Gandhi, N. Ramila

Martin, Nivetha

Pandiammal, P.

Pradeepa, I.

Smarandache, Florentine

English

University of New Mexico

Neutrosophic Sets and Systems 
Volume 35 Article 14 
7-14-2020 
Exploration of the Factors Causing Autoimmune Diseases using 
Fuzzy Cognitive Maps with Concentric Neutrosophic 
Hypergraphic Approach 
Nivetha Martin 
Florentine Smarandache 
I. Pradeepa 
N. Ramila Gandhi 
P. Pandiammal 
Follow this and additional works at: https://digitalrepository.unm.edu/nss_journal 
Recommended Citation 
Martin, Nivetha; Florentine Smarandache; I. Pradeepa; N. Ramila Gandhi; and P. Pandiammal. "Exploration 
of the Factors Causing Autoimmune Diseases using Fuzzy Cognitive Maps with Concentric Neutrosophic 
Hypergraphic Approach." Neutrosophic Sets and Systems 35, 1 (2020). https://digitalrepository.unm.edu/
nss_journal/vol35/iss1/14 
This Article is brought to you for free and open access by UNM Digital Repository. It has been accepted for 
inclusion in Neutrosophic Sets and Systems by an authorized editor of UNM Digital Repository. For more 
information, please contact amywinter@unm.edu, lsloane@salud.unm.edu, sarahrk@unm.edu. 
                                    Neutrosophic Sets and Systems, Vol. 35, 2020 
University of New Mexico  
 
Nivetha.et.al Exploration of the Factors Causing Autoimmune Diseases using Fuzzy Cognitive Maps with Concentric 
Neutrosophic Hypergraphic Approach 
 
 
Exploration of the Factors Causing Autoimmune Diseases using 
Fuzzy Cognitive Maps with Concentric Neutrosophic 
Hypergraphic Approach 
Nivetha Martin1, Florentine Smarandache2, I.Pradeepa3, N.Ramila Gandhi4, P.Pandiammal5 
1,3 Department of Mathematics, Arul Anandar College(Autonomous), Karumathur, India, nivetha.martin710@gmail.com 
2 Department of Mathematics, University of New Mexico, USA, smarand@unm.edu 
4 Department of Mathematics, PSNA CET,Dindigul, India,satrami@gmail.com 
5 Department of Mathematics, GTN Arts College (Autonomous), Dindigul, India,pandiammal1981@gmail.com 
*Correspondence: nivetha.martin710@gmail.com 
 
  Abstract: Neutrosophic sets are comprehensively used in decision making environment. The 
manifestation of neutrosophic sets in concentric hypergraphs is proposed in this research work. 
The intention of developing a decision making model using the combination of Fuzzy Cognitive 
Maps and concentric neutrosophic hypergraph is to rank the core factors of decision making 
problem and find the inter relational impacts. This proposed model is validated with the 
exploration of the causative factors of autoimmune diseases. The proposed model is highly 
compatible as it assists in determining the core factors and their inter association. This model will 
certainly benefit the decision maker at all managerial levels to design optimal decisions. 
 
Keywords: Autoimmune disease, fuzzy cognitive maps, neutrosophic hypergraphs, optimal decision making 
1. Introduction 
Westernization the cause of modernization has unlocked the portals of cultural, behavioural 
and environmental changes of the people which greatly influence the biological system of human 
and this also lays the core reason for the outbreak of novel diseases. Presently the people of the 
world are characterized by multicultural and multi technological adoption. The integration and the 
association between people of varied culture have brought diverse implications on the external and 
internal environment of the human. Not just the social interactions contribute to such modifications; 
also the technological advancement and the work space of an individual cause a varied range of 
changes in the mankind. The tendency of manhood repelling from indigenous practices is the 
gateway for several health woes. The health system of the human is getting affected by several 
factors and especially the vulnerable target group is the women. In recent days, the people are 
chained by diseases of various kinds, even the economy of the nation face huge falls due to the effect 
of epidemic diseases, amidst such miserable situations, the immunity of the human is the only 
armed force against these viruses, but if the immune system fails to be defensive in nature and if it 
joins hand with the external invaders the entire human health system collapses and it ends in 
fatality. This is the characterization of auto immune diseases and the women are greatly affected by 
these diseases. It is highly a dreadful circumstance to tackle the consequences of these self- 
destructing diseases. The autoimmune diseases predominantly affecting the women are Rheumatoid 
Arthritis, Multiple Sclerosis, Systemic lupus Erythematosus, Grave’s disease, Hashimoto’s 
thyroiditis and Myasthenia gravis. Presently the rate of occurrences of such diseases is at its pinnacle 
and the medical experts are investigating the ways and means of its mitigation. [1]  
Neutrosophic Sets and Systems, Vol. 35, 2020     233  
 
