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International Journal of Neutrosophic Science
Volume 20 , Issue 4, PP: 08-35 , 2023 | Cite this article as | XML | Html |PDF

Title

Applications of Extended Plithogenic Sets in Plithogenic Sociogram

  S.Sudha 1 * ,   Nivetha Martin 2 ,   Florentin Smarandache 3

1  School of Mathematics, Madurai Kamaraj University, Madurai, Tamil Nadu, India
    (sudhasikkanan@gmail.com)

2  Department of Mathematics, Arul Anandar College(Autonomous),Karumathur, Tamil Nadu, India
    (nivetha.martin710@gmail.com)

3  University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA
    (fsmarandache@gmail.com)


Doi   :   https://doi.org/10.54216/IJNS.200401

Received: November 12, 2022 Accepted: March 05, 2023

Abstract :

The theory of plithogeny developed by Smarandache is described as a more generalized form of representing sets of different nature such as crisp, fuzzy, intuitionistic and neutrosophic. Plithogenic set comprises degree of appurtenance and contradiction degree with respect only to the dominant attribute. This paper introduces extended plithogenic sets comprising degrees of appurtenance and contradiction with respect to both dominant and recessive attributes. The extension of the 5-tuple Plithogenic sets to a 7- tuple plithogenic sets helps in developing a more comprehensive kind of Plithogenic sociogram. The newly developed plithogenic sets and its implications in Plithogenic sociogram is validated by the decision making problem on food processing industries. The obtained results using extended plithogenic sets are more promising in comparison to the conventional plithogenic sets. The proposed kind of plithogenic sets will benefit the decision makers to make optimal decisions based on both optimistic and pessimistic approaches.

Keywords :

Plithogenic Sociogram; Extended Plithogenic Sets; Food Packaging materials; Decision making

References :

[1] Smarandache F., lithogeny, Plithogenic Set, Logic, Probability and Statistics, preprint arXiv:1808.03948, Infinite Study, (2017)

[2] Florentin Smarandache., Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets – Revisited. Neutrosophic Sets and Systems, vol. 21,pp. 153-166.,(2018) https://doi.org/10.5281/zenodo.1408740

[3] Florentin Smarandache., Plithogenic Probability & Statistics are generalizations of MultiVariate Probability & Statistics., Neutrosophic Sets and Systems, Vol. 43, 2021.

[4] Sankar C., Sujatha R., Nagarajan D., Topsis by using Plithogenic set in COVID-19 Decision Making., International Journal of Neutrosophic Science (IJNS) Vol. 10, No. 2, PP. 116-125. (2020)

[5] Mohamed Abdel-Basset & Rehab, A novel plithogenic TOPSIS-CRITIC model for sustainable supply chain risk management, Journal of Cleaner production, 247. (2020).

[6] Nivetha Martin., Plithogenic SWARA-TOPSIS Decision Making on Food Processing Methods with Different Normalization Techniques, (2021). DOI: 10.5772/intechopen.100548

[7] Abdullah Ozcil., Aysegul Tus., Gulin Zeynep Oztas., Esra Aytac Adali & TayfunOztas., “The Novel Integrated Model of Plithogenic Sets and MAIRCA Method for MCDM problems”. International Conference on Intelligent and fuzzy systems.pp 733-741. (2020) [8] Mohamed Grida, Rehab Mohamed and Abdel Nasser H. Zaied., A Novel Plithogenic MCDM Framework for Evaluating the Performance of IoT Based Supply Chain.” Neutrosophic sets and systems, Vol.33,1,pp-323-341,(2020).

[9] Shio Gai Quek , Ganeshsree Selvachandran , Florentin Smarandache J. Vimala , Son Hoang Le, Quang-Thinh Bui and Vassilis C. Gerogiannis., Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making., Mathematics, 8, 965, 2020; doi:10.3390/math8060965

[10] Mohamed Abdel-Basset, Rehab Mohamed, Florentin Smarandache, Mohamed Elhoseny., A New Decision-Making Model Based on Plithogenic Set for Supplier Selection., Computers, Materials & Continua., vol.66, no.3. (2021).

[11] Gomathy S., Nagarajan D., BroumiS., M. Lathamaheswari., Plithogenic sets and their application in decision making.,Neutrosophic Sets and Systems, Vol. 83, (2020) .

