N-soft rough sets and its applications

2021 ◽  
Vol 40 (1) ◽  
pp. 565-573
Author(s):  
Di Zhang ◽  
Pi-Yu Li ◽  
Shuang An
Keyword(s):  
Decision Making ◽  
Hybrid Model ◽  
Rough Sets ◽  
Real Life ◽  
Decision Problems ◽  
Multi Criteria Decision Making ◽  
Approximation Space ◽  
Soft Sets ◽  
Approximation Operators ◽  
Rough Approximation

In this paper, we propose a new hybrid model called N-soft rough sets, which can be seen as a combination of rough sets and N-soft sets. Moreover, approximation operators and some useful properties with respect to N-soft rough approximation space are introduced. Furthermore, we propose decision making procedures for N-soft rough sets, the approximation sets are utilized to handle problems involving multi-criteria decision-making(MCDM), aiming at electing the optional objects and the possible optional objects based on their attribute set. The algorithm addresses some limitations of the extended rough sets models in dealing with inconsistent decision problems. Finally, an application of N-soft rough sets in multi-criteria decision making is illustrated with a real life example.

scholarly journals A Decision-Making Approach Based on a Multi Q-Hesitant Fuzzy Soft Multi-Granulation Rough Model

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 711 ◽  
Author(s):  
Kholood Alsager ◽  
Noura Alshehri ◽  
Muhammad Akram
Keyword(s):  
Decision Making ◽  
Fault Detection ◽  
Hybrid Model ◽  
Rough Set ◽  
Rough Sets ◽  
General Framework ◽  
Fuzzy Soft Set ◽  
Rough Model ◽  
Approximation Operators ◽  
Rough Approximation

In this paper, we propose a new hybrid model, multi Q-hesitant fuzzy soft multi-granulation rough set model, by combining a multi Q-hesitant fuzzy soft set and multi-granulation rough set. We demonstrate some useful properties of these multi Q-hesitant fuzzy soft multi-granulation rough sets. Furthermore, we define multi Q-hesitant fuzzy soft ( M k Q H F S ) rough approximation operators in terms of M k Q H F S relations and M k Q H F S multi-granulation rough approximation operators in terms of M k Q H F S relations. We study the main properties of lower and upper M k Q H F S rough approximation operators and lower and upper M k Q H F S multi-granulation rough approximation operators. Moreover, we develop a general framework for dealing with uncertainty in decision-making by using the multi Q-hesitant fuzzy soft multi-granulation rough sets. We analyze the photovoltaic systems fault detection to show the proposed decision methodology.

scholarly journals Some More Results on IF Soft Rough Approximation Space

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Sharmistha Bhattacharya (Halder) ◽  
Bijan Davvaz
Keyword(s):  
Data Mining ◽  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Approximation Space ◽  
Rough Approximation ◽  
Frame Work ◽  
Set Approximation

Fuzzy sets, rough sets, and later on IF sets became useful mathematical tools for solving various decision making problems and data mining problems. Molodtsov introduced another concept soft set theory as a general frame work for reasoning about vague concepts. Since most of the data collected are either linguistic variable or consist of vague concepts so IF set and soft set help a lot in data mining problem. The aim of this paper is to introduce the concept of IF soft lower rough approximation and IF upper rough set approximation. Also, some properties of this set are studied, and also some problems of decision making are cited where this concept may help. Further research will be needed to apply this concept fully in the decision making and data mining problems.

scholarly journals Soft Covering Based Rough Sets and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Şaziye Yüksel ◽  
Zehra Güzel Ergül ◽  
Naime Tozlu
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Prostate Cancer Risk ◽  
Approximation Operator ◽  
Soft Sets ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Model Combining ◽  
Rough Approximation ◽  
Generalized Rough Set

Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft covering approximation space and soft covering rough approximation operators and present their basic properties. We show that a new type of the soft covering upper approximation operator is smaller than soft upper approximation operator. Also we present an example in medicine which aims to find the patients with high prostate cancer risk. Our data are 78 patients from Selçuk University Meram Medicine Faculty.

scholarly journals Soft Rough Approximation Operators and Related Results

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Zhaowen Li ◽  
Bin Qin ◽  
Zhangyong Cai
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Soft Sets ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Generalized Rough Set ◽  
Special Case

Soft set theory is a newly emerging tool to deal with uncertain problems. Based on soft sets, soft rough approximation operators are introduced, and soft rough sets are defined by using soft rough approximation operators. Soft rough sets, which could provide a better approximation than rough sets do, can be seen as a generalized rough set model. This paper is devoted to investigating soft rough approximation operations and relationships among soft sets, soft rough sets, and topologies. We consider four pairs of soft rough approximation operators and give their properties. Four sorts of soft rough sets are investigated, and their related properties are given. We show that Pawlak's rough set model can be viewed as a special case of soft rough sets, obtain the structure of soft rough sets, give the structure of topologies induced by a soft set, and reveal that every topological space on the initial universe is a soft approximating space.

scholarly journals A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Tianyu Xue ◽  
Zhan’ao Xue ◽  
Huiru Cheng ◽  
Jie Liu ◽  
Tailong Zhu
Keyword(s):  
Rough Sets ◽  
Rough Set Theory ◽  
Binary Relations ◽  
Approximation Space ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Binary Relation ◽  
Novel Method ◽  
Interval Valued

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators.

