• Journal of Information Processing Systems
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• v.14 no.3
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• pp.790-800
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• 2018

The simplified neutrosophic set (SNS) is a generalization of fuzzy set that is designed for some practical situations in which each element has truth membership function, indeterminacy membership function and falsity membership function. In this paper, we propose a new method to construct similarity measures of single valued neutrosophic sets (SVNSs) and interval valued neutrosophic sets (IVNSs), respectively. Then we prove that the proposed formulas satisfy the axiomatic definition of the similarity measure. At last, we apply them to pattern recognition under the single valued neutrosophic environment and multi-criteria decision-making problems under the interval valued neutrosophic environment. The results show that our methods are effective and reasonable.

• International Journal of Computer Science & Network Security
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• v.24 no.1
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• pp.85-94
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• 2024

In this paper, we present the very first time the generalized notion of (α, β, γ, δ) - convex (concave) function in mixed kind, which is the generalization of (α, β) - convex (concave) functions in 1^st and 2^nd kind, (s, r) - convex (concave) functions in mixed kind, s - convex (concave) functions in 1^st and 2^nd kind, p - convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (α, β, γ, δ) - convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function.