[12] Abdel-Basset M., Mohamed R., Zaied A. E. N. H, & Smarandache F., A Hybrid Plithogenic Decision-Making Approach with Quality Function Deployment for Selecting Supply Chain Sustainability Metrics. Symmetry, 11(7), 903, (2019).

[13] Priyadharshini S.P., Nirmala Irudayam F., A Novel approach of Refined Plithogenic Neutrosophic sets in Multi Criteria Decision Making., International Research Journal of Modernization in Engineering Technology and Science Volume:03/Issue:04/May-2021

[14] Priyadharshini S.P., Nirmala Irudayam F., A New Approach of Multi-Dimensional Single Valued Plithogenic Neutrosophic Set in Multi Criteria Decision Making., Neutrosophic Sets and Systems, Vol. 45, 2021

[15] Abdel-Basset M, Ding W, Mohamed , Metawa N., An integrated plithogenic MCDM approach for financial performance evaluation of manufacturing industries. Risk Management, (2020) .

[16] Abdel-Basset M, El-hoseny M, Gamal A, Smarandache F., A novel model for evaluation hospital medical care systems based on plithogenic sets. ArtifIntell Med 100:1–8,(2019). https://doi.org/10. 1016/j.artmed.2019.101710

[17] Smarandache, F. Extension of Soft set to Hypersoft Set, and then to Plithogenic Hypersoft Set, Neutrosophic set and Systems, 22, 168-170., (2018). [18] Shawkat Alkhazaleh., Plithogenic Soft Set., Neutrosophic Sets and Systems, Vol. 33, 2020

[19] Shazia Rana , Madiha Qayyum , Muhammad Saeed , Florentin Smarandache , and Bakhtawar Ali Khan. Plithogenic Fuzzy Whole Hypersoft Set, Construction of Operators and their Application in Frequency Matrix Multi Attribute Decision Making Technique. Neutrosophic Sets and Systems, Vol. 28, 2019

[20] Dhivya E , ArokiaLancy A., Near Plithogenic Neutrosophic Hypersoft Heronian Mean Aggregation Operators and their Application in Multiple Attribute Decision Making., International Journal of Mechanical Engineering., Vol. 7 No. 8 August, 2022. ISSN: 0974-5823

[21] Muhammad Rayees Ahmad , Muhammad Saeed , Usman Afzal .,Miin-Shen Yang., A Novel MCDM Method Based on Plithogenic Hypersoft Sets under Fuzzy Neutrosophic Environment., Symmetry 2020, 12, 1855; doi:10.3390/sym12111855

[22] Shazia Rana, Muhammad Saeed, Midha Qayyum, Florentin Smarandache, Plithogenic Subjective Hyper-Super-Soft Matrices with New Definitions & Local, Global, Universal Subjective Ranking Model., International Journal of Neutrosophic Science (IJNS)., Vol. 6, No. 2, PP. 56-79.,(2020). [23] Nivetha Martin, & Florentin Smarandache., Introduction to Combined Plithogenic Hypersoft Sets. Neutrosophic Sets and Systems, Vol. 35, 2020., https://doi.org/10.5281/zenodo.3951708

[24] Nivetha Martin, Florentin Smarandache and Said Broumi., COVID-19 Decision-Making Model using Extended Plithogenic Hypersoft Sets with Dual Dominant Attributes., International Journal of Neutrosophic Science (IJNS) Vol. 13, No. 2, PP. 75-86. (2021)

[25] Nivetha Martin and Florentin Smarandache ., Concentric Plithogenic Hypergraph based on Plithogenic Hypersoft sets – A Novel Outlook., Neutrosophic Sets and Systems, Vol. 33, 2020 [26] Vasantha WB, Ilanthenral K, Smarandache F. Plithogenic Graphs Bruxelles;vol. EuropaNova: 2020. . Available from: https://www.researchgate.net/ publication/343769158_Plithogenic_Graphs [27] Sultana F, Gulistan M, Ali M, Yaqoob N, Khan M, Rashid T, Ahmed T. A study of plithogenic graphs: applications in spreading coronavirus disease (COVID-19) globally. J Ambient Intell Humaniz Comput. 2022 Apr 4:1-21. doi: 10.1007/s12652-022-03772-6. Epub ahead of print. Erratum in: J Ambient Intell Humaniz Comput. 2022 Dec 6;:1. PMID: 35401852; PMCID: PMC8978528.

