AN APPLICATION OF SOFT SET IN DECISION MAKING

2015 ◽  
Vol 77 (13) ◽  
Author(s):  
M. K. Dauda ◽  
Mustafa Mamat ◽  
M. Y. Waziri
Keyword(s):  
Decision Making ◽  
Theoretical Study ◽  
Real Life ◽  
Soft Set ◽  
Soft Sets ◽  
Relative Complement ◽  
Definition Of

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.

scholarly journals An Approach toward a Q-Neutrosophic Soft Set and Its Application in Decision Making

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 139 ◽  
Author(s):  
Majdoleen Abu Qamar ◽  
Nasruddin Hassan
Keyword(s):  
Decision Making ◽  
Uncertain Data ◽  
Real Life ◽  
Soft Set ◽  
Neutrosophic Set ◽  
Uncertain Information ◽  
Soft Sets ◽  
Independent Functions ◽  
Axis Of Symmetry ◽  
Set Aggregation

A neutrosophic set was proposed as an approach to study neutral uncertain information. It is characterized through three memberships, T , I and F, such that these independent functions stand for the truth, indeterminate, and false-membership degrees of an object. The neutrosophic set presents a symmetric form since truth enrolment T is symmetric to its opposite false enrolment F with respect to indeterminacy enrolment I that acts as an axis of symmetry. The neutrosophic set was further extended to a Q-neutrosophic soft set, which is a hybrid model that keeps the features of the neutrosophic soft set in dealing with uncertainty, and the features of a Q-fuzzy soft set that handles two-dimensional information. In this study, we discuss some operations of Q-neutrosophic soft sets, such as subset, equality, complement, intersection, union, AND operation, and OR operation. We also define the necessity and possibility operations of a Q-neutrosophic soft set. Several properties and illustrative examples are discussed. Then, we define the Q-neutrosophic-set aggregation operator and use it to develop an algorithm for using a Q-neutrosophic soft set in decision-making issues that have indeterminate and uncertain data, followed by an illustrative real-life example.

scholarly journals The Interval-Valued Triangular Fuzzy Soft Set and Its Method of Dynamic Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaoguo Chen ◽  
Hong Du ◽  
Yue Yang
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Soft Set ◽  
Dynamic Decision Making ◽  
Optimal Decision ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Optimal Decision Making ◽  
Definition Of ◽  
Interval Valued

A concept of interval-valued triangular fuzzy soft set is presented, and some operations of “AND,” “OR,” intersection, union and complement, and so forth are defined. Then some relative properties are discussed and several conclusions are drawn. A dynamic decision making model is built based on the definition of interval-valued triangular fuzzy soft set, in which period weight is determined by the exponential decay method. The arithmetic weighted average operator of interval-valued triangular fuzzy soft set is given by the aggregating thought, thereby aggregating interval-valued triangular fuzzy soft sets of different time-series into a collective interval-valued triangular fuzzy soft set. The formulas of selection and decision values of different objects are given; therefore the optimal decision making is achieved according to the decision values. Finally, the steps of this method are concluded, and one example is given to explain the application of the method.

scholarly journals Similarity Measure of Lattice Ordered Multi-Fuzzy Soft Sets Based on Set Theoretic Approach and Its Application in Decision Making

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1255 ◽  
Author(s):  
Sabeena Begam S ◽  
Vimala J ◽  
Ganeshsree Selvachandran ◽  
Tran Thi Ngan ◽  
Rohit Sharma
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Similarity Measure ◽  
Real Life ◽  
Soft Set ◽  
Theoretic Approach ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets

Many effective tools in fuzzy soft set theory have been proposed to handle various complicated problems in different fields of our real life, especially in decision making. Molodtsov’s soft set theory has been regarded as a newly emerging mathematical tool to deal with uncertainty and vagueness. Lattice ordered multi-fuzzy soft set (LMFSS) has been applied in forecasting process. However, similarity measure is not used in this application. In our research, similarity measure of LMFSS is proposed to calculate the similarity between two LMFSSs. Moreover, some of its properties are introduced and proved. Finally, an application of LMFSS in decision making using similarity measure is analysed.

scholarly journals N-Bipolar Soft Sets and Their Application in Decision Making

2021 ◽  
Author(s):  
Muhammad Shabir ◽  
Javaria Fatima
Keyword(s):  
Decision Making ◽  
Algebraic Structure ◽  
Real Life ◽  
Conflict Analysis ◽  
Soft Set ◽  
Grading System ◽  
Soft Sets ◽  
Binary Model ◽  
Proposed Model ◽  
Feasible Action

Abstract The concept of soft set was extended to $N$-soft set by Fatimah et al. and used as grading system. Bipolar soft sets gave the concept of a binary model of grading. Kamacı and Petchimuchu defined bipolar $N$-soft set but our approach is different from their approach. We defined N-bipolar soft set which extends the concept of bipolar soft set. We explained the notions through some important examples. We discussed some vital definitions and were motivated towards their use and need. We also described some basic algebraic definitions and with their help, we developed the algebraic structure of our proposed model. We give decision making algorithms and applied them to real life examples to motivate towards its application. Conflict analysis has been a vast topic for research. It was first given by Pawlak. The first extension to this model was given by Pawlak itself. Then many researchers extended his idea. We also discussed here the application of $N$-bipolar soft set to conflict analysis. The combination of $N$-bipolar soft set and conflict analysis can give user the best way to decide suitable and feasible action.

