Intuitionistic Fuzzy Sets and Fuzzy Information Measure in Medical Diagnosis of Cataract
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A Comparative Study of Intuitionistic Fuzzy Sets and Fuzzy Information Measure in Medical Diagnosis of Cataract
Abstraction
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Medical scientific discipline trades with the care of wellness, bar and the intervention of diseases. A major undertaking of medical scientific discipline is to diagnosis. It, nevertheless, is non a direct and simple undertaking at all, because the information available to the doctor about his patient and their medical relationships in general is inherently unsure. In this paper, the construct of intuitionistic fuzzed sets ( IFS ) and fuzzed information step will be used for the betterment of the job. A conjectural instance survey incorporating medical information with assigned grade of rank, non-membership and vacillation index will be considered.
Keywords:Fuzzy Sets, Intuitionistic Fuzzy Sets ( IFS ) , Fuzzy Relations, Fuzzy Information Theory, Medical Information.
Introduction
Medical diagnosing is the art of finding a person’s pathological position from an available set of happening. Medical diagnosing probes are really complex and hard. Fuzzy sets are chiefly used for the qualitative analysis of informations that show the grade of rank and non-membership elements. Losch [ 9 ] suggested the procedure of diagnosing of glaucoma by utilizing fuzzed sets. Adlassing [ 1 ] has applied fuzzed set theory in medical diagnosing. Szmidt [ 10 ] proposes different steps for inuitionistic fuzzed sets. Ahn [ 2 ] used Intuitionistic fuzzed sets for medical diagnosing of concern. Ju Hong [ 6 ] used interval-valued fuzzed sets in back uping medical diagnostic logical thinking. Gupta and Kumar [ 4 ] have applied Sanchez’s method in the medical diagnosing of concern. Kumar and Bharti [ 8 ] used the Sanchez’s method and suggest the diagnosing process of the types of Glaucoma. Besides, Gupta and Prince [ 5 ] have used the Sanchez’s attack in the medical diagnosing of Diabetes. In this system, the physician uses his medical cognition to deduce a diagnosing from the symptoms displayed by the patient, his research lab trials consequences and medical history. Cataract is the most common cause of sightlessness and is conventionally treated with surgery. Ocular loss occurs because opacification of the lens focused on the retina at the dorsum to the oculus. The individuals enduring from cataract commonly experience such as: trouble in appreciating colourss and alterations in contrast, driving, reading and acknowledging faces and experience jobs get bying with blaze from bright visible radiations. In this paper, we describe an effort to supply a mathematical theoretical account of the procedure to name the types of cataract by utilizing IFS theory and Shannon’s Entropy Measure in the signifier of intervention recommendation system. We besides compare the consequences of these two methods. There are no warning marks or symptoms of cataract. A comprehensive medical history is of import in placing the disease. There are many types of cataract but the major types are as: atomic sclerosed cataract ( due to natural aging ) , cortical cataract ( due to diabetic ) , posterior sub-capsular cataract ( due to utilize of steroids for long term ) , radiation cataract ( due to ultraviolet visible radiation ) and traumatic cataract ( due to direct hurt or injury ) . The of import factors which influence the disease are as: age, household background, medical jobs, steroids, exposure to the Sun, X raies or radiation interventions, smoke and intoxicant etc. Based on the available information, a doctor has to happen a list of diagnostic possibities for the patient. The proposed process is illustrated as: foremost, we set up IF relation between patients and symptoms of cataract with assigned grade of rank and non-membership elements as explained in tabular array ( 1.1 ) . Second, we set up IF relation between symptoms of cataract and the types of cataract with assigned grade of rank and non-membership elements as explained in tabular array ( 1.2 ) . Finally, we determine a new step for diagnosing of the type of cataract on the footing of max-min-max composing of IF dealingss as explained in tabular array ( 1.3 ) . The highest weight for each patient from possible diagnosing gives the solution as explained in tabular array ( 1.4 ) . We besides use the Fuzzy Information Measure of information theory for the intent of comparing, in this diagnosing process as given in tabular array ( 1.5 ) .
