Title of paper:

Distances between intuitionistic fuzzy sets of second type with application to diagnostic medicine

Author(s):

P. A. Ejegwa

Department of Mathematics/Statistics/Computer Science, University of Agriculture, P. M. B. 2373, Makurdi, Nigeria

ejegwa.augustine@uam.edu.ng , ocholohi@gmail.com

I. M. Adamu

Department of Mathematics, Federal University Dutse, P. M. B. 7156, Dutse, Nigeria

idreesmuhammadadam@gmail.com


Published in:

Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 3, pages 53–70

DOI:

10.7546/nifs.2019.25.3.5370

Download:

PDF (180 Kb, Info)

Abstract:

The concept of intuitionistic fuzzy sets of second type (IFSST) generalizes intuitionistic fuzzy sets (IFS) and thus, has many applications in decision making problems. The main feature of IFSST is that it is characterized by three parameters, namely: membership degree, nonmembership degree and degree of indeterminacy in such a way that the sum of the square of each of the parameters is one. The purpose of this paper is to present the axiomatic definition of distance between IFSST, taking into account the three parameters that describe the sets and to investigate numerically, the validity of some distances between intuitionistic fuzzy sets introduced by E. Szmidt and J. Kacprzyk in IFSST environment. Finally, we explore the application of IFSST in diagnostic medicine by employing normalized Hamming distance of IFSST to calculate the distance between patients and diseases, because it provides a reliable distance with respect to other distances. Actually, by using the distance between patients and diseases (both in IFSST values), with recourse to the corresponding symptoms observe in the patients and of the diseases, we determine the illness of the paients. These distances are suggestible to be deployed in solving multicriteria decision making problems.

Keywords:

Diagnostic medicine, Distance measure, Fuzzy set, Intuitionistic fuzzy set, Intuitionistic fuzzy set of second type.

AMS Classification:

20N20, 03E72.

References:

 Atanassov, K. T. (1983). Intuitionistic Fuzzy Sets, VII ITKR Session, Sofia, 2023 June 1983 (Deposed in Centr. Sci.Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6 (in English).
 Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy Set Syst., 20, 87–96.
 Atanassov, K. T. (1989). Geometrical Interpretation of the Elements of the Intuitionistic Fuzzy Objects, Mathematical Foundations of Artificial Intelligence Seminar, Sofia, Preprint IMMFAIS189. Reprinted: Int J Bioautomation, 2016, 20(S1), S27–S42.
 Atanassov, K. T. (1994). New operations defined on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
 Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, PhysicaVerlag, Heidelberg.
 Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets Theory, Springer, Berlin.
 Davvaz, B., & Sadrabadi, E. H. (2016). An application of intuitionistic fuzzy sets in medicine, Int. J. Biomath., 9(3), 1650037 (15 pages).
 De, S. K., Biswas, R., & Roy, A. R. (2001). An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Set Syst., 117(2), 209–213.
 Ejegwa, P. A. (2015). Intuitionistic fuzzy sets approach in appointment of positions in an organization via maxminmax rule, Global J. Sci. Frontier Research: F Math. Decision Sci., 15(6), 1–6.
 Ejegwa, P. A., Akubo, A. J., & Joshua, O. M. (2014). Intuitionistic fuzzzy sets in career determination, J. Info. Computing Sci., 9(4), 285–288.
 Ejegwa, P. A., & Modom, E. S. (2015). Diagnosis of viral hepatitis using new distance measure of intuitionistic fuzzy sets, Intern. J. Fuzzy Mathematical Archive, 8(1), 1–7.
 Ejegwa, P. A., & Onasanya, B. O. (2019). Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process, Notes on Intuitionistic Fuzzy Sets, 25(1), 43–58.
 Ejegwa, P. A., & Onyeke, I. C. (2018). An object oriented approach to the application of intuitionistic fuzzy sets in competency based test evaluation, Ann. Commun. Math., 1(1), 38–47.
 Parvathi, R., & Palaniappan, N. (2004). Some operations on intuitionistic fuzzy sets of second type, Notes on Intuitionistic Fuzzy Sets, 10(2), 1–19.
 Szmidt, E. (2014). Distances and similarities in intuitionistic fuzzy sets, Springer International Publishing, Switzerland, 2014
 Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets, Fuzzy Set Syst., 114, 505–518.
 Szmidt, E., & Kacprzyk, J. (2001). Intuitionistic fuzzy sets in some medical applications, Notes on Intuitionistic Fuzzy Sets, 7(4), 58–64.
 Szmidt, E., & Kacprzyk, J. (2002). An intuitionistic fuzzy set based approach to intelligent data analysis: an application to medical diagnosis. In: Recent Advances in Intelligent Paradigms and Applications, Springer, Berlin, 57–70.
 Szmidt, E., & Kacprzyk, J. (2004). Medical diagnostic reasoning using a similarity measure for intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 10(4), 61–69.
 Szmidt, E., & Kacprzyk, J. (2005). A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In: Lecture Notes in Artificial Intelligence, Vol. 3070, Springer, Berlin, 388–393.
 Todorova, L., Atanassov, K. T., Hadjitodorov, S., & Vassilev, P. (2007). On an intuitionistic fuzzy approach for decisionmaking in medicine (Part 1), Int. J. Bioautomation, 6, 92–101.
 Todorova, L., Atanassov, K. T., Hadjitodorov, S., & Vassilev, P. (2007). On an intuitionistic fuzzy approach for decisionmaking in medicine (Part 2), Int. J. Bioautomation, 7, 64–69.
 Yager, R. R. (2013). Pythagorean fuzzy subsets, In: Proceedings of the Joint IFSAWorld Congress and NAFIPS Annual Meeting, 57–61.
 Zadeh, L. A. (1965) Fuzzy sets, Inform. Control, 8, 338–353.

Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.

