Modified Szmidt and Kacprzyk’s Intuitionistic Fuzzy Distances and their Applications in Decision-making

P. A. Ejegwa; I. C.  Onyeke; B. T.  Terhemen; M. P.  Onoja; A.  Ogiji; C. U.  Opeh

doi:10.46481/jnsps.2022.530

Authors

P. A. Ejegwa
[email protected]
Department of Mathematics, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria
I. C. Onyeke Department of Computer Science, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria
B. T. Terhemen Department of Mathematics, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria
M. P. Onoja Department of Mathematics, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria
A. Ogiji Department of Mathematics, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria
C. U. Opeh Department of Mathematics, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria

Keywords:

Decision-making, Distance measure, Intuitionistic fuzzy set, Pattern recognition, Medical diagnosis

Abstract

Intuitionistic fuzzy models are significant in resolving decision-making. Distance measures under intuitionistic fuzzy environment are reliable techniques deployed to express the application of IFSs. Some approaches of estimating distances between IFSs have been explored by Szmidt and Kacprzyk, where the complete parameters of IFSs are considered. Albeit, the distance operators lack reliability because of certain setbacks. In this paper, we modified Szmidt and Kacprzyk's distance operators between IFSs to enhance reliability in terms of applications. Some theorems are given to substantiate the validity of the modified intuitionistic fuzzy distance operators. Futhermore, decision-making cases of pattern recognition and disease identification are discussed using the Szmidt and Kacprzyk's distances and their improved versions where information are represented in intuitionistic fuzzy pairs. From the study, it is observed that the modified Szmidt and Kacprzyk's distance operators between IFSs yield better results compare to the Szmidt and Kacprzyk's distance operators between IFSs.

Dimensions

REFERENCES

L. A. Zadeh, “Fuzzy sets”, Information and Control 8 (1965) 338.

K. T. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems 20 (1986) 87.

K. T. Atanassov, Intuitionistic fuzzy sets: theory and applications, Physica-Verlag, Heidelberg, 1999.

P. A. Ejegwa, A.M. Onoja & S. N. Chukwukelu, “Application of intuitionistic fuzzy sets in research questionnaire”, Journal of Global Research in Mathematical Archives 2(5) (2014) 51.

E. Szmidt & J. Kacprzyk, “Intuitionistic fuzzy sets in some medical applications”, Notes on Intuitionistic Fuzzy Sets 7(4) (2001) 58.

S. M. Chen, Y. Randyanto & S. H. Cheng, “Fuzzy queries processing based on intuitionistic fuzzy social relational networks”, Information Sciences 327 (2016) 110.

S. K. De, R. Biswas & A. R. Roy, “An application of intuitionistic fuzzy sets in medical diagnosis”, Fuzzy Sets and Systems 117(2) (2001) 209.

P. A. Ejegwa & B.O. Onasanya, “Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process”, Notes on Intuitionistic Fuzzy Sets 25(1) (2019) 43.

P. Liu & S. M. Chen, “Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers”, IEEE Transaction on Cybernetics, 47(9) (2017) 2514.

P. A. Ejegwa, “Novel correlation coefficient for intuitionistic fuzzy sets and its application to multi-criteria decision-making problems”, International Journal of Fuzzy System Applications 10(2) (2021) 39.

P. A. Ejegwa, “Modified and generalized correlation coeffcient between intuitionistic fuzzy sets with applications”, Notes on Intuitionistic Fuzzy Sets 26(1) (2020) 8-22.

P. A. Ejegwa, “An improved correlation coefficient between intuitionistic fuzzy sets and its applications to real-life decision-making problems”, Notes on Intuitionistic Fuzzy Sets 26(2) 1-14.

P. A. Ejegwa & I. C. Onyeke, “Intuitionistic fuzzy statistical correlation algorithm with applications to multi-criteria based decision-making processes”, International Journal of Intelligent Systems 36(3) (2021) 1386-1407.

N. X. Thao, “A new correlation coefficient of the intuitionistic fuzzy sets and its application”, Journal of Intelligent and Fuzzy Systems 35(2) (2018) 1959-1968.

