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1
Content available A new method for decision making problems with redundant and incomplete information based on incomplete soft sets: From crisp to fuzzy
Xia Sisi, Chen Lin, Liu Siya, Yang Haoran
International Journal of Applied Mathematics and Computer Science
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2022
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Vol. 32, no. 4
657--669
EN
This research is focused on decision-making problems with redundant and incomplete information under a fuzzy environment. Firstly, we present the definition of incomplete fuzzy soft sets and analyze their data structures. Based on that, binary relationships between each pair of objects and the “restricted/relaxed AND” operations in the incomplete fuzzy soft set are discussed. After that, the definition of incomplete fuzzy soft decision systems is proposed. To reduce the inconsistency caused by the redundant information in decision making, the significance of the attribute subset, the reduct attribute set, the optimal reduct attribute set and the core attribute in incomplete fuzzy soft decision systems is also discussed. These definitions can be applied in an incomplete fuzzy soft set directly, so there is no need to convert incomplete data into complete one in the process of reduction. Then a new decision-making algorithm based on the above definitions can be developed, which can deal with redundant information and incomplete information simultaneously, and is independent of some unreliable assumptions about the data generating mechanism to forecast the incomplete information. Lastly, the algorithm is applied in the problem of regional food safety evaluation in Chongqing, China, and the corresponding comparison analysis demonstrates the effectiveness of the proposed method.
2
Content available An incomplete soft set and its application in MCDM problems with redundant and incomplete information
Xia Sisi, Yang Haoran, Chen Lin
International Journal of Applied Mathematics and Computer Science
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2021
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Vol. 31, no. 3
417--430
EN
Multiple criteria decision making (MCDM) problems in practice may simultaneously contain both redundant and incomplete information and are difficult to solve. This paper proposes a new decision-making approach based on soft set theory to solve MCDM problems with redundant and incomplete information. Firstly, we give an incomplete soft set a precise definition. After that, the binary relationships of objects in an incomplete soft set are analyzed and some operations on it are provided. Next, some definitions regarding the incomplete soft decision system are also given. Based on that, an algorithm to solve MCDM problems with redundant and incomplete information based on an incomplete soft set is presented and illustrated with a numerical example. The results show that our newly developed method can be directly used on the original redundant and incomplete data set. There is no need to transform an incomplete information system into a complete one, which may lead to bad decision-making due to information loss or some unreliable assumptions about the data generating mechanism. To demonstrate its practical applications, the proposed method is applied to a problem of regional food safety evaluation in Chongqing, China.
3
Content available remote A Soft Interval Based Decision Making Method and Its Computer Application
Yaylalı Gözde, Polat Nazan Çakmak, Tanay Bekir
Foundations of Computing and Decision Sciences
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2021
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Vol. 46, No. 3
273--296
EN
In today’s society, decision making is becoming more important and complicated with increasing and complex data. Decision making by using soft set theory, herein, we firstly report the comparison of soft intervals (SI) as the generalization of interval soft sets (ISS). The results showed that SIs are more effective and more general than the ISSs, for solving decision making problems due to allowing the ranking of parameters. Tabular form of SIs were used to construct a mathematical algorithm to make a decision for problems that involves uncertainties. Since these kinds of problems have huge data, constructing new and effective methods solving these problems and transforming them into the machine learning methods is very important. An important advance of our presented method is being a more general method than the Decision-Making methods based on special situations of soft set theory. The presented method in this study can be used for all of them, while the others can only work in special cases. The structures obtained from the results of soft intervals were subjected to test with examples. The designed algorithm was written in recently used functional programing language C# and applied to the problems that have been published in earlier studies. This is a pioneering study, where this type of mathematical algorithm was converted into a code and applied successfully.
4
Content available remote Tolerance Soft Set Relation on a Soft Set and its Matrix Applications
Polat N. Ç, Yaylalı G., Tanay B.
Fundamenta Informaticae
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2017
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Vol. 152, nr 2
107--122
EN
In this paper the tolerance soft set relation on a soft set is defined and some examples are given with their matrix representations. Also, pre-class and tolerance class concepts for a given tolerance soft set relation are introduced and some examples related to these definitions are illustrated. Some theoretical results are proved such as every pre-class contained by a tolerance class and intersection of two pre-classes is a pre-class as well. Moreover, a method to find out the tolerance classes and pre-classes by using matrix representation of a tolerance soft set relation is explained with examples.
5
Content available remote On Characterization of Fuzzy Soft Rough Sets Based on a Pair of Border Implicators
Gong Z., Zhang X.
Fundamenta Informaticae
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2015
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Vol. 137, nr 4
457--491
EN
Fuzzy set theory, soft set theory and rough set theory are powerfulmathematical tools for dealing with various types of uncertainty. This paper is devoted to define a broad family of soft fuzzy rough sets, each one of which, called an (I, J)-soft fuzzy rough set, is determined by a pair of border implicators (I, J). Alternatively, it shows that a fuzzy soft set can induce a T -equivalence fuzzy relation which is used to granulate the universe. In particular, we prove that (I, J)-fuzzy soft rough sets in our work are equivalent to (I, J)-fuzzy rough sets of Yao et al. by using a T -equivalence fuzzy relation determined by a fuzzy soft set. Furthermore, basic properties of (I, J)-fuzzy soft rough sets are investigated. Meanwhile, an operator-oriented characterization of (I, J)-fuzzy soft rough sets is proposed. Finally, an example is given to illustrate the approach of present paper.
6
Content available remote Soft set theory applied to general algebras
Dymek G., Walendziak A.
Demonstratio Mathematica
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2015
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Vol. 48, nr 1
13--20
EN
The notions of a soft general algebra and a soft subalgebra are introduced and studied. The operations on them such as a restricted intersection, an extended intersection, a restricted union, a ^-intersection, a ˅-union and a cartesian product are established.
7
Content available remote N-group SI-action and its applications to N-group theory
Sezer A S, Atagün A O, Ҫaǧman N
Fasciculi Mathematici
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2014
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Nr 52
139--153
EN
In this paper, we define a new concept, called N-group soft intersection action (SI) on a soft set. This new notion gathers soft set theory, set theory and N-group theory together and it shows how a soft set effects on an N-group structure in the mean of intersection and inclusion of sets. We then obtain its basic properties with illustrative examples and derive some analog of classical N-group theoretic concepts for N-group SI-actions. Finally, we give the applications of N-group SI-actions to N-group theory.
8
Content available remote Soft Nearness Approximation Spaces
Öztürk M. A., İnan E.
Fundamenta Informaticae
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2013
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Vol. 124, nr 1/2
231--250
EN
In 1999, Molodtsov introduced the theory of soft sets, which can be seen as a new mathematical approach to vagueness. In 2002, near set theory was initiated by J. F. Peters as a generalization of Pawlak's rough set theory. In the near set approach, every perceptual granule is a set of objects that have their origin in the physical world. Objects that have, in some degree, affinities are considered perceptually near each other, i.e., objects with similar descriptions. Also, the concept of near groups has been investigated by İnan and Öztürk [30]. The present paper aims to combine the soft sets approach with near set theory, which gives rise to the new concepts of soft nearness approximation spaces (SNAS), soft lower and upper approximations. Moreover, we give some examples and properties of these soft nearness approximations.
9
Content available Soft set mappings and their properties
Matłoka M.
Control and Cybernetics
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2012
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Vol. 41, no. 3
595-604
EN
In the present paper we introduce the concept of soft set mapping. Next, we present some basic properties of such mappings.
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