An Application of Pentagonal Valued Hesitant Fuzzy Set in Medical Diagnosis

 

M. Muthumeenakshi

Department of Commerce, School of Social Sciences and Languages, VIT University, Vellore-632014. India.

 

ABSTRACT:

This paper provides a decision-making method with linguistic assessments using pentagonal fuzzy numbers. It is proposed to solve the multi criteria decision-making algorithm based on expected values of pentagonal valued hesitant fuzzy sets in which the criteria weights are completely unknown and the criteria values for an alternative can be given by the linguistic values by a group of decision makers to transform them into pentagonal valued hesitant fuzzy sets. Finally, a practical example in a medical diagnosis situation is analyzed to demonstrate the application of the proposed decision-making method.

 

 

 

 

1. INTRODUCTION:

After Zadeh¹ initiated the notion of fuzzy set in 1965, several authors apply fuzzy logic in medical diagnosis. Nguyen Hoang Phuong² et al. used fuzzy logic in the broad sense to formalize approximate reasoning in medical systems in 2001. Chetia³ et. al discussed an application of interval valued fuzzy soft set in medical diagnosis. Also Shapu Ren⁴ et. al gave a Multicriteria decision-making method using cosine similarity measures for reduct fuzzy sets of interval-valued fuzzy sets.

 

The generalization of fuzzy set is an intuitionistic fuzzy set which was introduced by Atanassov⁵ in 1986. It has most significant in handling vagueness. Ejegwa⁶  et  al. dealt some application of intuitionistic fuzzy set in diagnostic medicine using some distance measures. In 2015, Ismat Beg⁷ et al. proposed a new approach for medical diagnosis by using trapezoidal valued intuitionistic fuzzy relations.

 

Vasile Patrascu⁸ gave a new notion called penta-valued fuzzy set with five scalar functions: the strong membership, the weak membership, the uncertainty, the weak non-membership and the strong non-membership which represents an extension for the intuitionistic fuzzy sets. In 2010, Torra⁹, dealt Hesitant fuzzy sets. Recently Manimaran¹⁰ et. al reviewed fuzzy environmental study in medical diagnosis.

 

Motivated by these, this paper illustrates an application of pentagonal valued hesitant fuzzy sets in medical decision making situation. The rest of the paper is organized as follows. Section 2 introduces some concepts related to fuzzy set, hesitant fuzzy set, pentagonal fuzzy number and pentagonal valued hesitant fuzzy sets. Section 3 proposed a multicriteria decision-making algorithm based on expected values for pentagonal valued hesitant fuzzy sets, which deals with the linguistic assessments and completely unknown criteria weights. In Section 4, an example is given with an application of pentagonal valued hesitant fuzzy set in Medical Diagnosis to demonstrate the proposed decision-making algorithm. Finally, some final remarks of the proposed decision-making method and further research are given in Section 5.

 

Table 1. Linguistic values of pentagonal valued hesitant fuzzy element for linguistic terms

Linguistic terms	Linguistic values of PVHFE
Very low(VL)	(0.0, 0.0, 0.0, 0.1, 0.2)
Low(L)	(0.0, 0.0, 0.1, 0.2, 0.3)
Fairly low(FL)	(0.0, 0.1, 0.2, 0.3, 0.4)
Fair(F)	(0.1, 0.2, 0.3, 0.4, 0.5)
Fairly high(FH)	(0.2, 0.3, 0.4, 0.5, 0.7)
High(H)	(0.3, 0.5, 0.6, 0.7, 0.8)
Very high(VH)	(0.5, 0.6, 0.7, 0.9, 1.0)

 

 

4. DIAGNOSING THE HEALTH ISSUES OF WORKING WOMEN:

In this section, a practical case for a multicriteria decision-making problem of alternatives is used as the demonstration of the application of the proposed multicriteria decision-making method in a realistic scenario, as well as the implementation process of the proposed method.