Brief Introduction to Intuitionistic Fuzzy Sets ( IFS ) and Intuitionistic Fuzzy Relations ( IFR )
Intuitionistic fuzzy sets ( IFS ) , developed by Atanassov [ 3 ] is a powerful tool to cover with vagueness. There are some state of affairss where fuzzy set theory is non applicable in that instance we use the Intuitionistic fuzzy set ( IFS ) theory.
For a fixed set X, IFS of A is defined as:
, where U_{A}_{}_{}( ten ) : Ten i‚® [ 0, 1 ] and V_{A}_{}( ten ) : Ten i‚® [ 0, 1 ]
defines the grade of rank and grade of non-membership of the component tenTen to the set A. Further szmidt [ 11 ] introduces another map viz. intuitionstic index or hesitance gradefor each component ten in a finite set X.
For every tenTen, 0U_{A}( ten ) + V_{A}( ten )1 and the sumis called the intuitionistic index or vacillation index, which may necessitate to rank value, non-membership value or both.
Again, allow A be an IFS of the set X and allow R be an IF relation from X i‚® Y, so max-min-max composing of IFS X with the IF relation R ( X i‚® Y ) is defined as B = R o A with rank and non-membership map defined as:
and
LetS = { s_{1}, s_{2}…….s_{m}} ; D = { vitamin D_{1}, vitamin D_{2}…….d_{N}} ; P = { P_{1}, P_{2}…….p_{Q}_{}} ; be the finite set of symptoms, types of diseases and patients severally.
Harmonizing to Biswas [ 7 ] , two fuzzed dealingss Q and R are defined as:
Q = { & A ; lt ; ( P, s ) , u_{Q}( P, s ) , V_{Q}( P, s ) & A ; gt ; | ( P, s )P ? S }
R = { & A ; lt ; ( s, vitamin D ) , u_{Roentgen}( s, vitamin D ) , V_{Roentgen}( s, vitamin D ) & A ; gt ; | ( s, vitamin D )S ? D } ,
Where U_{Q}( P, s ) indicate the grade to which the symptom s appear in the patient P and V_{Q}( P, s ) indicate the grade to which the symptom s does non look in the patient P.
Similarly u_{Roentgen}( s, vitamin D ) indicate the grade to which the symptom s confirm the disease vitamin D and V_{Roentgen}( s, vitamin D ) indicate the grade to which the symptom s does non corroborate the disease vitamin D.
The composing T of IFR R and Q ( T = R o Q ) describe the province of patient P_{I}in footings of the diagnosing of disease cataract from P to D given by rank and non-membership as:
and
From Q and R, one may finish new step of IFR T for which, in general the diagnostic labels of patient P for any disease vitamin D such that the followers is to be satisfied:
( I ) Second_{Thymine}_{}= U_{Thymine}– V_{Thymine}*is greatest and ( two ) The equality T = R o Q is retained.
This step of T will interpret the higher grade of association of symptoms every bit good as lower grades of intuitionistic index to the diagnosing. If there is about equal values for different diagnosing in T is obtained, we consider the instance for which intuitionistic index is least.
Case Study
Let us analyze the process by taking a conjectural instance survey as:
Let P = { P_{1}, P_{2}, P_{3}, P_{4,}P_{5}} be the set of patients and S = { S_{1}, S_{2,}Second_{3,}Second_{4,}Second_{5}} be the set of symptoms present in the patients that may impact.
Now let the IFR: Q ( P i‚® S ) is given by
Table – 1.1
Q |
Second_{1} |
Second_{2} |
Second_{3} |
Second_{4} |
Second_{5} |
|||||
Patients |
U_{Q} |
V_{Q} |
U_{Q} |
V_{Q} |
U_{Q} |
V_{Q} |
U_{Q} |
V_{Q} |
U_{Q} |
V_{Q} |
Phosphorus_{1} |
0.6 |
0.2 |
0.7 |
0.2 |
0.5 |
0.4 |
0.4 |
0.0 |
0.0 |
0.5 |
Phosphorus_{2} |
0.3 |
0.4 |
0.4 |
0.7 |
0.2 |
0.5 |
0.5 |
0.1 |
0.6 |
0.2 |
Phosphorus_{3} |
0.5 |
0.5 |
0.2 |
0.1 |
0.6 |
0.3 |
0.3 |
0.6 |
0.3 |
0.7 |
Phosphorus_{4} |
0.7 |
0.1 |
0.0 |
0.9 |
0.1 |
0.1 |
0.1 |
0.3 |
0.1 |
0.4 |
Phosphorus_{5} |
0.1 |
0.8 |
0.9 |
0.0 |
0.3 |
0.5 |
0.5 |
0.4 |
0.8 |
0.2 |
Now D = { Nuclear Sclerotic Cataract, Cortical Cataract, Posterior Subcapsular Cataract, Radiation Cataract, Traumatic Cataract, } be the set of diseases due to which the patient may endure.
