity embedded approach for quasi-brittle fracture, Finite Elem. Anal. Des., 144 (2018), 84–100. https://doi.org/10.1016/j.finel.2017.10.007 doi: 10.1016/j.finel.2017.10.007
    [46] Y. M. Zhang, X. Y. Zhuang, Cracking elements method for dynamic brittle fracture, Theor. Appl. Fract. Mec., 102 (2019), 1–9. https://doi.org/10.1016/j.tafmec.2018.09.015 doi: 10.1016/j.tafmec.2018.09.015
    [47] Y. M. Zhang, H. A. Mang, Global cracking elements: A novel tool for Galerkin‐based approaches simulating quasi‐brittle fracture, Int. J. Numer. Meth. Eng., 121 (2020), 2462–2480. https://doi.org/10.1002/nme.6315 doi: 10.1002/nme.6315
    [48] Y. M. Zhang, X. Y. Zhuang, R. Lackner, Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization, Int. J. Numer. Anal. Met., 42 (2018), 1199–1216. https://doi.org/10.1002/nag.2775 doi: 10.1002/nag.2775
    [49] Y. M. Zhang, M. Zeiml, C. Pichler, R. Lackner, Model-based risk assessment of concrete spalling in tunnel linings under fire loading, Eng. Struct., 77 (2014), 207–215. https://doi.org/10.1016/j.engstruct.2014.02.033 doi: 10.1016/j.engstruct.2014.02.033
    [50] Y. M. Zhang, R. Lackner, M. Zeiml, H. A. Mang, Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations, Comput. Method. Appl. M., 287 (2015), 335–366. https://doi.org/10.1016/j.cma.2015.02.001 doi: 10.1016/j.cma.2015.02.001
    [51] Y. M. Zhang, Z. R. Gao, Y. Y. Li, X. Y. Zhuang, On the crack opening and energy dissipation in a continuum based disconnected crack model, Finite Elem. Anal. Des., 170 (2020), 103333. https://doi.org/10.1016/j.finel.2019.103333 doi: 10.1016/j.finel.2019.103333
    [52] Y. M. Zhang, X. Q. Yang, X. Y. Wang, X. Y. Zhuang, A micropolar peridynamic model with non-uniform horizon for static damage of solids considering different nonlocal enhancements, Theor. Appl. Fract. Mec., 113 (2021), 102930. https://doi.org/10.1016/j.tafmec.2021.102930 doi: 10.1016/j.tafmec.2021.102930
    [53] Y. M. Zhang, J. G. Huang, Y. Yuan, H. A. Mang, Cracking elements method with a dissipation-based arc-length approach, Finite Elem. Anal. Des., 195 (2021), 103573. https://doi.org/10.1016/j.finel.2021.103573 doi: 10.1016/j.finel.2021.103573
    [54] Y. M. Zhang, Z. R. Gao, X. Y. Wang, Q. Liu, Predicting the pore-pressure and temperature of fire-loaded concrete by a hybrid neural network, Int. J. Comp. Meth., 19 (2022), 2142011. https://doi.org/10.1142/S0219876221420111 doi: 10.1142/S0219876221420111
    [55] Y. M. Zhang, X. Y. Wang, X. Q. Wang, H. A. Mang, Virtual displacement-based discontinuity layout optimization, Int. J. Numer. Meth. Eng., 123 (2022), 5682–5694. https://doi.org/10.1002/nme.7084 doi: 10.1002/nme.7084
    [56] Y. M. Zhang, Z. R. Gao, X. Y. Wang, Q. Liu, Image representations of numerical simulations for training neural networks, Comput. Model. Eng. Sci., 134 (2023), 821–833. https://doi.org/10.32604/cmes.2022.022088 doi: 10.32604/cmes.2022.022088
    [57] Z. Ali, K. Hayat, D. Pamucar, Analysis of coupling in geographic information systems based on WASPAS method for bipolar complex fuzzy linguistic Aczel-Alsina power aggregation operators, PloS One, 19 (2024), e0309900. https://doi.org/10.1371/journal.pone.0309900 doi: 10.1371/journal.pone.0309900