[28] Gayen S, Smarandache F, Jha S, Singh MK, Broumi S, and Kumar R ., Introduction to plithogenic subgroup. In: Neutrosophic graph theory and algorithm. p 209–233., (2019) IGIGlobal, Pennsylvania

[29] Nivetha Martin, FlorentinSmarandache and Said Broumi., PROMTHEE Plithogenic Pythagorean Hypergraphic Approach in Smart Materials Selection., International Journal of Neutrosophic Science (IJNS) Vol. 13, No. 1, PP. 52-60.,(2021) [30] Prem Kumar Singh., Single-valued Plithogenic graph for handling multi-valued attribute data and its context., International Journal of Neutrosophic Science (IJNS) Vol. 15, No. 2, PP. 98-112. (2021). [31] Prem Kumar Singh., Air Quality Index Analysis Using Single-Valued Neutrosophic Plithogenic Graph for Multi-Decision Process., International Journal of Neutrosophic Science (IJNS) Vol. 16, No. 1, PP. 28-41. (2021)

[32] Prem Kumar Singh., Dark data analysis using Intuitionistic Plithogenic graphs., International Journal of Neutrosophic Science (IJNS) Vol. 16, No. 2, PP. 80-100 (2021), [33] Bharathi T, Leo S., A Study on Plithogenic Product Fuzzy Graphs with Application in Social network. Indian Journal of Science and Technology 14(40): 3051-3063. (2021) ., https://doi.org/ 10.17485/IJST/v14i40.1298

[34] Gayen S, Smarandache F, Jha S, Singh MK, Broumi S, Kumar R ., Introduction to plithogenic hypersoft subgroup. Neutrosophic Sets and Syst 33:208–233 (2020)

[35] Priyadharshini S.P., NirmalaIrudayam F., Plithogenic Neutrosophic set and Plithogenic Neutrosophic Topological Spaces (Submitted), 2021.

[36] Bhimraj Basumatary , Nijwm Wary , Muhammad Saeed and Muhammad Saqlain., On Some Properties of Plithogenic Neutrosophic Hypersoft Almost Topological Group., Neutrosophic Sets and Systems, Vol. 43, 2021 [37] Singh, P.K. , Complex Plithogenic Set. International Journal of Neutrosophic Sciences, 18, 57-72. (2022) .https://doi.org/10.54216/IJNS.180106

[38] Nivetha Martin, Florentin Smarandache, Priya R., Introduction to Plithogenic Sociogram with preference representations by Plithogenic Number., Journal of Fuzzy Extension & Application., 1(1). (2021).

[39] Noel Batista Hernández, Maikel Y. Leyva Vázque, Erick González Caballero, Lilia E. Valencia Cruzaty, Wilmer Ortega Chávez, and Florentin Smarandache., A New Method to Assess Entrepreneurship Competence in University Students Using Based on Plithogenic Numbers and SWOT Analysis., International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(3): 280-292

[40] Raúl Comas Rodríguez , Sharon Dinarza Álvarez Gómez , Edgar Ramón Arredondo Domínguez , Lisenia Karina Baque Villanueva and Karina Pérez Teruel., A Novel Evaluative Method of the Subject “Education and Society” of the Autonomous University of the Andes, Ecuador, based on Plithogenic Numbers., Neutrosophic Sets and Systems ., Vol. 44, 2021

[41] Nivetha Martin and Florentin Smarandach., Plithogenic Cognitive Maps in Decision Making”., International Journal of Neutrosophic Science (IJNS) Vol. 9, No. 1, PP. 09-21. (2020)

[42] Nivetha Martin., Priya R., Smarandache F, New Plithogenic Sub Cognitive Maps Approach with Mediating Effects of Factors in Covid-19 Diagnostic Model, Journal of Fuzzy Extension and Applications, 2, 1-14, (2021).

