As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.

https://www.mdpi.com/2227-7390/8/1/142/pdf

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

Molodtsov introduced soft set theory as a new mathematical approach to handle uncertainty. Hybrid models have been found to be more useful than the individual components. Following this trend fuzzy soft sets (FSS) and intuitionistic fuzzy soft sets (IFSS) were introduced. Recently, soft sets were introduced by Tripathy and Arun (Int J Reasoning-Based Intell Syst 7(3/4):244–253, 2015) [6] using the notion of characteristic function. This led to the redefinitions of concepts like complement, intersection, union of IFSS, Null and absolute IFSS. In this paper, we follow the approach of Tripathy et al. in redefining IFSS and present an application of IFSS in decision-making which substantially improve and is more realistic than the algorithms proposed earlier by several authors.

On Intuitionistic Fuzzy Soft Sets and Their Application in Decision-Making

The global demand for electricity has visualized high growth with the rapid growth in population and economy. It thus becomes necessary to efficiently distribute electricity to households and industries in order to reduce power loss. Smart Grids (SG) have the potential to reduce such power losses during power distribution. Machine learning and artificial intelligence techniques have been successfully implemented on SGs to achieve enhanced accuracy in customer demand prediction. There exists a dire need to analyze and evaluate the various machine learning algorithms, thereby identify the most suitable one to be applied to SGs. In the present work, several state-of-the-art machine learning algorithms, namely Support Vector Machines (SVM), K-Nearest Neighbor (KNN), Logistic Regression, Naive Bayes, Neural Networks, and Decision Tree classifier, have been deployed for predicting the stability of the SG. The SG dataset used in the study is publicly available collected from UC Irvine (UCI) machine learning repository. The experimentation results highlighted the superiority of the Decision Tree classification algorithm, which outperformed the other state of the art algorithms yielding 100% precision, 99.9% recall, 100% F1 score, and 99.96% accuracy.

Comparative analysis of machine learning algorithms for prediction of smart grid stability

Improving decision making approaches based on fuzzy soft sets and rough soft sets

Soft set theory was introduced by Molodtsov to handle uncertainty. It uses a family of subsets associated with each parameter. Hybrid models have been found to be more useful than the individual components. Earlier fuzzy set and soft set were combined to form fuzzy soft sets (FSS). Soft sets were defined from a different point of view in Tripathy et al. (Int J Reasoning-Based Intell Syst 7(3/4), 224–253, 2015) where they used the notion of characteristic functions. Hence, many related concepts were also redefined. In Tripathy et al. (Proceedings of ICCIDM-2015, 2015) membership function for FSSs was defined. We propose a new algorithm by following this approach which provides an application of FSSs in group decision making. The performance of this algorithm is substantially improved than that of the earlier algorithm.

Fuzzy Soft Set Theory and Its Application in Group Decision Making

Soft set theory is a new mathematical approach to vagueness introduced by Molodtsov (1999). This is a parameterised family of subsets defined over a universal set using a set of parameters. In this paper, we introduce the notion of characteristic function of a soft set, which helps us in defining the basic operations on soft sets concisely; several concepts associated with it efficiently and make the proofs of properties more elegant. We rectified the definition of complement of a soft set and the earlier definition of complement is now called as the negation of a multiset. Like the crisp multisets, soft multiset is a notion which allows multiple occurrences of elements in a model. So far, more than one attempt has been made to define this concept. Out of these the one put forth by Majumdar (2012) is the most appropriate one and so we use it in this paper. We redefined the concepts of complement of a soft multiset, null soft multiset and absolute soft multiset and introduced many operations on soft multisets like the union and intersection of soft multisets and cardinality of soft multisets. Also, we defined the concepts of addition and deletion of elements from a soft multiset. Two new operations, called the addition and difference of two soft multisets are introduced. We establish several properties of these operations on soft multisets including the De Morgan's Law, associative and distributive properties. A real life example is being used for the purpose of illustration of the notions and concepts.

A new approach to soft sets, soft multisets and their properties

Soft set theory (Comput Math Appl 44:1007–1083, 2002) is introduced recently as a model to handle uncertainty. Recently, characteristic functions for soft sets and hence operations on them using this approach were introduced in (Comput Math Appl 45:555–562, 2003). Following this approach, in this paper we redefine intuitionistic fuzzy soft sets (IFSS) and define operations on them. We also present an application of IFSS in decision-making which substantially improve and is more realistic than the algorithms proposed earlier by several authors.

A New Approach to Intuitionistic Fuzzy Soft Sets and Its Application in Decision-Making

Soft sets were introduced by Molodtsov to handle uncertainty based problems. In 2003, Maji et al. extended the soft set approach to decision making. Decision making plays an integral role in daily life. In this chapter we describe soft sets and its impact in decision making problems. In this chapter, we discuss some of the basic notions of fuzzy soft sets and interval valued fuzzy soft sets. We also discuss application of fuzzy soft sets and interval valued fuzzy soft sets in decision making. In this chapter, we are going to see how parameter reduction is used in soft set theory.

K. R. Arun

Papers

A new approach to soft sets, soft multisets and their properties

A New Approach to Intuitionistic Fuzzy Soft Sets and Its Application in Decision-Making

Parameter Reduction in Soft Set Models and Application in Decision Making