P. A. Ejegwa & I. C. Onyeke, “A novel intuitionistic fuzzy correlation algorithm and its applications in pattern recognition and student admission process”, International Journal of Fuzzy System Applications, 11(1) (2022) https://doi.org/10.4018/IJFSA.285984.

P. A. Ejegwa & I. C. Onyeke, “Medical diagnostic analysis on some selected patients based on modified Thao et al.’s correlation coefficient of intuitionistic fuzzy sets via an algorithmic approach”, Journal of Fuzzy Extension and Applications 1(2) (2020) 130-141.

P. A. Ejegwa, I. C. Onyeke & V. Adah, “An algorithm for an improved intuitionistic fuzzy correlation measure with medical diagnostic application”, Annals of Optimization Theory and Practice 3(3) (2020) 51-66.

N. X. Thao, M. Ali & F. Smarandache, “An intuitionistic fuzzy clustering algorithm based on a new correlation coefficient with application in medical diagnosis”, Journal of Intelligent and Fuzzy Systems 36(1) (2019) 189-198.

H. Garg, “Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process”, Journal of Industrial and Management Optimization 14(4) (2018) 1501-1519.

H. Garg & K. Kumar, “A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application”, Scientia Iranica 25(4) (2018) 2373-2388.

H. Garg & D. Rani, “A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making”, Applied Intelligence DOI: 10.1007/s10489-018-1290-3.

H. Garg & R. Arora, “TOPSIS method based on correlation coefficient for solving decision-making problems with intuitionistic fuzzy soft set information”, AIMS Mathematics 5(4) (2020) 2944-2966.

F. E. Boran & D. Akay, “A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition”, Information Sciences 255(10) (2014) 45-57.

S. M. Chen & C. H. Chang, “A novel similarity measure between Atanassov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition”, Information Sciences 291 (2015) 96-114.

S. M. Chen & Y. Randyanto, “A novel similarity measure between intuitionistic fuzzy sets and its applications”, International Journal of Pattern Recognition and Artificial Intelligence 27(7) (2013) 1350021.

E. Szmidt & J. Kacprzyk, “Medical diagnostic reasoning using a similarity measure for intuitionistic fuzzy sets”, Notes on Intuitionistic Fuzzy Sets 10(4) (2004) 61-69.

P. Burillo & H. Bustince, “Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets”, Fuzzy Sets and Systems 78 (1996) 305-315.

E. Szmidt & J. Kacprzyk, “Distances between intuitionistic fuzzy sets”, Fuzzy Sets and Systems 114 (2000) 505-518.

A. G. Hatzimichailidis, A. G. Papakostas & V. G. Kaburlasos, “A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems”, International Journal of Intelligent Systems 27 (2012) 396-409.

W. Wang & X. Xi, “Distance measure between intuitionistic fuzzy sets”, Pattern Recognition Letters 26 (2000) 2063-2069.

B. Davvaz & E. H. Sadrabadi, “An application of intuitionistic fuzzy sets in medicine”, International Journal of Biomathematics 9(3) (2016) 1650037.

P. A. Ejegwa, A. J. Akubo & O. M. Joshua, “Intuitionistic fuzzy set andits application in career determination via normalized Euclidean distance method”, European Scientific Journal 10(15) (2014) 529-536.

P. A. Ejegwa, A. J. Akubo & O. M. Joshua, “Intuitionistic fuzzy sets in career determination”, Journal of Information and Computing Science 9(4) (2014) 285-288.

I. M. Adamu, “Application of intuitionistic fuzzy sets to environmental management”, Notes on Intuitionistic Fuzzy Sets 27(3) (2021) 40-50.

P. A. Ejegwa, S. N. Chukwukelu & D. E. Odoh, “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.

P. A. Ejegwa & I. C. Onyeke, “An object oriented approach to the application of intuitionistic fuzzy sets in competency based test evaluation”, Annals of Communications in Mathematics 1(1) (2018) 38-47.

K. T. Atanassov, “New operations defined on intuitionistic fuzzy sets”, Fuzzy Sets and Systems 61 (1994) 137-142.

P. Diamond & P. Kloeden, Metric spaces of fuzzy sets theory and applications. Singapore: Word Scientific, 1994.