[43] Priya R, and Nivetha Martin., Induced Plithogenic Cognitive Maps with Combined Connection Matrix to investigate the glitches of online learning system., Neutrosophic Sets and Systems, Vol. 43, 2021 [44] Sujatha R., Poomagal.S., KuppuswamiG., Said Broumi., An Analysis on Novel Corona Virus by a Plithogenic Approach to Fuzzy Cognitive Map., International Journal of Neutrosophic Science (IJNS) Vol. 11, No.2, PP. 62-75. (2020) [45] Smarandache F, Physical Plithogenic sets., 71st Annual Gaseous Electronics conference, Session LW1, Oregon Convention Center Room, Portland, Oregon, USA, November 5-9, 2018;http://meetings.aps.org/Meeting/GEC18/Session/LW1.110

[46] Smarandache F., Aggregation plithogenic operators in physical fields. In: 71st annual meeting of the APS division of fluid dynamics. Bulletin of the American Physical Society, vol 63. (2018) https://meetings.aps.org/Meeting/DFD18/ Event/334150

[47] Bala George., Information Fusion Using Plithogenic Set and Logic., Acta scientific computer sciences Volume 2 Issue 8 August 2020.

[48] Walid Abdelfattah ., Variables Selection Procedure for the DEA Overall Efficiency Assessment Based Plithogenic Sets and Mathematical Programming., IJSRM Volume 10 Issue 05May 2022.

[49] Ariel Romero Fernández , Gustavo Álvarez Gómez , Sary del Rocío Álvarez Hernández , William Roberto ÁlvarezArboleda and Adonis Ricardo Rosales García., Selection of Investment Projects in a Plithogenic Environment., Neutrosophic Sets and Systems ,Vol. 44, 2021

[50] Fernández Villacrés Gustavo Eduardo., Fausto Alberto Viscaino Naranjo., Roberto Rolando López Domínguez.,Plithogenic Logic for Determination of Strategic Solutions for Ergonomic Occupational Health Risks., Neutrosophic Sets and Systems 44, 1. https://digitalrepository.unm.edu/nss_journal/ vol44/iss1/38

[51] Piyush Thakur A , Shivam Agarwal , Amisha Raghuvanshi , Rashmi Sharma., Role of Packaging in Different Stages of Decision Making., International Journal of Science and Research (IJSR) ISSN: 2319-7064 SJIF (2020): 7.803

[52] Kenneth Marsh., Betty Bugusu., Food Packaging—Roles, Materials, and Environmental Issues., Journal of Food Science., Vol. 72, Nr. 3, 2007. doi: 10.1111/j.1750-3841.2007.00301.x

[53] Alamri M.S., Akram A.A. Qasem, Abdellatif A. Mohamed, Shahzad Hussain, Mohamed A. Ibraheem, Ghalia Shamlan, Hesham A. Alqah, Ali S. Qasha., Food packaging’s materials: A food safety perspective,Saudi Journal of Biological Sciences, Volume 28, Issue 8,2021,Pages 4490-4499,ISSN 1319-562X,https://doi.org/10.1016/j.sjbs.2021.04.047.

[54] Isabelle Maillet, Ariane Gaunand, Laurence Colinet, Safety analysis and decision making tools for the food-packaging sector. [Technical Report] auto-saisine. 2013, 14 p. ffhal-01605483

[55] Dikky Indrawan., Stevia Septian., Replacing Plastic: An Assessment of New Material for Food Production Package to Re-Engineer Packaging Industry Based on Multi-Criteria Analyses., Advances in Economics, Business and Management Research, Series volume number 141 Proceedings of the First ASEAN Business, Environment, and Technology Symposium (ABEATS 2019).

[56] Norton V., Waters C., Oloyede O.O., Lignou S., Exploring Consumers Understanding and Perception of Sustainable Food Packaging in the UK. Foods., 2022, 11, 3424. https://doi.org/10.3390/ foods11213424

[57] Cooksey K.., Effectiveness of antimicrobial food packaging materials., Food Additives and Contaminants, October 2005; 22(10): 980–987

[58] Muhammad Asgher, Sarmad Ahmad Qamar, Muhammad Bilal, Hafiz M.N., Iqbal,Bio-based active food packaging materials: Sustainable alternative to conventional petrochemical-based packaging materials,Food Research International,Volume 137,2020109625,ISSN 0963-9969, https://doi.org/10.1016/j.foodres.2020.109625.

