• 한국지능시스템학회논문지
• /
• 제21권3호
• /
• pp.389-394
• /
• 2011

The notion of generalized intuitionistic fuzzy soft set theory is proposed. Our generalized intuitionistic fuzzy soft set theory is a combination of the generalized intuitionistic fuzzy set theory and the soft set theory. In other words, our generalized intuitionistic fuzzy soft set theory is an extension of the intuitionistic fuzzy soft set theory. The complement, "and" and "or" operations are defined on the generalized intuitionistic fuzzy soft sets. Their basic properties for the generalized intuitionistic fuzzy soft sets are also presented and discussed.

• Annals of Fuzzy Mathematics and Informatics
• /
• 제16권3호
• /
• pp.261-284
• /
• 2018

In this paper, we recall the definition of soft set, fuzzy soft set, hesitant fuzzy set and hesitant fuzzy soft set and some of their examples. We define the concept of hesitant fuzzy soft multiset which combines hesitant fuzzy soft set and soft multiset theory. We also define basic terms in hesitant fuzzy soft multiset with relevant examples. Some basic operations such as restricted intersection, extended intersection, union, restricted union, AND-product and OR-product and their properties are given, supported with illustrative examples. We finally establish some important results, including De Morgan's inclusions and laws.

• Kyungpook Mathematical Journal
• /
• 제50권1호
• /
• pp.123-129
• /
• 2010

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft BL-algebras by using the soft set theory. The notion of filteristic soft BL-algebras is introduced and some related properties are investigated.

• Journal of applied mathematics & informatics
• /
• 제35권3_4호
• /
• pp.331-347
• /
• 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 Information Processing Systems
• /
• 제15권6호
• /
• pp.1489-1502
• /
• 2019

This work introduces a novel unweighted combination method (UCSS) for business failure perdition (BFP). With considering features of BFP in the age of big data, UCSS integrates the quantitative and qualitative analysis by utilizing soft set theory (SS). We adopt the conventional expert system (ES) as the basic qualitative classifier, the logistic regression model (LR) and the support vector machine (SVM) as basic quantitative classifiers. Unlike other traditional combination methods, we employ soft set theory to integrate the results of each basic classifier without weighting. In this way, UCSS inherits the advantages of ES, LR, SVM, and SS. To verify the performance of UCSS, it is applied to real datasets. We adopt ES, LR, SVM, combination models utilizing the equal weight approach (CMEW), neural network algorithm (CMNN), rough set and D-S evidence theory (CMRD), and the receiver operating characteristic curve (ROC) and SS (CFBSS) as benchmarks. The superior performance of UCSS has been verified by the empirical experiments.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제11권3호
• /
• pp.184-189
• /
• 2011

Generalized intuitionistic fuzzy soft set theory, proposed by Park et al. [Journal of Korean Institute of Intelligent Systems 21(3) (2011) 389-394], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we prove that certain De Margan's law hold in generalized intuitionistic fuzzy soft set theory with respect to union and intersection operations on generalized intuitionistic fuzzy soft sets. We discuss the basic properties of operations on generalized intuitionistic fuzzy soft sets such as necessity and possibility. Moreover, we illustrate their interconnections between each other.

• 대한수학회논문집
• /
• 제23권3호
• /
• pp.313-324
• /
• 2008

Molodtsov [8] 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 subtraction algebras. The notion of soft WS-algebras, soft subalgebras and soft deductive systems are introduced, and their basic properties are derived.

• Journal of Information Processing Systems
• /
• 제12권1호
• /
• pp.109-128
• /
• 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
• /
• 제27권5_6호
• /
• pp.1293-1305
• /
• 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.

• Kyungpook Mathematical Journal
• /
• 제52권1호
• /
• pp.61-79
• /
• 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.