SOFT DISEMIGRAPHS: EXPLORATION OF CERTAIN EXTENDED AND RESTRICTED OPERATIONS

A Pythagorean fuzzy set is very effective mathematical framework to represent parameter-wise imprecision which is the property of linguistic communication. A Pythagorean fuzzy soft graph is more potent than the intuitionistic fuzzy soft as well as the fuzzy soft graph as it depicts the interactions among the objects of a system using Pythagorean membership grades with respect to different parameters. This article addresses the content of competition graphs as well as economic competition graphs like k-competition graphs, m-step competition graphs and p-competition graphs in Pythagorean fuzzy soft environment. All these concepts are illustrated with examples and fascinating results. Furthermore, an application which describes the competition among distinct forest trees, that grow together in the mixed conifer forests of California, for plant resources is elaborated graphically. An algorithm is also designed for the construction of Pythagorean fuzzy soft competition graphs. It is worthwhile to express the competing and non-competing interactions in various networks with the help of Pythagorean fuzzy soft competition graphs wherein a variation in competition relative to different attributes is visible.

On some new operations in soft set theory

Semantic operations of multiple soft sets under conflict

Emerging trends in soft set theory and related topics.

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In particular, we develop efficient algorithms to solve decision-making problems.

An intuitionistic fuzzy soft set plays a significant role as a mathematical tool for mathematical modeling, system analysis and decision making. This mathematical tool gives more precision, flexibility and compatibility to the system when compared to systems that are designed using fuzzy graphs and fuzzy soft graphs. In this paper, we use intuitionistic fuzzy soft graphs and possibility intuitionistic fuzzy soft graphs for parameterized representation of a system involving some uncertainty. We present novel multiple-attribute decision-making methods based on an intuitionistic fuzzy soft graph and possibility intuitionistic fuzzy soft graph. We also present our methods as algorithms that are used in our applications.

In this paper, the definition of soft set and a detailed theoretical study of basic operations of soft sets such as intersection, extended intersection, restricted intersection, union, restricted union, complement and relative complement, Null and universal soft set are given. With the aid of definition of AND operation of soft sets and tabular representation of soft set, we are able to show that soft set has vital and real life application in decision making. The main aim of this paper is to use the concept of AND operation to sort out two best candidates out of five applicants in an interview conducted by a certain bank. Also the identification of Idempotent Property of “AND” and “OR” operation of soft sets is given and proved.

Lattices, soft sets, fuzzy sets and their generalizations have always been important for Mathematicians and the researchers working on uncertaities. In this paper our aim is to introduce the concept of lattice ordered intuitionistic fuzzy soft sets. After introducing extended union, extended intersection, AND-product, OR-product, basic union, basic intersection of intuitionistic fuzzy soft sets, in this paper the affects of lattice ordered intuitionistic fuzzy soft sets and anti-lattice ordered intuitionistic fuzzy soft sets on restricted union, restricted intersection, extended union, extended intersection,AND-product, OR-product, basic union, basic intersection of intuitionistic fuzzy sets are discussed. Further a decision making problem is solved by using these concepts.

In this manuscript we demonstrate interval-valued bipolar complex fuzzy set (IVBCFS) and then interval-valued bipolar complex fuzzy soft set (IVBCFSS), as a generalization of fuzzy set, interval-valued fuzzy set, bipolar fuzzy set, complex fuzzy set and soft set. We also initiate operational laws and basic results and properties for IVBCFS and IVBCFSS. Further explanation is given for the basic algebraic operations like complement, extended union, extended intersection, restricted union, and restricted intersection, AND product and OR product for IVBCFSS. Moreover, we demonstrate some fundamental aggregation operators like IVBCFS average aggregation, IVBCFS geometric and as well as their properties. To emphasize the usefulness and application of the system, we also develop the decision-making method and joint instances of the IVBCFSS (set-ups 1 and 2). In order to describe the effectiveness and influence of the approaching novel work, this study uses a comparative analysis of the new creating concept with prevailing ideas.

Soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. The main purpose of soft rough set is reducing the soft boundary region by increasing the lower approximation and decreasing the upper approximation. This paper is devoted to the further generalization of the soft rough set theory by using the ideal notion to reduce the soft boundary region. A new soft rough set model, called soft ideal approximation space, is proposed and its properties are derived. The new soft ideal lower and upper approximation operators are presented and their related properties are surveyed.

After the paper of Molodtsov [Molodtsov D. Soft set theory — First results, Computers and Mathematics with Applications, 1999, vol. 37, no. 4-5, pp. 19-31.] first appeared, soft set theory grew at a breakneck pace. Several authors have introduced various operations, relations, results, etc. as well as other aspects in soft set theory and hybrid structures incorrectly, despite their widespread use in mathematics and allied areas. In his paper [Molodtsov D.A. Equivalence and correct operations for soft sets, International Robotics and Automation Journal, 2018, vol. 4, no. 1, pp. 18-21.], Molodtsov, the father of soft set theory, pointed out several wrong results and notions. Molodtsov [Molodtsov D.A. Structure of soft sets, Nechetkie Sistemy i Myagkie Vychisleniya, 2017, vol. 12, no. 1, pp. 5-18.] also stated that the concept of soft set had not been fully understood and used everywhere. As a result, it is important to revisit the quirks of those conceptions and provide a formal account of the notion of soft set equivalency. Molodtsov already explored many correct operations on soft sets. We use some notions and results of Molodtsov [Molodtsov D.A. Structure of soft sets, Nechetkie Sistemy i Myagkie Vychisleniya, 2017, vol. 12, no. 1, pp. 5-18.] to create matrix representations as well as related operations of soft sets, and to quantify the similarity between two soft sets.

A weighted intuitionistic fuzzy soft set (WIFSS) is an important generalization of intuitionistic fuzzy soft set (IFSS). In this research work, the authors define the basic binary set operations, such as union, restricted union, restricted intersection, extended intersection, restricted difference, sum, AND-product, OR-product, and some concepts on weighted intuitionistic fuzzy soft set. They also present some properties of the operations and established some fundamental results including various De Morgan's type of results in weighted intuitionistic fuzzy soft set context.

This paper presents an introduction to soft hypergraph operations, namely extended union, extended intersection, restricted union, and restricted intersection, along with the concept of soft semisubhypergraph. We explore various properties of these operations and provide illustrative examples.

Extending fuzzy soft sets with fuzzy description logics

The concept of soft set is fundamentally important in almost every scientific field. Soft set theory is a new mathematical tool for dealing with uncertainties and is a set associated with parameters and has been applied in several directions. Since Molodtsov originated the idea of soft sets, some research on soft sets has been done in the literature. This theory represents a promising technique in imperfect data analysis which has found interesting extensions and various applications that handle imperfect knowledge, such as Bayesian inference, fuzzy set etc. In this paper, define the notion of soft sets, and the study that are interesting and valuable in the theory of soft sets, which emphasis on a series of applications especially in decision making problems. Also presents comprehensive study, development and survey of its existing literature. Keywords—BCI; BCK; FCM; Fuzzy Set; Fuzzy Soft Set; Soft Rough Set; Soft Semi Rings; Soft Set; Uncertainty.