In the present work, we consider the global optimization problem of obtaining distance between two subsets of a fuzzy metric space and solve it by fixed point methodology through the determination of two different pairs of points each of which determines the fuzzy distance. We use fuzzy weak coupled contractions for that purpose. The problem is well studied in metric spaces where it is known as a proximity point problem. We use geometric notions in fuzzy metric spaces. Our result is valid for arbitrary continuous t-norms associated with the fuzzy metric space. The problem is solved by reducing it to that of finding optimal approximate solution of a fuzzy coupled fixed point equation. We also obtain a coupled fixed point result as a consequence of our main theorem. The main result is illustrated with an example.
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Conflicts of interest
The corresponding author is a senior research fellow sponsored by UGC, India, and therefore, he is grateful to UGC for the support. At the same time, all the authors are thankful to IIEST, Shibpur, India, for their support. There is no conflict of interest among the authors.
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Saha, P., Guria, S., Choudhury, B.S. et al. Solution of a fuzzy global optimization problem by fixed point methodology using a weak coupled contraction. Soft Comput 24, 4121–4129 (2020). https://doi.org/10.1007/s00500-019-04179-w
- Fuzzy metric space
- Coupled contraction
- Coupled proximity point
- Fuzzy P-property
- Global optimality