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Pragmatic results in Taiwan education system based IVFG & IVNG

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Abstract

An interval-valued fuzzy graph (IVFG) and degree of vertices have been applied for performance evaluation in an educational system. The approach is mainly developed based on real membership values of vertices of an IVFG. In this manuscript, some definitions of generalized fuzzy graphs and neutrosophic graphs structures are improved. First, we have concentrated to improve the existing definitions for union and join of two IVFG’s, complete IVFG with supporting examples. Then, their modified version is developed. Secondly, the modified version of interval-valued neutrosophic graph (IVNG) is given. Third, an algorithm and a flowchart of the proposed method are described. Fourth, the generalized form of complete and strong IVNG is given with examples. Finally, a real-life application using interval-valued fuzzy graph in education system in Taiwan is exhibited.

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Abbreviations

FG:

Fuzzy graph

IVFG:

Interval-valued fuzzy graph

IVNG:

Interval-valued neutrosophic graph

TWAEA:

Taiwan Assessment and Evaluation Association

\(\mu ^l_A\) :

Lower bound of membership value of vertex in IVFG

\(\mu ^h_A\) :

Upper bound of membership value of vertex in IVFG

\(\mu ^l_B\) :

Lower bound of membership value of edge in IVFG

\(\mu ^h_B\) :

Upper bound of membership value of edges in IVFG

\(S^l, I^l, D^l\) :

Lower bounds of membership, neutral & non-membership values of vertices of IVNG, respectively

\(S^u, I^u, D^u\) :

Upper bounds of membership, neutral & non-membership values of vertices of IVNG, respectively

\({\hat{S}}^l, {\hat{I}}^l, {\hat{D}}^l\) :

Lower bounds of membership, neutral & non-membership values of edges of IVNG, respectively

\({\hat{S}}^u, {\hat{I}}^u, {\hat{D}}^u\) :

Upper bounds of membership, neutral & non-membership values of edges of IVNG, respectively

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Acknowledgements

The first author is thankful to the Department of Higher Education, Science and Technology and Biotechnology, Government of West Bengal, India, for the award of Swami Vivekananda merit-cum-means scholarship (Award No. 52-Edn (B)/5B-15/2017 dated 07/06/2017) to meet up the financial expenditure to carry out the research work. The third author is supported by Research Council Faroe Islands and University of the Faroe Islands. The authors are grateful to the learned reviewers for their valuable comments and suggestions to improve the quality of the article.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721 102, India

    Soumitra Poulik & Ganesh Ghorai

  2. Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100, Tórshavn, Faroe Islands

    Qin Xin

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  1. Soumitra Poulik
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  2. Ganesh Ghorai
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  3. Qin Xin
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Correspondence to Ganesh Ghorai.

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Poulik, S., Ghorai, G. & Xin, Q. Pragmatic results in Taiwan education system based IVFG & IVNG. Soft Comput 25, 711–724 (2021). https://doi.org/10.1007/s00500-020-05180-4

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