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Integration of compact set-valued functions [PDF]

Pacific Journal of Mathematics, 1975
provided by applying the McShane ^-integral. This integral is a Riemann-type integral and includes the Bochner, Lebesgue and other types of integrals, and by using Riemann sums it avoids deep measure theory. Thus, the ^-integral of set-valued functions contains other types of integrals such as the Hukuhara and Debreu integrals. Generalizations of known
Artstein, Zvi, Burns, John A.
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(α, β, γ)-Equalities of single valued neutrosophic sets [PDF]

Neutrosophic Sets and Systems, 2018
The single valued neutrosophic set (SVNS) is a subclass of neutrosophic set, which can describe and handle indeterminate information and inconsistent information. Since a SVNS is characterized independently by three functions: a truth-membership function,
Songsong Dai
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Pentapartitioned Neutrosophic Soft Set with Interval Membership [PDF]

Neutrosophic Sets and Systems
In this article, the concept of Interval valued pentapartitioned neutrosophic soft set (IVPNSS) has been introduced, which is a hybrid method by combining Pentapartitioned Neutrosophic set and Interval valued soft set.
Mithun Datta, Kalyani Debnath , Surapati Pramanik   +2 more
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Interval Subsethood Measures with Respect to Uncertainty for the Interval-Valued Fuzzy Setting

International Journal of Computational Intelligence Systems, 2020
In this paper, the problem of measuring the degree of subsethood in the interval-valued fuzzy setting is addressed. Taking into account the widths of the intervals, two types of interval subsethood measures are proposed.
Barbara Pękala, Urszula Bentkowska, Mikel Sesma-Sara, Javier Fernandez, Julio Lafuente, Abdulrahman Altalhi, Maksymilian Knap, Humberto Bustince, Jesús M. Pintor   +8 more
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Ekeland's Variational Principle for Set-Valued Functions [PDF]

SIAM Journal on Optimization, 2011
The authors extend Ekeland's variational principle to the case of set-valued mappings by using a set of directions and some particular partial orders related to it. Then, as an application they establish some sufficient conditions for the existence of an error bound of a finite system of inequalities of lower semicontinuous functions on a Banach space.
C. G. Liu, K. F. Ng
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Jensen m-Convexity on Set-Valued Function

Cauchy: Jurnal Matematika Murni dan Aplikasi
This paper discusses the class of Jensen m-convex functions and their properties, leading to enhancements of these functions and Jensen's inequalities for set-valued functions.
Eko Dedi Pramana, Ratno Bagus Edy Wibowo, Mohamad Muslikh   +2 more
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Interpolation of set-valued functions

IMA Journal of Numerical Analysis
Abstract Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently. In the first stage, we develop an efficient algorithm for computing an interpolant to $F$, inspired by the ‘metric polynomial ...
Qusay Muzaffar, Nira Dyn, David Levin
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Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment

Journal of Intelligent Systems, 2015
On the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set,
Ye Jun
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Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion

Journal of Function Spaces, 2022
Hypersoft set is a novel area of study which is established as an extension of soft set to handle its limitations. It employs a new approximate mapping called multi-argument approximate function which considers the Cartesian product of attribute-valued ...
Atiqe Ur Rahman, Muhammad Saeed, Khuram Ali Khan, Rostin Matendo Mabela   +3 more
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Inclusion measure for intuitionistic fuzzy sets and embedding of intervals [PDF]

Notes on IFS
Comparison of measuring the degree of inclusion for two intuitionistic fuzzy sets (IF-sets) and measuring the degree of embedding of two intervals is considered. Embedding is understood as the classical inclusion of intervals.
Michaela Bruteničová, Vladimír Janiš
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