 
Nivetha et al Exploration of the Factors Causing Autoimmune Diseases using Fuzzy Cognitive Maps with Concentric 
Neutrosophic Hypergraphic Approach 
 
Generally the women are highly susceptible to these autoimmune diseases as the immune system 
gets weakened during pre and post pregnancy stages. This scenario has gained the medical concerns 
and medical researchers are on their study, to render support to it, this paper aims to underlie the 
core factors contributing to autoimmune diseases in women and to find the inter association 
between the core factors. Optimal decisions can be made by applying scientific methods in the 
process of decision making process. The entire scenario of decision making must be modeled based 
on decisive factors of the study. One of the realistic tools of decision making is fuzzy cognitive maps 
(FCM), introduced by Kosko [2], later several academicians extended this FCM tool based on the 
requirements. FCM is a directed graph representing the casual relationship between factors 
considered for study. The nodes and the edges of the graph represent the study factors and their 
association. The weights [-1,1] represent the nature of the association. The integration of FCM with 
other graphic structures was initiated by Nivetha and Pradeepa [3]. The hypergraphic and fuzzy 
hypergraphic approaches with FCM unlocked the construction of concentric fuzzy hypergraphs and 
its integration with FCM [4,5]. This field of integrated FCM with fuzzy hypergraphs has made the 
researchers explore by introducing various types of concentric fuzzy hypergraphs. 
In this research work, a fuzzy cognitive map with concentric neutrosophic hypergraphic approach is 
introduced. The notion of neutrosophic fuzzy sets and neutrosophic logic was first coined by 
Smarandache [6] and presently many researchers are highly interested to carry out their research  in 
this field, the concepts of neutrosophic is applied in almost all types of decision making tools. 
Neutrosophic sets, play significant role in making decisions in uncertain environment as it provides 
space for the pragmatic representation of the expert’s opinion. Abdel Basset et al [7]developed a 
decision making model for evaluating the framework for smart disaster response system in an 
uncertain environment, neutrosophic sets are used for uncertainty assessments of linear time-cost 
tradeoffs [8]; resource levelling problem[9] in construction project was modeled under neutrosophic 
environment. The concept of neutrosophic sets was extended to bipolar neutrosophic representation 
[10] and it is used in multi criteria decision making framework for professional selection. Das et al 
[11] developed neutrosophic fuzzy matrices and algebraic operation that had some utility in 
decision making. Plithogenic sets, the extension of neutrosophic sets are used in solving supply 
chain problem with the development of a novel plithogenic model [12]. Such massive applications of 
neutrosophic sets in decision making and its robust nature triggered the idea of integrating 
neutrosophic sets to concentric hypergraphs. To the best of our knowledge, the integration of 
neutrosophic concentric fuzzy hypergraphs with FCM has not been instituted and so this is a new 
arena of research towards optimal decision making. 
 Fuzzy Cognitive Maps are more useful in determining the association between study factors, if 
the number of study factors is less, FCM’s are highly compatible, but if the number of factors is 
more, then comparative analysis between the factors is difficult and tedious, to resolve such crisis, 
the core factors of the problem are to be decided and then the inter association between the core 
factors can be determined easily. To find the core factors, the intervention of various experts is 
mandatory, based on which the factors can be ranked and the core factors are decided based on the 
rank positions of the factors. This eases the process of making decisions as it helps in filtering the 
non- core factors. Generally in medicinal environment, the medical experts analyze the factors 
contributing to diseases, initially the causative factors taken for study will be more in number, but 
the factors have to drop at each stage of their research to find the prime causative factors. In the 
process of factor filtration, the expert’s opinions play a vital role. The role of each causative factor of 
a disease cannot be certainly express but representation using neutrosophic sets makes it possible 
and more meaningful. Thus the integration of FCM with concentric neutrosophic hypergraph will 
help to tackle the difficulties in handling large number of study factors. 
Neutrosophic Sets and Systems, Vol. 35, 2020     234  
 
