Fuzzy points relation with nonfuzzy or crisp set
*Sopan Raosaheb ShindeCorresponding authorscholarswapnil@gmail.comDepartment of Computer EngineeringDr. D. Y. Patil College of Engineering and InnovationPune, Maharashtra, 410507, IndiaView full profile → , Kalyani Vishal Dokejivansagharsh@gmail.comDepartment of Engineering Science and HumanitiesSandip Institute of Technology and Research Centre (SITRC)Mahiravani Trimbak Road, Nashik, Maharashtra, 422213, IndiaView full profile → , Santosh Dnyandev Jadhavsdjmaths23@gmail.comDepartment of General EngineeringN. K. Orchid College of Engineering and TechnologySolapur, Maharashtra, 413002, IndiaView full profile →
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- Received:
- 01 Feb 2026
- Published Online:
- 25 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2631
- Pages:
- 2463–2471
Abstract
This Manuscript explores fixed point theory in both fuzzy and non-ℱℳ𝒮s, focusing on two distinct contractive mappings and their associated fixed point theorems. We redefine ℱℳ𝒮s by employing fuzzy constant with real numbers, providing a approach that differs from previous definitions.
It is shown that any corresponding ℱℳ𝒮 that preserves completeness. The findings highlight significance of mappings in establishing fixed point results and shows how the nature of these mappings influences the proof and application of fixed point theorems.
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References
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