Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals

Muhammad Bilal Khan; Hari Mohan Srivastava; Pshtiwan Othman Mohammed; Dumitru Baleanu; Taghreed M. Jawa; Muhammad Bilal Khan; Hari Mohan Srivastava; Pshtiwan Othman Mohammed; Dumitru Baleanu; Taghreed M. Jawa

doi:10.3934/math.2022089

AIMS Mathematics

2022, Volume 7, Issue 1: 1507-1535. doi: 10.3934/math.2022089

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Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals

1.
Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
2.
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
5.
Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy
6.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
7.
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, TR-06530, Ankara
8.
Turkey Institute of Space Sciences, P.O. Box, MG-23, R-76900 Magurele-Bucharest, Romania
9.
Department of Mathematics and Statistics, College of Sciences, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 15 August 2021 Accepted: 17 October 2021 Published: 27 October 2021
MSC : 26A33, 26A51, 26D10

The objective of the authors is to introduce the new class of convex fuzzy-interval-valued functions (convex-FIVFs), which is known as $ p $-convex fuzzy-interval-valued functions ($ p $-convex-FIVFs). Some of the basic properties of the proposed fuzzy-interval-valued functions are also studied. With the help of $ p $-convex FIVFs, we have presented some Hermite-Hadamard type inequalities ($ H-H $ type inequalities), where the integrands are FIVFs. Moreover, we have also proved the Hermite-Hadamard-Fejér type inequality ($ H-H $ Fejér type inequality) for $ p $-convex-FIVFs. To prove the validity of main results, we have provided some useful examples. We have also established some discrete form of Jense's type inequality and Schur's type inequality for $ p $-convex-FIVFs. The outcomes of this paper are generalizations and refinements of different results which are proved in literature. These results and different approaches may open new direction for fuzzy optimization problems, modeling, and interval-valued functions.
Citation: Muhammad Bilal Khan, Hari Mohan Srivastava, Pshtiwan Othman Mohammed, Dumitru Baleanu, Taghreed M. Jawa. Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals[J]. AIMS Mathematics, 2022, 7(1): 1507-1535. doi: 10.3934/math.2022089

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Abstract

The objective of the authors is to introduce the new class of convex fuzzy-interval-valued functions (convex-FIVFs), which is known as $ p $-convex fuzzy-interval-valued functions ($ p $-convex-FIVFs). Some of the basic properties of the proposed fuzzy-interval-valued functions are also studied. With the help of $ p $-convex FIVFs, we have presented some Hermite-Hadamard type inequalities ($ H-H $ type inequalities), where the integrands are FIVFs. Moreover, we have also proved the Hermite-Hadamard-Fejér type inequality ($ H-H $ Fejér type inequality) for $ p $-convex-FIVFs. To prove the validity of main results, we have provided some useful examples. We have also established some discrete form of Jense's type inequality and Schur's type inequality for $ p $-convex-FIVFs. The outcomes of this paper are generalizations and refinements of different results which are proved in literature. These results and different approaches may open new direction for fuzzy optimization problems, modeling, and interval-valued functions.

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