 
Nivetha et al Exploration of the Factors Causing Autoimmune Diseases using Fuzzy Cognitive Maps with Concentric 
Neutrosophic Hypergraphic Approach 
 
The paper is structured as follows: section 2consists of the methodology in which the algorithm of 
finding optimal decision is presented; section 3 comprises of the adaptation of the proposed model 
to the decision making problem; section 4 discusses the results and the last section summarizes the 
research work. 
2. Methodology and its application  
The steps in making optimal decisions is presented as an algorithm as follows, 
Step 1: The expert’s opinion of the study factors are represented by concentric fuzzy hypergraphs 
with neutrosophic fuzzy sets representations of the envelope. 
Step 2: The score values of the neutrosophic fuzzy sets are determined. 
Step 3:   The factors are ranked based on the score values. 
Step 4:   The core factors are determined based on the ranking positions. 
Step5:   The inter association between the core factors is obtained based on the conventional FCM  
          procedure. 
The case histories of patients belonging to women gender suffering from autoimmune diseases are 
taken as the source of data collection and the factors contributing to the occurrence of auto immune 
disease in women [13] are presented below based on the medical expert’s opinion and data obtained 
from questionnaire.  
F1. Excess presence of VGLL3 (Vestigial Like Family Member 3) in skin cells 
F2. Changes in the gene system 
F3. Exposure to ultraviolet radiation from sunlight 
F4. Acquaintance with organic mercury 
F5. Alteration in food habits 
F6. Gene-Environment interface 
F7. Fluctuations in sex hormones 
F8. Modifications in Nutritional diet  
F9. Post pregnancy impacts 
F10. Genetic vulnerability 
F11. Genetic differences in immunity 
 
 
 
 
 
 
 
 
 
                            Fig.3.1.Concentric Neutrosophic Fuzzy Hypergraphic representation 
Neutrosophic Sets and Systems, Vol. 35, 2020     235  
 
 
Nivetha et al Exploration of the Factors Causing Autoimmune Diseases using Fuzzy Cognitive Maps with Concentric 
Neutrosophic Hypergraphic Approach 
 
The concentric neutrosophic fuzzy hyper envelopes with neutrosophic representations of the 
expert’s opinion are presented below in Table 3.1. 
                                 Table 3.1 Representations of Expert’s opinion 
Experts F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 
E1 (0.3,0.2, 
0.8) 
(0.5,0.2, 
0.3) 
(0.4,0.1, 
0.5) 
(0.3,0.4, 
0.6) 
(0.8,0.1, 
0.2) 
(0.7,0.2, 
0.3) 
(0.7,0.3, 
0.4) 
(0.7,0.2, 
0.3) 
(0.3,0.2, 
0.8) 
(0.5,0.2, 
0.3) 
(0.5,0.2, 
0.3) 
E2 (0.2,0.2, 
0.9) 
(0.4,0.3, 
0.5) 
(0.5,0.2, 
0.3) 
(0.2,0.2, 
0.9) 
(0.7,0.2, 
0.3) 
(0.6,0.2, 
0.3) 
(0.7,0.5, 
0.4) 
(0.6,0.2, 
0.3) 
(0.4,0.3, 
0.5) 
(0.6,0.2, 
0.3) 
(0.8,0.3, 
0.2) 
E3 (0.3,0.4, 
0.6) 
(0.3,0.5, 
0.6) 
(0.4,0.3, 
0.5) 
(0.3,0.2, 
0.8) 
(0.8,0.3, 
0.2) 
(0.9,0.2, 
0.3) 
(0.9,0.1, 
0.3) 
(0.6,0.2, 
0.3) 
(0.3,0.5, 
0.6) 
(0.7,0.3, 
0.4) 
(0.6,0.2, 
0.3) 
E4 (0.5,0.2, 
0.3) 
(0.2,0.2, 
0.9) 
(0.5,0.2, 
0.3) 
(0.4,0.4, 
0.6) 
(0.7,0.1, 
0.2) 
(0.7,0.3, 
0.4) 
(0.6,0.2, 
0.3) 
(0.7,0.1, 
0.2) 
(0.2,0.2, 
0.9) 
(0.6,0.2, 
0.3) 
(0.4,0.3, 
0.5) 
E5 (0.2,0.5 
,0.6) 
(0.3,0.2, 
0.8) 
(0.6,0.2, 
0.3) 
(0.5,0.2, 
0.3) 
(0.6,0.2, 
0.3) 
(0.8,0.1, 
0.2) 
(0.6,0.2, 
0.3) 
(0.9,0.2, 
0.3) 
(0.4,0.4, 
0.6) 
(0.5,0.2, 
0.3) 
(0.7,0.3, 
0.4) 
The score values of the factors are presented in Table 3.2 and it is represented graphically in Fig.3.2 
                               Table 3.2 Score values of the Factors 
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 
0.571 0.571 0.546 0.538 0.667 0.783 0.756 0.573 0.445 0.636 0.667 
7 7 8 9 5 1 2 6 10 3 4 
0
0.2
0.4
0.6
0.8
1
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11
Ranking of the Factors
 
