• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.3
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• pp.316-322
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• 2008

We introduce the concept of interval-valued intuitionistic fuzzy soft sets, which is an extension of the interval-valued fuzzy soft set. We also introduce the concepts of operations for the interval-valued intuitionistic fuzzy soft sets and study basic some properties.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1341-1356
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• 2018

The author devotes this paper to defining a new class of generalized soft open sets, namely soft somewhere dense sets and to investigating its main features. With the help of examples, we illustrate the relationships between soft somewhere dense sets and some celebrated generalizations of soft open sets, and point out that the soft somewhere dense subsets of a soft hyperconnected space coincide with the non-null soft ${\beta}$-open sets. Also, we give an equivalent condition for the soft csdense sets and verify that every soft set is soft somewhere dense or soft cs-dense. We show that a collection of all soft somewhere dense subsets of a strongly soft hyperconnected space forms a soft filter on the universe set, and this collection with a non-null soft set form a soft topology on the universe set as well. Moreover, we derive some important results such as the property of being a soft somewhere dense set is a soft topological property and the finite product of soft somewhere dense sets is soft somewhere dense. In the end, we point out that the number of soft somewhere dense subsets of infinite soft topological space is infinite, and we present some results which associate soft somewhere dense sets with some soft topological concepts such as soft compact spaces and soft subspaces.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.317-331
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• 2018

This paper aims to extend the notion of hesitant fuzzy sets on UP-algebras to hesitant fuzzy soft sets over UP-algebras by merging the notions of hesitant fuzzy sets and soft sets. Further, we discuss the notions of hesitant fuzzy soft strongly UP-ideals, hesitant fuzzy soft UP-ideals, hesitant fuzzy soft UP-filters, and hesitant fuzzy soft UP-subalgebras of UP-algebras, and provide some properties.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.221-236
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• 2014

This paper introduces semiopen and semiclosed soft sets in soft topological spaces and then these are used to generalize the notions of interior and closure. Further, we study the properties of semiopen soft sets, semiclosed soft sets, semi interior and semi closure of soft set in soft topological spaces. Various forms of soft functions, like semicontinuous, irresolute, semiopen and semiclosed soft functions are introduced and characterized including those of soft semicompactness, soft semiconnectedness. Besides, soft semiseparation axioms are also introduced and studied.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.59-68
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• 2018

In this paper, We define and explore the characterizations and properties of soft regular open(closed) and soft semi-regular sets in soft topological spaces. The properties of soft extremally disconnected spaces are also introduced and discussed. The findings in this paper will help researcher to enhance and promote further study on soft topology to carry out a general framework for their applications in practical life.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.3
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• pp.412-415
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• 2008

In this paper, we show that the concepts of null interval-valued fuzzy and absolute interval-valued fuzzy soft sets are not reasonable. Thus we introduce the modified concepts for them and study some properties. Also we introduce an operation for the interval-valued fuzzy soft set theory and study basic properties.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.335-349
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• 2020

We present inverse soft rough sets by using inverse soft sets and soft rough sets. We study different approaches for inverse soft rough set and examine the relationships between them. We also discuss and explore the basic properties for these approaches. Moreover we develop an algorithm following these concepts and apply it to a decision-making problem to demonstrate the applicability of the proposed methods.

• East Asian mathematical journal
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• v.28 no.1
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• pp.1-11
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• 2012

In this paper, the concept of fuzzy soft module is introduced, some of their properties are discussed. Furthermore, the concept of fuzzy soft exactness is also given.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.263-281
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• 2022

The main aim of this paper is to discuss two different types of soft hemirings, soft intersection and soft union. We discuss applications and results related to soft intersection hemirings or soft intersection k-ideals and soft union hemirings or soft union k-ideals. The deep concept of k-closure, intersection and union of soft sets, ∧-product and ∨-product among soft sets, upper 𝛽-inclusion and lower 𝛽-inclusion of soft sets is discussed here. Many applications related to soft intersection-union sum and soft intersection-union product of sets are investigated in this paper. We characterize k-hemiregular hemirings by the soft intersection k-ideals and soft union k-ideals.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.2
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• pp.201-208
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• 2014

Park et al. introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, we introduce new operations such as restricted union and restricted intersection and study their basic properties, and deal with the algebraic structure of generalized intuitionistic fuzzy soft sets. The lattice structures of generalized intuitionistic fuzzy soft sets are constructed.