• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.61-79
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• 2012

In this paper, we investigate soft hemirings by fuzzy theory. Some characterizations of hemirings are introduced by means of soft sets. In particular, the $h$-hemiregular hemirings and $h$-intra-hemiregular hemirings are also characterized.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.331-347
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• 2017

Soft sets are fantastic mathematical tools to handle imprecise and uncertain information in complicated situations. In this paper, we defined the hybrid structure which is the combination of soft set and complex number representation of intuitionistic fuzzy set. We defined basic set theoretic operations such as complement, union, intersection, restricted union, restricted intersection etc. for this hybrid structure. Moreover, we developed this theory to establish some more set theoretic operations like Disjunctive sum, difference, product, conjugate etc.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.671-686
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• 2015

The notion of soft α-ideals and α-idealistic soft BCI-algebras is introduced and their basic properties are discussed. Relations between soft ideals and soft α-ideals of soft BCI-algebras are provided. Also idealistic soft BCI-algebras and α-idealistic soft BCI-algebras are being related. The restricted intersection, union, restricted union, restricted difference and "AND" operation of soft α-ideals and α-idealistic soft BCI-algebras are established. The characterizations of (fuzzy) α-ideals in BCI-algebras are given by using the concept of soft sets. Relations between fuzzy α-ideals and α-idealistic soft BCI-algebras are discussed.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.183-196
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• 2011

Molodtsov [5] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to an implicative ideal of BCK-algebras. The notion of implicative soft ideals in BCK-algebras and implicative idealistic soft BCK-algebras is introduced, and related properties are investigated. Relations between implicative soft ideals and commutative (resp. positive implicative) soft ideals are discussed. Also, relations between implicative idealistic soft BCK-algebras and commutative (resp. positive implicative) idealistic soft BCK-algebras are provided.

• Journal of Information Processing Systems
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• v.12 no.1
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• pp.109-128
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• 2016

This paper presents a new combined forecasting method that is guided by the soft set theory (CFBSS) to predict business failures with different sample sizes. The proposed method combines both qualitative analysis and quantitative analysis to improve forecasting performance. We considered an expert system (ES), logistic regression (LR), and support vector machine (SVM) as forecasting components whose weights are determined by the receiver operating characteristic (ROC) curve. The proposed procedure was applied to real data sets from Chinese listed firms. For performance comparison, single ES, LR, and SVM methods, the combined forecasting method based on equal weights (CFBEWs), the combined forecasting method based on neural networks (CFBNNs), and the combined forecasting method based on rough sets and the D-S theory (CFBRSDS) were also included in the empirical experiment. CFBSS obtains the highest forecasting accuracy and the second-best forecasting stability. The empirical results demonstrate the superior forecasting performance of our method in terms of accuracy and stability.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.657-685
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• 2023

This paper aims to apply the concept of Pythagorean fuzzy soft sets (PFSSs) to UP-algebras. Then we introduce five types of PFSSs over UP-algebras, study their generalization, and provide illustrative examples. In addition, we study the results of four operations of two PFSSs over UP-algebras, namely, the union, the restricted union, the intersection, and the extended intersection. Finally, we will also discuss t-level subsets of PFSSs over UP-algebras to study the relationships between PFSSs and special subsets of UP-algebras.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.583-588
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• 2018

In this manuscript, we show that the equality relations of the two assertions (ix) and (x) of [Theorem 2.11, p.p.224] in [3] do not hold in general, by giving a concrete example. Also, we illustrate that Example 6.3, Example 6.7, Example 6.11, Example 6.15 and Example 6.20 do not satisfy a soft semi $T_0$-space, a soft semi $T_1$-space, a soft semi $T_2$-space, a soft semi $T_3$-space and a soft semi $T_4$-space, respectively. Moreover, we point out that the three results obtained in [3] which related to soft subspaces are false, by presenting two examples. Finally, we construct an example to illuminate that Theorem 6.18 and Remark 6.21 made in [3] are not valid in general.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1293-1305
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• 2009

Molodtsov [D. Molodtsov, Soft set theory First results, Comput. Math. Appl. 37 (1999) 19-31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCC-algebras. The notion of (trivial, whole) soft BCC-algebras and soft BCC-subalgebras are introduced, and several examples are provided. Relations between a fuzzy subalgebra and a soft BCC-algebra are given, and the characterization of soft BCC-algebras is established.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.707-720
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• 2008

Molodtsov [12] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to commutative ideals of BCK-algebras, The notions of commutative soft ideals and commutative idealistic soft BCK-algebras are introduced, and their basic properties are investigated. Examples to show that there is no relations between positive implicative idealistic soft BCK-algebras and commutative idealistic soft BCK-algebras are provided.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.661-690
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• 2019

The soft compactness notion via soft topological spaces was first studied in [10,29]. In this work, soft semi-open sets are utilized to initiate seven new kinds of generalized soft semi-compactness, namely soft semi-$Lindel{\ddot{o}}fness$, almost (approximately, mildly) soft semi-compactness and almost (approximately, mildly) soft semi-$Lindel{\ddot{o}}fness$. The relationships among them are shown with the help of illustrative examples and the equivalent conditions of each one of them are investigated. Also, the behavior of these spaces under soft semi-irresolute maps are investigated. Furthermore, the enough conditions for the equivalence among the four sorts of soft semi-compact spaces and for the equivalence among the four sorts of soft semi-$Lindel{\ddot{o}}f$ spaces are explored. The relationships between enriched soft topological spaces and the initiated spaces are discussed in different cases. Finally, some properties which connect some of these spaces with some soft topological notions such as soft semi-connectedness, soft semi $T_2$-spaces and soft subspaces are obtained.