Novel possibility Pythagorean interval valued fuzzy soft set method for a decision making

We discuss the theory of possibility Pythagorean interval valued fuzzy soft set, possibility interval valued fuzzy soft set and define some related the operations namely complement, union, intersection, AND and OR. The possibility Pythagorean interval valued fuzzy soft sets are a generalization of soft sets. Notably, we showed DeMorgan’s laws that are valid in possibility Pythagorean interval valued fuzzy soft set theory. Also, we propose an algorithm to solve the decision making problem based on soft set method. To compare two possibilities Pythagorean interval valued fuzzy soft sets for dealing with decision making problems and find a similarity measure is obtained. Finally, an illustrative example is discussed to prove that they can be effectively used to solve problems with uncertainties.Publisher's Versio

(R1500) Type-I Generalized Spherical Interval Valued Fuzzy Soft Sets in Medical Diagnosis for Decision Making

In the present communication, we introduce the concept of Type-I generalized spherical interval valued fuzzy soft set and define some operations. It is a generalization of the interval valued fuzzy soft set and the spherical fuzzy soft set. The spherical interval valued fuzzy soft set theory satisfies the condition that the sum of its degrees of positive, neutral, and negative membership does not exceed unity and that these parameters are assigned independently. We also propose an algorithm to solve the decision making problem based on a Type-I generalized soft set model. We introduce a similarity measure based on the Type-I generalized soft set model for two Type-I generalized spherical interval valued fuzzy soft sets and discuss its application in a medical diagnosis problem. Illustrative examples are mentioned to show that they can be successfully used to solve problems with uncertainties

Multiaspect soft sets and its generalizations / Nor Hashimah Sulaiman

The theory of soft sets introduced in 1999 by Molodtsov is an alternative mathematical tool for dealing with uncertainties. It basically deals with information representations of objects characterized by parameters which are defined over a single common universal set. Combinations of the theory with fuzzy sets and interval-valued fuzzy sets have resulted in the so-called fuzzy soft sets and interval-valued fuzzy soft sets. Various theoretical studies on these theories and the variants have been made, and applications of the theories in various areas particularly in the area of decision making are continuously explored. Soft sets, fuzzy soft sets and interval-valued fuzzy soft sets have greater potential in information representation should the universe sets of elements not be restricted to only a common universal set. Real life situations may involve descriptions of objects, situations or entities based on certain characteristics or attributes which may be associated with different sets of elements of different types of universal sets. In this thesis, we introduce the concepts of multiaspect soft set (MASS), multiaspect fuzzy soft set (MAFSS) and multiaspect interval-valued fuzzy soft set (MAIVFSS) which are generalizations of soft sets, fuzzy soft sets and intervalvalued fuzzy soft sets, respectively. These concepts provide platforms for information representations that allow elements from different universal sets be taken into consideration in the description of a particular object, item or entity. MASS is defined for crisp data representation while MAFSS and MAIVFSS are respectively defined for fuzzy data representation with single and interval-valued membership degrees. For each concept, the set operations are established and the algebraic properties are studied. The concepts of mapping for multiaspect soft classes, multiaspect fuzzy soft classes and multiaspect interval-valued fuzzy soft classes are presented. In addition, we put forward the axiomatic definitions of distance, distance-based similarity measures and entropy for MAFSS and MAIVFSS. We introduce weighted and nonweighted distances and similarity measures based on the Hamming distance and the Euclidean distance. Relationships between the three measures are investigated. In the final part of the thesis, we highlight the applicability of some of the introduced concepts in solving group decision making problem under MAFSS and MAIVFSS environment

Similarity measure fuzzy soft set for phishing detection

Phishing is a serious web security problem, and the internet fraud technique involves mirroring genuine websites to trick online users into stealing their sensitive information and taking out their personal information, such as bank account information, usernames, credit card, and passwords. Early detection can prevent phishing behavior makes quick protection of personal information. Classification methods can be used to predict this phishing behavior. This paper presents an intelligent classification model for detecting Phishing by redefining a fuzzy soft set (FSS) theory for better computational performance. There are four types of similarity measures: (1) Comparison table, (2) Matching function, (3) Similarity measure, and (4) Distance measure. The experiment showed that the Similarity measure has better performance than the others in accuracy and recall, reached 95.45 % and 99.77 %, respectively. It concludes that FSS similarity measured is more precise than others, and FSS could be a promising approach to avoid phishing activities. This novel method can be implemented in social media software to warn the users as an early warning system. This model can be used for personal or commercial purposes on social media applications to protect sensitive data

Alternative Technique Reducing Complexity of Maximum Attribute Relation

Clustering refers to the method grouping the large data into the smaller groups based on the similarity measure. Clustering techniques have been applied on numerical, categorical and mix data. One of the categorical data clustering technique based on the soft set theory is Maximum Attribute Relation (MAR). The MAR technique allows calculating all of pair multi soft set made. However, the computational complexity is still an issue of the technique. To overcome the drawback, the paper proposes the alternative algorithm to decrease the complexity so get the faster response time. In this paper, to get the similar results as MAR without calculating all pair of soft set is proved. The alternative algorithm is implemented in MATLAB Software, and then experimental is run on the 10 benchmark datasets. The results show that the alternative algorithm improves the computational complexity in term of response time up to 36.46%

Distance and Similarity Measures for Soft Sets

In [P. Majumdar, S. K. Samanta, Similarity measure of soft sets, New Mathematics and Natural Computation 4(1)(2008) 1-12], the authors use matrix representation based distances of soft sets to introduce matching function and distance based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corllary of our result. The fundamental assumption of Majumdar et al has been shown to be flawed. This motivates us to introduce set operations based measures. We present a case (Example 28) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed herein decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.Comment: 14 pages, accepted manuscript, to appear in New Mathematics and Natural Computatio