Soft Sets

2014 ◽  
pp. 445-494
Author(s):  
Pinaki Majumdar
Keyword(s):  
Decision Making ◽  
Medical Diagnosis ◽  
Real Life ◽  
Soft Set ◽  
Soft Sets ◽  
Soft Topology ◽  
Soft Mapping ◽  
Life Problems ◽  
Fuzzy Soft Sets ◽  
Sets Theory

This chapter is about soft sets. A brief account of the developments that took place in last 14 years in the field of Soft Sets Theory (SST) has been presented. It begins with a brief introduction on soft sets and then it describes many generalizations of it. The notions of generalized fuzzy soft sets are defined and their properties are studied. After that, a notion of mapping, called soft mapping, in soft set setting is introduced. Later, algebraic structures on soft sets like soft group, soft ring, etc. are discussed. Then the next section deals with the concept of topology on soft sets. Here two notions of topology in soft sets are introduced, which are the topology of soft subsets and the soft topology, respectively. The idea of entropy for soft sets is defined in the later section. Next, some applications of hybrid soft sets in solving real life problems like medical diagnosis, decision-making, etc. are shown. Issues like measurement of similarity of soft sets are also addressed.

scholarly journals A Novel MADM Framework under q-Rung Orthopair Fuzzy Bipolar Soft Sets

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2163
Author(s):  
Ghous Ali ◽  
Hanan Alolaiyan ◽  
Dragan Pamučar ◽  
Muhammad Asif ◽  
Nimra Lateef
Keyword(s):  
Decision Making ◽  
Real Life ◽  
Soft Set ◽  
Soft Data ◽  
Soft Sets ◽  
Life Problems ◽  
Mathematical Problems ◽  
Multi Attribute Decision Making ◽  
Comprehensive Framework ◽  
Selection Of

In many real-life problems, decision-making is reckoned as a powerful tool to manipulate the data involving imprecise and vague information. To fix the mathematical problems containing more generalized datasets, an emerging model called q-rung orthopair fuzzy soft sets offers a comprehensive framework for a number of multi-attribute decision-making (MADM) situations but this model is not capable to deal effectively with situations having bipolar soft data. In this research study, a novel hybrid model under the name of q-rung orthopair fuzzy bipolar soft set (q-ROFBSS, henceforth), an efficient bipolar soft generalization of q-rung orthopair fuzzy set model, is introduced and illustrated by an example. The proposed model is successfully tested for several significant operations like subset, complement, extended union and intersection, restricted union and intersection, the ‘AND’ operation and the ‘OR’ operation. The De Morgan’s laws are also verified for q-ROFBSSs regarding above-mentioned operations. Ultimately, two applications are investigated by using the proposed framework. In first real-life application, the selection of land for cropping the carrots and the lettuces is studied, while in second practical application, the selection of an eligible student for a scholarship is discussed. At last, a comparison of the initiated model with certain existing models, including Pythagorean and Fermatean fuzzy bipolar soft set models is provided.

On Possibility Interval-Valued Fuzzy Soft Sets

2013 ◽  
Vol 336-338 ◽  
pp. 2288-2302 ◽  
Author(s):  
Yong Yang ◽  
Cong Cong Meng
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
New Approach ◽  
Relative Complement ◽  
Fuzzy Soft Sets ◽  
Interval Valued

Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of possibil­ity interval-valued fuzzy soft sets are proposed. Their operations and basic properties are studied which are subset, equal, relative complement, union, intersection, restricted union, extended intersection, “AND”, “OR” and De Morgan Laws. Furthermore, an application of the new approach in decision making based on possibility interval-valued fuzzy soft set is illustrated.

scholarly journals Generalised Interval-Valued Fuzzy Soft Set

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.

Neutrosophic Soft Block Matrices And Some Of Its Properties

2020 ◽  
pp. 39-49
Author(s):  
admin admin ◽  
Keyword(s):  
Decision Making ◽  
Crucial Role ◽  
Real Life ◽  
Decision Making Process ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Neutrosophic Sets ◽  
Block Matrices ◽  
Inconsistent Information

In real life situations, there are many issues in which there are uncertainties, vagueness, complexities and unpredictability. Neutrosophic sets are a mathematical tool to address some issues which cannot be met using the existing methods. Neutrosophic soft matrices play a crucial role in handling indeterminant and inconsistent information during decision making process. The main focus of this article is to discuss the concept of neutrosophic sets, neutrosophic soft sets, neutrosophic soft matrices theory and finally to discuss about neutrosophic soft block matrics which are very useful and applicable in various situations involving uncertainties and imprecisions. In this article, neutrosophic soft block matrices, various types of neutrosophic soft block matrices, some operations on it along with some properties associated with it are discussed in details.

scholarly journals An algorithm for fuzzy soft set based decision making approach

2020 ◽  
Vol 30 (1) ◽  
pp. 59-70
Author(s):  
Shehu Mohammed ◽  
Akbar Azam
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Group Decision Making ◽  
Group Decision ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets ◽  
Priority Table

The notion of soft set theory was initiated as a general mathematical tool for handling ambiguities. Decision making is viewed as a cognitive-based human activity for selecting the best alternative. In the present time, decision making techniques based on fuzzy soft sets have gained enormous attentions. On this development, this paper proposes a new algorithm for decision making in fuzzy soft set environment by hybridizing some existing techniques. The first novelty is the idea of absolute scores. The second concerns the concept of priority table in group decision making problems. The advantages of our approach herein are stronger power of objects discrimination and a well-determined inference.

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