         Fig.3.2 
 
Based on the scores, the following factors are considered as the core factors and their inter 
association is expressed as linguistic variables, which then later quantified by heptagonal fuzzy 
numbers. 
HP1. Alteration in food habits 
HP2. Gene-Environment interface 
Neutrosophic Sets and Systems, Vol. 35, 2020     236  
 
 
Nivetha et al Exploration of the Factors Causing Autoimmune Diseases using Fuzzy Cognitive Maps with Concentric 
Neutrosophic Hypergraphic Approach 
 
 
HP1 
 HP3 
HP2 
 
HP4 
 
HP5 
1 
HP3. Fluctuations in sex hormones 
HP4. Genetic vulnerability 
HP5. Genetic differences in immunity 
The connection matric between the factors, based on the expert’s opinion 
 
 
 
 
 
The modified matrix based on the values of quantification in Table 3.3 
 
 
 
 
 
 
 
 
The interrelationship between the factors is determined by the similar application of FCM 
methodology [9-10] and it is presented graphically in Fig 3.2 
 
 
 
 
 
 
 
 
 
                      Fig.3.2 FCM representation of the inter association of the core factors 
 
 HP1 HP2 HP3 HP4 HP5 
HP1 0 M H L L 
HP2 L 0 M H H 
HP3 L M 0 M L 
HP4 L M H 0 M 
HP5 L M M H 0 
Linguistic  
Variable 
Heptagonal Weight Membership 
value 
Low (0,0.1,0.2,0.3,0.35,0.4,0.45) 0.26 
Medium (0.4,0.45,0.5,0.55,0.6,0.65,0.7) 0.55 
High (0.65,0.7,0.8,0.9,1,1,1) 0.86 
 HP1 HP2 HP3 HP4 HP5 
HP1 0 0.55 0.86 0.26 0.26 
HP2 0.26 0 0.55 0.86 0.86 
HP3 0.26 0.55 0 0.55 0.26 
HP4 0.26 0.55 0.86 0 0.55 
HP5 0.26 0.55 0.55 0.86 0 
Neutrosophic Sets and Systems, Vol. 35, 2020     237  
 
 
Nivetha et al Exploration of the Factors Causing Autoimmune Diseases using Fuzzy Cognitive Maps with Concentric 
Neutrosophic Hypergraphic Approach 
 