    [58] Z. Ali, Fairly aggregation operators based on complex p, q-rung orthopair fuzzy sets and their application in decision-making problems, Spectrum of Operational Research, 2 (2025), 113–131. https://doi.org/10.31181/sor21202514 doi: 10.31181/sor21202514
    [59] K. Hayat, R. A. Shamim, H. AlSalman, A. Gumaei, X. P. Yang, M. Azeem Akbar, Group generalized q‐rung orthopair fuzzy soft sets: new aggregation operators and their applications, Math. Probl. Eng., 2021 (2021), 5672097. https://doi.org/10.1155/2021/5672097 doi: 10.1155/2021/5672097
    [60] M. S. Raja, K. Hayat, A. Munshi, T. Mahmood, R. Sheraz, I. Matloob, Aggregation operators on group-based generalized q-rung orthopair fuzzy N-soft sets and applications in solar panel evaluation, Heliyon, 10 (2024), e27323. https://doi.org/10.1016/j.heliyon.2024.e27323 doi: 10.1016/j.heliyon.2024.e27323
    [61] S. Petchimuthu, M. F. Banu, C. Mahendiran, T. Premala, Power and energy transformation: Multi-criteria decision-making utilizing complex q-rung picture fuzzy generalized power prioritized Yager operators, Spectrum of Operational Research, 2 (2025), 219–258. https://doi.org/10.31181/sor21202525 doi: 10.31181/sor21202525
    [62] S. Petchimuthu, B. Palpandi, P. Pirabaharan, M. F. Banu, Sustainable urban innovation and resilience: Artificial intelligence and q-rung orthopair fuzzy expoLogarithmic framework, Spectrum of Decision Making and Applications, 2 (2025), 242–267. https://doi.org/10.31181/sdmap21202526 doi: 10.31181/sdmap21202526
    [63] P. D. Liu, S. Naz, M. Akram, M. Muzammal, Group decision-making analysis based on linguistic q-rung orthopair fuzzy generalized point weighted aggregation operators, Int. J. Mach. Learn. & Cyber., 13 (2022), 883–906. https://doi.org/10.1007/s13042-021-01425-2 doi: 10.1007/s13042-021-01425-2
    [64] S. Naz, M. Akram, A. B. Saeid, A. Saadat, Models for MAGDM with dual hesitant q-rung orthopair fuzzy 2-tuple linguistic MSM operators and their application to the COVID-19 pandemic, Expert Syst., 39 (2022), e13005. https://doi.org/10.1111/exsy.13005 doi: 10.1111/exsy.13005
    [65] M. Akram, U. Noreen, M. M. A. Al-Shamiri, D. Pamucar, Integrated decision-making methods based on 2-tuple linguistic m-polar fuzzy information, AIMS Math, 7 (2022), 14557–14594. https://doi.org/10.3934/math.2022802 doi: 10.3934/math.2022802
    [66] J. C. Jiang, X. D. Liu, Z. W. Wang, W. P. Ding, S. T. Zhang, Large group emergency decision-making with bi-directional trust in social networks: A probabilistic hesitant fuzzy integrated cloud approach, Inform. Fusion, 102 (2024), 102062. https://doi.org/10.1016/j.inffus.2023.102062 doi: 10.1016/j.inffus.2023.102062
    [67] J. C. Jiang, X. D. Liu, Z. W. Wang, W. P. Ding, S. T. Zhang, H. Xu, Large group decision-making with a rough integrated asymmetric cloud model under multi-granularity linguistic environment, Inform. Sciences, 678 (2024), 120994. https://doi.org/10.1016/j.ins.2024.120994 doi: 10.1016/j.ins.2024.120994
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