Incomplete Soft Sets: New Solutions for Decision Making Problems

International Journal of Pure and Applied Mathematics

We introduce the concept of possibility vague soft sets and its operations. We give applications of this theory in solving a decision-making problem. We also introduce the similarity measure of two possibility vague soft sets and discuss their application in a medical diagnosis problem.

Computers & Mathematics with Applications, 2002

this paper, we apply the theory of soft sets to solve a decision making problem using rough mathematics.

International Journal of Intelligent Systems and Applications, 2012

This paper aims to introduce the theory of imprecise soft sets which is a hybrid model of soft sets and imprecise sets. It has been established that two independent laws of randomness are necessary and sufficient to define a law of fuzziness. Further, in case of fuzzy sets, the set theoretic axioms of exclusion and contradiction are not satisfied. Accordingly, the theory of imprecise sets has been developed where these mistakes arising in the literature of fuzzy sets are absent. Our work is an endeavor to combine imprecise sets with soft sets resulting in imprecise soft sets. We have put forward a matrix representation of imprecise soft sets. Finally we have studied the notion of similarity of two imprecise soft sets and put forward an application of similarity in a decision problem.

Journal of Computational and Applied Mathematics, 2007

The problem of decision making in an imprecise environment has found paramount importance in recent years. A novel method of object recognition from an imprecise multiobserver data has been presented here. The method involves construction of a Comparison Table from a fuzzy soft set in a parametric sense for decision making.

Procedia Computer Science, 2011

The theory of soft set proposed by Molodtsovin 1999[1]is a new method for handling uncertain data and can be defined as a Boolean-valued information system. Ithas been applied to data analysis and decision support systems based on large datasets. In this paper, it is shown that calculated support value can be used to determine missing attribute value of an object. However, in cases when more than one value is missing, the aggregate values and calculated support values will be used in determining the missing values. By successfully recovering missing attribute values, the integrity of a dataset can still been maintained.

International Journal of Applied Mathematics and Computer Science, 2012

The research on incomplete soft sets is an integral part of the research on soft sets and has been initiated recently. However, the existing approach for dealing with incomplete soft sets is only applicable to decision making and has low forecasting accuracy. In order to solve these problems, in this paper we propose a novel data filling approach for incomplete soft sets. The missing data are filled in terms of the association degree between the parameters when a stronger association exists between the parameters or in terms of the distribution of other available objects when no stronger association exists between the parameters. Data filling converts an incomplete soft set into a complete soft set, which makes the soft set applicable not only to decision making but also to other areas. The comparison results elaborated between the two approaches through UCI benchmark datasets illustrate that our approach outperforms the existing one with respect to the forecasting accuracy.

2021

In this study, we first define expansion and reduction of the soft sets that are based on the linguistic modifiers. By using these new notions we then construct a decision making method called soft reduction method, which selects a set of optimum alternatives. We finally present an example which shows that the methods can be successfully applied to many problems containing uncertainties.

Journal of Intelligent & Fuzzy Systems, 2016

In this paper, we propose soft decision making methods based on fuzzy and soft set theory. We also use matrix representation of the soft sets that is very useful for computations of the method. We finally present an example which shows that the method can be successfully applied to many problems that contain uncertainties.

Handbook of Research on Generalized and Hybrid Set Structures and Applications for Soft Computing

In this chapter the notions of two hybrid soft sets, namely fuzzy parameterized soft sets and vague soft sets has been discussed and some operations on them are defined. Some properties of these two hybrid soft sets under these operations are also studied. Application of fuzzy parameterized soft sets and vague soft sets in decision making has also been shown. Then the notion of similarity measure between two hybrid soft sets has been introduced and their basic properties are studied. Applications of these similarity measures in various problems like medical diagnosis and decision making have been shown. The idea of entropy of a fuzzy parameterized soft set has been introduced.

Lecture Notes in Computer Science, 2014

Soft set theory as a new mathematical tool for dealing with uncertainties was first introduced by Molodtsov has experienced rapid growth. Various applications of soft set for the purpose of decision-making have been shown by several researchers. From various studies presented mostly shows the role of soft sets as a tool in the collection of the various attributes needed by a person to determine which decisions will be taken. In this paper, we show how soft set can play a role in the decision made by a person based on a history of decisions that have been made earlier and used as a reference for the next decision. Therefore, we introduce an (if-then) multi soft sets as a developments of application of soft set which is stated in the form if (antecedent) and then (consequence). The antecedent and consequence are derived from previously several decisions that have been made by people when using a soft set as a tool to help them for making a decision.