Now suppose the IFR: R ( Si‚®D ) is given by
Table – 1.2
Roentgen |
Nuclear Sclerotic Cataract |
Cortical Cataract |
Posterior Subcapsular Cataract |
Radiation Cataract |
Traumatic Cataract |
|||||
Symptoms |
U_{Roentgen} |
V_{Roentgen} |
U_{Roentgen} |
V_{Roentgen} |
U_{Roentgen} |
V_{Roentgen} |
U_{Roentgen} |
V_{Roentgen} |
U_{Roentgen} |
V_{Roentgen} |
Second_{1} |
0.3 |
0.3 |
0.8 |
0.1 |
0.1 |
0.9 |
0.7 |
0.2 |
0.0 |
0.1 |
Second_{2} |
0.2 |
0.7 |
0.5 |
0.5 |
0.6 |
0.1 |
0.4 |
0.0 |
0.3 |
0.3 |
Second_{3} |
0.8 |
0.2 |
0.4 |
0.3 |
0.2 |
0.2 |
0.1 |
0.8 |
0.1 |
0.4 |
Second_{4} |
0.6 |
0.3 |
0.2 |
0.7 |
0.0 |
0.5 |
0.4 |
0.1 |
0.4 |
0.6 |
Second_{5} |
0.5 |
0.4 |
0.8 |
0.0 |
0.4 |
0.4 |
0.2 |
0.6 |
0.3 |
0.7 |
Now the composing T = R o Q is as follows:
Table – 1.3
Thymine |
Nuclear Sclerotic Cataract |
Cortical Cataract |
Posterior Subcapsular Cataract |
Radiation Cataract |
Traumatic Cataract |
|||||
Patients |
U_{Q} |
V_{Q} |
U_{Q} |
V_{Q} |
U_{Q} |
V_{Q} |
U_{Q} |
V_{Q} |
U_{Q} |
V_{Q} |
Phosphorus_{1} |
0.4 |
0.3 |
0.6 |
0.2 |
0.6 |
0.3 |
0.6 |
0.1 |
0.3 |
0.2 |
Phosphorus_{2} |
0.7 |
0.2 |
0.6 |
0.2 |
0.4 |
0.2 |
0.4 |
0.1 |
0.4 |
0.4 |
Phosphorus_{3} |
0.3 |
0.5 |
0.5 |
0.5 |
0.3 |
0.6 |
0.5 |
0.5 |
0.3 |
0.5 |
Phosphorus_{4} |
0.8 |
0.2 |
0.7 |
0.1 |
0.2 |
0.2 |
0.7 |
0.2 |
0.4 |
0.1 |
Phosphorus_{5} |
0.5 |
0.3 |
0.8 |
0.2 |
0.6 |
0.1 |
0.4 |
0.0 |
0.3 |
0.3 |
Now we Calculate S_{Thymine}
Table – 1.4
Second_{Thymine} |
Nuclear Sclerotic Cataract |
Cortical Cataract |
Posterior Subcapsular Cataract |
Radiation Cataract |
Traumatic Cataract |
Phosphorus_{1} |
0.31 |
0.56 |
0.57 |
0.57 |
0.20 |
Phosphorus_{2} |
0.68 |
0.56 |
0.32 |
0.35 |
0.32 |
Phosphorus_{3} |
0.20 |
0.50 |
0.24 |
0.50 |
0.20 |
Phosphorus_{4} |
0.80 |
0.68 |
0.08 |
0.68 |
0.35 |
Phosphorus_{5} |
0.44 |
0.80 |
0.57 |
0.40 |
0.18 |
From the tabular array ( 1.4 ) , we conclude that patients P_{4}and P_{2}are enduring from the Nuclear Sclerotic cataract, patient P_{5}is enduring from Cortical cataract, patient P_{1}is set uping from Posterior Subcapsular cataract and Radiation cataract, while the patient P_{3}is enduring from the Cortical and Radiation cataract.