4. Results and Discussion 
          Fig. 3.2 clearly states the factor, fluctuations in sex hormone is the core causative factor of auto 
immune diseases. The findings of this research will certainly assist the medical experts to ascertain 
the causes of the auto immune disease in women and give treatment in accordance to it. Hormonal 
imbalance is quite common in the life of the women as they undergo various stages of puberty, 
maternity, menopause, but still proper medications has to be given to avoid the risks of such fatal 
diseases. The representation of the imprecise data in the form neutrosophic sets is the pragmatic 
reflection of the expert’s opinion, as the factors contributing to the diseases are quite uncertain. The 
degree of truth values, indeterminacy and false values are indeed very essential in making optimal 
decisions. 
5. Conclusion 
The proposed decision making tool with the integration of FCM and concentric neutrosophic fuzzy 
hypergraphs is a highly feasible tool to obtain optimal decisions. The difficulty in handling several 
factors in FCM is reduced and this integrated approach facilitate the determination of inter 
association between the factors. This method of decision making can be extended to other kinds of 
concentric fuzzy hypergraphs with various representations. Plithogenic sets representation is the 
future extension of this proposed research work. 
References 
1. Shashi Pratab Singh., Pranay Wal1., Ankita Wal1., Vikas Srivastava., , Ratnakar Tiwari., , Radha Dutt 
Sharma., Understanding autoimmune disease: an update review, IJPTB. 2016,3,51-65. 
2. Kosko B.Fuzzy Cognitive Maps, International Journal of Man-Machine Studies,1986, 24 65-75. 
3. Nivetha Martin, Pradeepa.I., Pandiammal.P., Evolution of Concentric Fuzzy Hypergraph for Inclusive 
Decision Making, International Journal of Engineering and Advanced Technology,2019, 8, 358-362.  
4. Nivetha Martin., Pradeepa.I.,Pandiammal.P., Student’s Low Academic Performance Appraisal Model 
with Hypergraphic Approach in Fuzzy Cognitive Maps , Journal of Information and    Computational 
Science,2019, 9,661-671. 
5. Pradeepa.I., Nivetha Martin, Pandiammal.P., Prioritizing the obstacles in building swipe and touch 
classroom environment using blended method, Journal of Interdisciplinary Cycle Research, 2019, 9, 
383-392. 
6. Smarandache,F.,Neutrosophic set, a generalization of the Intuitionistic Fuzzy Sets, International Journal of 
Pure and Applied Mathematics, 2005,24, 287-297. 
7. Abdel-Basset, M., Mohamed, R., Elhoseny, M., & Chang, V.,Evaluation framework for smart disaster 
response systems in uncertainty environment. Mechanical Systems and Signal Processing, 2020, 145, 
106941. 
8. Abdel-Basset, M., Ali, M., & Atef, A., Uncertainty assessments of linear time-cost tradeoffs using 
neutrosophic set. Computers & Industrial Engineering,2020, 141, 106286. 
9. Abdel-Basset, M., Ali, M., & Atef, A., Resource levelling problem in construction projects under 
neutrosophic environment. The Journal of Supercomputing, 2020,76(2), 964-988. 
10. Abdel-Basset, M., Gamal, A., Son, L. H., & Smarandache, F.,A Bipolar Neutrosophic Multi Criteria 
Decision Making Framework for Professional Selection. Applied Sciences,2020, 10(4), 1202. 
Neutrosophic Sets and Systems, Vol. 35, 2020     238  
 
 
Nivetha et al Exploration of the Factors Causing Autoimmune Diseases using Fuzzy Cognitive Maps with Concentric 
Neutrosophic Hypergraphic Approach 
 
11. R. Das, F. Smarandache and B.C. Tripathy, Neutrosophic fuzzy matrices and some algebraic operation, 
Neutrosophic Sets and Systems, 2020,32,401-409. 
12. Abdel-Basset, M., Mohamed, R., Zaied, A. E. N. H., Gamal, A., & Smarandache, F.,Solving the supply 
chain problem using the best-worst method based on a novel Plithogenic model. In Optimization Theory 
Based on Neutrosophic and Plithogenic Sets,2020, (pp. 1-19). Academic Press. 
13. Autoimmune Disease. Available at http://www.nlm.nih.gov/medlineplus/ autoimmunediseases.html 
(April 2016).  
 
 
Received: Apr 24, 2020.  Accepted: July 14, 2020 
 
 


Exploration of the Factors Causing Autoimmune Diseases using Fuzzy Cognitive Maps with Concentric Neutrosophic Hypergraphic Approach

https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1568&amp;context=nss_journal

Exploration of the Factors Causing Autoimmune Diseases using Fuzzy Cognitive Maps with Concentric Neutrosophic Hypergraphic Approach

Abstract

Similar works

Full text

Available Versions

University of New Mexico