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 A Decision Making Method using Fuzzy Soft Sets

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
Samsiah Abdul Razak ◽  
Daud Mohamad
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Uncertain Data ◽  
Soft Set ◽  
Decision Makers ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Analytic Hierarchy ◽  
Fuzzy Soft Sets

The introduction of soft set theory by Molodstov has gained attention by many as it is useful in dealing with uncertain data. It is advantageous to use due to its parameterization form of data. This concept has been used in solving many decision making problems and has been generalized in various aspects in particular to fuzzy soft set (FSS) theory. In decision making using FSS, the objective is to select an object from a set of objects with respect to a set of choice parameter using fuzzy values. Although FSS theory has been extensively used in many applications, the importance of weight of parameters has not been highlighted and thus is not incorporated in the calculation. As it depends on one’s perception or opinion, the importance of the parameters may differ from one decision maker to another. Besides, existing methods in FSS only consider one or two decision makers to select the alternatives. In reality, group decision making normally involves more than two decision makers. In this paper we present a method for solving group decision making problems that involves more than two decision makers based on fuzzy soft set by taking into consideration the weight of parameters. The method of lambda – max which frequently utilize in fuzzy analytic hierarchy process (FAHP) has been applied to determine the weight of parameters and an algorithm for solving decision making problems is presented. Finally we illustrate the effectiveness of our method with a numerical example.

scholarly journals A Generalized Approach towards Soft Expert Sets via Neutrosophic Cubic Sets with Applications in Games

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 289 ◽  
Author(s):  
Muhammad Gulistan ◽  
Nasruddin Hassan
Keyword(s):  
Decision Making ◽  
Necessary Conditions ◽  
Neutrosophic Set ◽  
Uncertain Information ◽  
Combined Approach ◽  
Soft Sets

Games are considered to be the most attractive and healthy event between nationsand peoples. Soft expert sets are helpful for capturing uncertain and vague information.By contrast, neutrosophic set is a tri-component logic set, thus it can deal with uncertain,indeterminate, and incompatible information where the indeterminacy is quantified explicitly andtruth membership, indeterminacy membership, and falsity membership independent of each other.Subsequently, we develop a combined approach and extend this concept further to introduce thenotion of the neutrosophic cubic soft expert sets (NCSESs) by using the concept of neutrosophiccubic soft sets, which is a powerful tool for handling uncertain information in many problems andespecially in games. Then we define and analyze the properties of internal neutrosophic cubicsoft expert sets (INCSESs) and external neutrosophic cubic soft expert sets (ENCSESs), P-order,P-union, P-intersection, P-AND, P-OR and R-order, R-union, R-intersection, R-AND, and R-OR ofNCSESs. The NCSESs satisfy the laws of commutativity, associativity, De Morgan, distributivity,idempotentency, and absorption. We derive some conditions for P-union and P-intersection of twoINCSESs to be an INCSES. It is shown that P-union and P-intersection of ENCSESs need not be anENCSES. The R-union and R-intersection of the INCSESs (resp., ENCSESs) need not be an INCSES(resp. ENCSES). Necessary conditions for the P-union, R-union and R-intersection of two ENCSESsto be an ENCSES are obtained. We also study the conditions for R-intersection and P-intersectionof two NCSESs to be an INCSES and ENCSES. Finally, for its applications in games, we use thedeveloped procedure to analyze the cricket series between Pakistan and India. It is shown that theproposed method is suitable to be used for decision-making, and as good as or better when comparedto existing models.

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 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 A Novel Approach to Decision Making Based on Interval-Valued Fuzzy Soft Set

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2274
Author(s):  
Hongwu Qin ◽  
Yanan Wang ◽  
Xiuqin Ma ◽  
Jin Wang
Keyword(s):  
Decision Making ◽  
Extreme Values ◽  
Uncertain Data ◽  
Real Life ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Novel Approach ◽  
Comparison Results ◽  
New Perspective ◽  
Interval Valued

Interval-valued fuzzy soft set theory is a powerful tool that can provide the uncertain data processing capacity in an imprecise environment. The two existing methods for decision making based on this model were proposed. However, when there are some extreme values or outliers on the datasets based on interval-valued fuzzy soft set for making decisions, the existing methods are not reasonable and efficient, which may ignore some excellent candidates. In order to solve this problem, we give a novel approach to decision making based on interval-valued fuzzy soft set by means of the contrast table. Here, the contrast table has symmetry between the objects. Our proposed algorithm makes decisions based on the number of superior parameter values rather than score values, which is a new perspective to make decisions. The comparison results of three methods on two real-life cases show that, the proposed algorithm has superiority to the existing algorithms for the feasibility and efficiency when we face up to the extreme values of the uncertain datasets. Our proposed algorithm can also examine some extreme or unbalanced values for decision making if we regard this method as supplement of the existing algorithms.

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.

Generalized Possibility Neutrosophic Soft Set And Its Application

2021 ◽  
Author(s):  
S. Bhuvaneshwari ◽  
◽  
C. Antony Crispin Sweety ◽  
Keyword(s):  
Decision Making ◽  
Soft Set ◽  
Neutrosophic Set ◽  
Soft Sets ◽  
Numerical Example ◽  
Basic Properties

Today, experts are emphasizing establishing innovative ideas to cope with the complexity, imprecision, and ambiguity that exist in practical problems, together with suitable examples to elucidate their hypotheses. The neutrosophic set and its hybridizations are broadly adopted in many decision-making challenges. More researchers are working to discuss the validity of neutrosophy and its combinations in decision-making issues. In this work, we develop a new hybridized structure of neutrosophic soft set named Generalized Possibility Neutrosophic Soft Set (GPNSS) and discuss its basic properties. We define set-theoretical operations between two possibility neutrosophic soft sets and study some of their features. We also present the GPNS decision-making approach, which is based on the AND-product of GPNSS. Finally, we provide a numerical example to demonstrate how the technique may be effectively applied to the circumstances investigated.

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.

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.

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