Again here we apply the Shannon’s information step as intuitionistic fuzzed step in the signifier of
++,
Wheredenotes the grade of rank anddenotes the grade of non-membership anddenotes the vacillation index. But in instance of Shannon’s information step the lower limit weight for each patient will be consider as the solution. We apply this information step on the values of tabular array ( 1.3 ) and obtained the consequences as table ( 1.5 ) as:
Table – 1.5
Second |
Nuclear Sclerotic Cataract |
Cortical Cataract |
Posterior Subcapsular Cataract |
Radiation Cataract |
Traumatic Cataract |
Phosphorus_{1} |
0.47 |
0.41 |
0.38 |
0.38 |
0.44 |
Phosphorus_{2} |
0.34 |
0.41 |
0.45 |
0.40 |
0.45 |
Phosphorus_{3} |
0.44 |
0.30 |
0.38 |
0.30 |
0.44 |
Phosphorus_{4} |
0.21 |
0.34 |
0.41 |
0.34 |
0.40 |
Phosphorus_{5} |
0.44 |
0.21 |
0.38 |
0.29 |
0.47 |
From the tabular array ( 1.5 ) , once more we get the same consequence as tabular array ( 1.4 ) , we find that patients P_{4}and P_{2}are enduring from the Nuclear Sclerotic cataract, patient P_{5}is enduring from Cortical cataract, patient P_{1}is set uping from Posterior Subcapsular cataract and Radiation cataract, while the patient P_{3}is enduring from the Cortical and Radiation cataract.
Decision
Both of the processs that we have used give same consequences in the medical diagnosing of cataract as shown in tabular arraies ( 1.4 ) and ( 1.5 ) . These methods may turn out effectual tool for determination devising jobs and can be extended to medical diagnosing of some other type of diseases and determination devising jobs.
Mentions
- Adlassing K. P. ; Fuzzy set theory in medical diagnosing. IEEE Trans. on Systems, Man, and Cybernetics SMC ; Vol. 16, pp 260-265, 1986.
- Ahn J. Y. , Han K. S. , Oh S. Y. and Lee C. D. ; An application of interval-valued intuitionistic fuzzy sets for medical diagnosing of concern. Int. J. Inn. Comp. Info. Cont. 7 ( 5 ( B ) ) , pp 2755-2762, 2011.
- Atanassov K. ; Intuitionistic fuzzy sets. Fuzzy Sets and Systems ( 20 ) , pp 87-96.
- Gupta P. and Kumar V. ; Application of intuitionistic fuzzed sets in medical diagnosing of concern. In the Proceeding of 4^{Thursday}International Conference on Quality, Reliability and Infocom Technology, pp 356-359, 2011.
- Gupta P. , Prince and Kumar V. ; An application of intuitionistic fuzzed sets and fuzzed dealingss for medical diagnosing of diabetes. In the Proceedings of International Conference on Recent Trends in Material and Devices, pp 193-197, 2013.
- Ju Hong-mei and Wang Feng-Ying ; A similarity step for interval-valued fuzzed sets and its applications in back uping medical diagnostic logical thinking. In the Tenth International Symposium on Operation Research and Its Applications, pp 251-257, 2011.
- Kumar S. , Biswas R. and Roy A. R. ; An application of intuitionistic fuzzed sets in medical diagnosing. Fuzzy Sets and Systems, Vol. 117 pp 209-213, 2001.
- Kumar V. , Bharti I. and Sharma Y. K. ; Fuzzy diagnosing process of the types of glaucoma. International Journal of Applied Information Systems, Vol. 1, No. 6, 2012.
- Losch B. ; Application of fuzzed sets to the diagnosing of glaucoma. In 18^{Thursday}Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1997.
- Szmidt E. and Kacprzyk J. ; A step for inuitionistic fuzzed sets. Fuzzy Sets and Systems, Vol. 121, 2003.
- Szmidt E. , Kacprzyk J. ; New steps of information for intuitionistic fuzzed sets. Ninth International Conference on IFS_{s}; 2005.
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