Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions

Maysaa Al-Qurashi; Mohammed Shehu Shagari; Saima Rashid; Y. S. Hamed; Mohamed S. Mohamed; Maysaa Al-Qurashi; Mohammed Shehu Shagari; Saima Rashid; Y. S. Hamed; Mohamed S. Mohamed

doi:10.3934/math.2022022

AIMS Mathematics

2022, Volume 7, Issue 1: 315-333. doi: 10.3934/math.2022022

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Research article

Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions

1.
Department of Mathematics, King Saud University, P.O.Box 22452, Riyadh 11495, Saudi Arabia
2.
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Nigeria
3.
Department of Mathematics, Government College University, Faisalabad, Pakistan
4.
Department of Mathematics, Faculty of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 28 July 2021 Accepted: 08 October 2021 Published: 12 October 2021
MSC : 46S40, 47H10, 54H25

In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of $ b $-metric spaces are examined. A few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every functional inclusion is a subset of an appropriate space. In this direction, intuitionistic fuzzy fixed point problem involving $ (\alpha, \beta) $-level set of an intuitionistic fuzzy set-valued map is initiated. Moreover, novel sufficient criteria for existence of solutions to an integral inclusion are investigated to indicate a possible application of the ideas presented herein.
- intuitionistic fuzzy set,
- intuitionistic fuzzy fixed point,
- $ b $-metric space,
- Ulam-Hyers stability,
- integral inclusion
Citation: Maysaa Al-Qurashi, Mohammed Shehu Shagari, Saima Rashid, Y. S. Hamed, Mohamed S. Mohamed. Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions[J]. AIMS Mathematics, 2022, 7(1): 315-333. doi: 10.3934/math.2022022

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Abstract

In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of $ b $-metric spaces are examined. A few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every functional inclusion is a subset of an appropriate space. In this direction, intuitionistic fuzzy fixed point problem involving $ (\alpha, \beta) $-level set of an intuitionistic fuzzy set-valued map is initiated. Moreover, novel sufficient criteria for existence of solutions to an integral inclusion are investigated to indicate a possible application of the ideas presented herein.

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