 

Most of the working women due to work environment, they get some serious diseases. They want to balance the work and life. Work Life Balance (WLB) is a critical task now-a-days. All sectors are like private corporates. It causes imbalance in work and life. Due to the imbalances of work and life, the diseases such as Head ache (C1), Diabetic(C2), Mental fatigue(C3) and High blood pressure(C4) easily occupy in their body and constantly irritates them. Sometimes it causes sudden death to their life. But it is very difficult to identify particular reason for these diseases. The experts of medical diagnosis expressed that the major reason for these diseases are depression(A1), mental stress(A2) and irregular diet(A3). Taking consideration of these criteria the probabilities of getting the diseases have been found out. For this purpose, fifty women respondents those who are in the job and also have the symptoms of the diseases have been interviewed through snow ball sampling technique.

Based on their responses,the ratings of each symptom with respect to diseases are given in the Table 2. These values are taken as linguistic variable for the purpose of the analysis.

 

Table 2

	D1	D2	D3	D4
A1	VH H H VH	F FL F L	VH VH H VH	VH H VH H
A2	VH H H FH	FH F F FH	VH H H FH	H FH H H
A3	H H VH FH	FL FL L L	FL F FH FL	H H FH F

 

5. CONCLUSION:

Hesitant fuzzy set theory is a newly emerging mathematical tool to deal with uncertain problems. This paper proposed a hesitant fuzzy set based on the combination of pentagonal fuzzy number. Then, we presented a decision-making method based on expected values for pentagonal valued hesitant fuzzy sets, which can deal with the decision-making problem with linguistic assessments and completely unknown criteria weights. According to the numerical example, we can conclude that the proposed decision-making method can be applied into many real selection and decision problems such as supplier selection, place selection, and conceptual design scheme decision. So further researches can combine other membership functions with hesitant fuzzy sets to propose some novel hesitant fuzzy sets and decision-making methods which have different forms.

 

6. REFERENCES:

1.     Zadeh. L. A., Fuzzy set, Information and Control, 8(1965), 338–353.

2.     Nguyen Hoang Phuong and Vladik Kreinovich, Fuzzy logic and its applications in medicine, International Journal of Medical Informatics 62 (2001) 165–173.

3.     Chetia, B. and Das, P.K, An application of interval valued fuzzy soft set in medical diagnosis, Int. J. Contempt. Math. Science, 5 (38) 2010, 1887-1894.

4.     Shapu Ren and Jun Ye, Multicriteria decision-making method using cosine similarity measures for reduct fuzzy sets of  interval-valued fuzzy sets, Journal of Computers,    9 (1) (2014), 107-111.

5.     Atanassov. K.,  Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986) 87–96.

6.     Ejegwa, P. A., Chukwukelu. S. N. and Odoh. D. E., Test of Accuracy of Some Distance Measures Use in the Application of Intuitionistic Fuzzy Sets in Medical Diagnosis, Journal of Global Research in Mathematical Archives, 2(5) (2014),55-60.

7.     Ismat Beg and Tabasam Rashid, A system for medical diagnosis based on intuitionistic fuzzy relation, Notes on Intuitionistic Fuzzy Sets, 21(3) (2015), 80–89.

8.     VasilePatrascu, Penta-Valued Fuzzy Set, IEEE International Conference on Fuzzy Systems, 2007, DOI: 10.1109/FUZZY.2007.4295354

9.     Torra. V., “Hesitant fuzzy sets,” International Journal of Intelligent Systems,  25(6) (2010), 529–539.

10.   Manimaran. A., Chandrasekaran. V.M. and Praba. B., A Review of Fuzzy Environmental Study in Medical Diagnosis System, Research J. Pharm. and Tech. 9(2) 2016, 177-184.

11.   Xia . M. and Xu. Z., “Hesitant fuzzy information aggregation in decision making,” International Journal of Approximate Reasoning, 52(3) (2011),395-407.

12.   Pathinathan. T. and Ponnivalavan. K., Pentagonal Fuzzy Number, International Journal of Computing Algorithm, 3(2014), 1003-1005.

13.   Herrera, F. and E. Herrera-Viedma, “Linguistic decision analysis: steps for solving decision Problems under linguistic information”, Fuzzy Sets and Systems, 115(2000). 67-82.

14.   Rodriguez. R.M., Martinez. L. and Herrera. F., “Hesitant fuzzy linguistic term sets for decision making”, IEEE Transactions on Fuzzy Systems, 20(2012), 109-119.

 

 

 

Accepted on 05.07.2016        © RJPT All right reserved

Research J. Pharm. and Tech 2016; 9(10):1823-1826.