[59] Karina Petersen, Per Vñggemose Nielsen, Grete Bertelsen, Mark Lawther, Mette B. Olsen, Nils H. Nilsson and Grith Mortensen., Potential of biobased materials for food packaging., Trends in Food Science & Technology 10 (1999).

[60] Michael G. Kontominas., Use of Alginates as Food Packaging Materials., Foods 2020, 9, 1440; doi:10.3390/foods9101440

[61] Dele Raheem., Application of plastics and paper as food packaging materials – An overview., Emir. J. Food Agric. 2012. 25 (3): 177-188 doi: 10.9755/ejfa.v25i3.11509

[62] Ioannis S. Arvanitoyannis & Loulouda Bosnea (2004) Migration of Substances from Food Packaging Materials to Foods, Critical Reviews in Food Science and Nutrition, 44:2, 63-76, DOI: 10.1080/10408690490424621

[63] Jung H. Han., New technologies in food packaging: Overiew., Innovations in Food Packaging Food Science and Technology,2005, Pages 3-11

[64] Md. Wadud Ahmed , Md. Azizul Haque, Md. Mohibbullah , Md. Sirajul Islam Khan, Mohammed ., Ariful Islam , Md. Hasan Tarek Mondal , Raju Ahmmed., A review on active packaging for quality and safety of foods: Current trends, applications, prospects and challenge Food Packaging and Shelf Life., Volume 33, September 2022, 100913

[65] Hao Cheng , Hao Xu, David Julian.,McClements , Long Chen , Aiquan Jiao , Yaoqi Tian , Ming Miao, Zhengyu Jin., Recent advances in intelligent food packaging materials: Principles, preparation and applications., Food Chemistry., Volume 375, 1 May 2022, 131738 [66] Porta R, Sabbah M, Di Pierro P. Biopolymers as Food Packaging Materials. International Journal of Molecular Sciences. 2020; 21(14):4942. https://doi.org/10.3390/ijms21144942

[67] Saurabh Sid, Rahul S Mor, Anand Kishore, Vijay Singh Sharanagat., Bio-sourced polymers as alternatives to conventional food packaging materials: A review., Trends in Food Science & Technology., Volume 115, September 2021, Pages 87-104


Cite this Article as :
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MLA S.Sudha, Nivetha Martin, Florentin Smarandache. "Applications of Extended Plithogenic Sets in Plithogenic Sociogram." International Journal of Neutrosophic Science, Vol. 20, No. 4, 2023 ,PP. 08-35 (Doi   :  https://doi.org/10.54216/IJNS.200401)
APA S.Sudha, Nivetha Martin, Florentin Smarandache. (2023). Applications of Extended Plithogenic Sets in Plithogenic Sociogram. Journal of International Journal of Neutrosophic Science, 20 ( 4 ), 08-35 (Doi   :  https://doi.org/10.54216/IJNS.200401)
Chicago S.Sudha, Nivetha Martin, Florentin Smarandache. "Applications of Extended Plithogenic Sets in Plithogenic Sociogram." Journal of International Journal of Neutrosophic Science, 20 no. 4 (2023): 08-35 (Doi   :  https://doi.org/10.54216/IJNS.200401)
Harvard S.Sudha, Nivetha Martin, Florentin Smarandache. (2023). Applications of Extended Plithogenic Sets in Plithogenic Sociogram. Journal of International Journal of Neutrosophic Science, 20 ( 4 ), 08-35 (Doi   :  https://doi.org/10.54216/IJNS.200401)
Vancouver S.Sudha, Nivetha Martin, Florentin Smarandache. Applications of Extended Plithogenic Sets in Plithogenic Sociogram. Journal of International Journal of Neutrosophic Science, (2023); 20 ( 4 ): 08-35 (Doi   :  https://doi.org/10.54216/IJNS.200401)
IEEE S.Sudha, Nivetha Martin, Florentin Smarandache, Applications of Extended Plithogenic Sets in Plithogenic Sociogram, Journal of International Journal of Neutrosophic Science, Vol. 20 , No. 4 , (2023) : 08-35 (Doi   :  https://doi.org/10.54216/IJNS.200401)