Multi-Criteria Decision Making

2019 ◽  
pp. 155-184
Author(s):  
Tolga Temucin
Keyword(s):  
Decision Making ◽  
Real Life ◽  
Multiple Criteria ◽  
Decision Problems ◽  
Multi Criteria Decision Making ◽  
Military Operations ◽  
Military Organizations ◽  
Decision Making Problem ◽  
The Military ◽  
Life Decision

Multi-criteria decision making (MCDM) is a discipline that explicitly considers assessing alternatives in a decision problem with respect to multiple criteria. Those methods are frequently used to solve real-life decision problems that incorporate multiple, conflicting, and incommensurate criteria. Considering the chaotic, complex, and ambiguous nature and the dynamics of the military operations, most decision problems observed in military organizations also follow a similar structure involving multiple criteria. This chapter gives an overview of the basic decision-making problem types and decision processes observed in military organizations and provides information on the MCDM methodologies adopted to solve those problems.

Multi-Criteria Decision Making

2021 ◽  
pp. 469-497
Author(s):  
Tolga Temucin
Keyword(s):  
Decision Making ◽  
Real Life ◽  
Multiple Criteria ◽  
Decision Problems ◽  
Multi Criteria Decision Making ◽  
Military Operations ◽  
Military Organizations ◽  
Decision Making Problem ◽  
The Military ◽  
Life Decision

Multi-criteria decision making (MCDM) is a discipline that explicitly considers assessing alternatives in a decision problem with respect to multiple criteria. Those methods are frequently used to solve real-life decision problems that incorporate multiple, conflicting, and incommensurate criteria. Considering the chaotic, complex, and ambiguous nature and the dynamics of the military operations, most decision problems observed in military organizations also follow a similar structure involving multiple criteria. This chapter gives an overview of the basic decision-making problem types and decision processes observed in military organizations and provides information on the MCDM methodologies adopted to solve those problems.

Multi-Criteria Decision Making

2021 ◽  
pp. 48-76
Author(s):  
Tolga Temucin
Keyword(s):  
Decision Making ◽  
Real Life ◽  
Multiple Criteria ◽  
Decision Problems ◽  
Multi Criteria Decision Making ◽  
Military Operations ◽  
Military Organizations ◽  
Decision Making Problem ◽  
The Military ◽  
Life Decision

Multi-criteria decision making (MCDM) is a discipline that explicitly considers assessing alternatives in a decision problem with respect to multiple criteria. Those methods are frequently used to solve real-life decision problems that incorporate multiple, conflicting, and incommensurate criteria. Considering the chaotic, complex, and ambiguous nature and the dynamics of the military operations, most decision problems observed in military organizations also follow a similar structure involving multiple criteria. This chapter gives an overview of the basic decision-making problem types and decision processes observed in military organizations and provides information on the MCDM methodologies adopted to solve those problems.

scholarly journals The Parameter Reduction of Fuzzy Soft Sets Based on Soft Fuzzy Rough Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Zhiming Zhang
Keyword(s):  
Set Theory ◽  
Rough Sets ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Fuzzy Rough Sets ◽  
Soft Sets ◽  
Parameter Reduction ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Soft Sets

Fuzzy set theory, rough set theory, and soft set theory are three effective mathematical tools for dealing with uncertainties and have many wide applications both in theory and practise. Meng et al. (2011) introduced the notion of soft fuzzy rough sets by combining fuzzy sets, rough sets, and soft sets all together. The aim of this paper is to study the parameter reduction of fuzzy soft sets based on soft fuzzy rough approximation operators. We propose some concepts and conditions for two fuzzy soft sets to generate the same lower soft fuzzy rough approximation operators and the same upper soft fuzzy rough approximation operators. The concept of reduct of a fuzzy soft set is introduced and the procedure to find a reduct for a fuzzy soft set is given. Furthermore, the concept of exclusion of a fuzzy soft set is introduced and the procedure to find an exclusion for a fuzzy soft set is given.

An algebraic approach to N-soft sets with application in decision-making using TOPSIS

2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Real World ◽  
Algebraic Approach ◽  
Multi Criteria Decision Making ◽  
Commutative Monoids ◽  
Soft Sets ◽  
Algebraic Properties ◽  
Different Types ◽  
Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

Sign in / Sign up

Export Citation Format

Share Document