On Bipolar Soft Sets

Shabir, Muhammad; Naz, Munazza

doi:10.48550/arxiv.1303.1344

Cited by 16 publications

(37 citation statements)

References 11 publications

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“…Definition 4: [47] Let C be a set of parameters. Then, NOT set of C, denoted by ⌉C, is defined by ⌉C = {⌉ ε : ε ∈ C} where ⌉ ε = not ε for ε ∈ C. Definition 5: [66] The triplet ψ = ( F, H, C) is called a bipolar soft set over a universe ℑ, in which F, H are mappings given by F : C −→ P(ℑ) , H : ⌉C −→ P(ℑ) such that F( ε) ∩ H( ⌉ ε) = / 0. Thus, a bipolar soft set over ℑ gives two parameterized families of subsets of the universe ℑ and the condition…”

Section: Perliminariesmentioning

confidence: 99%

“…From now onward, set of all bipolar soft sets over the universe ℑ will be referred to by BS ℑ Definition 6: [66] Let ( F, H, C) ∈ BS ℑ . Then, the complement of ( F, H, C), denoted by ( F, H, C) c , is defined by ( F, H, C) c = ( F c , H c , C) where F c and H c are mappings given by F c ( ε) = H(⌉ ε) and H c (⌉ ε) = F( ε) for all ε ∈ C.…”

Section: Perliminariesmentioning

confidence: 99%

“…The soft sets, the fuzzy sets, and the rough sets are not appropriate tools to handle this bipolarity. Based on the need of presenting both positive and negative sides of data, notion of bipolar soft set and its operations such as union, intersection and complement were first defined by Shabir and Naz [66]. After this research, BSSs have become increasingly popular with researchers.…”

Section: Introductionmentioning

confidence: 99%

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A Comparison of Promethee and TOPSIS Techniques Based on Bipolar Soft Covering-Based Rough Sets

2022

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The uncertainty in the data is an obstacle in decision-making problems. In order to solve problems with a variety of uncertainties a number of useful mathematical approaches together with fuzzy sets, rough sets, soft sets, bipolar soft sets have been developed. The rough set theory is an effective technique to study the uncertainty in data, while bipolar soft sets have the ability to handle the vagueness, as well as bipolarity of the data in a variety of situations. This study develops a new methodology, which we call the theory of Bipolar soft covering-based rough sets (BSCB-RSs), which will be used to propose a new technique to solve decision-making problems. The idea introduced in this study has never been discussed earlier. Furthermore, this concept has been explored by means of a detailed study of the structural properties. By combining the BSCB-RSs model with two traditional decision-making methods (the PROMETHE-II method and the TOPSIS method), we introduce a novel method for addressing multi-criteria group decisionmaking (MCGDM) problems. We give an application in multi-criteria group decision making (MCGDM) to show that the proposed technique can be successfully applied to some real world problems including uncertainty, namely, the selection of site for renewable energy pro ject ( Earth Dam ). The effectiveness of the proposed method is validated by comparing it with existing methods. The showed techniques exhibit the practicability, feasibility and sustainability of Site selection. Both MCGDM methods give one Site as conclusion.

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Section: Perliminariesmentioning

confidence: 99%

Section: Perliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Comparison of Promethee and TOPSIS Techniques Based on Bipolar Soft Covering-Based Rough Sets

2022

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“…Due to the importance of bipolarity, Shabir and Naz [49] laid the foundation of the bipolar soft sets (BSs) and proposed their set-theoretic operations with applications to DM. Following this study, BSs have grown in popularity among researchers.…”

Section: Introductionmentioning

confidence: 99%

Multigranulation Modified Rough Bipolar Soft Sets and Their Applications in Decision-Making

et al. 2022

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The classical theory of rough sets (RSs) established by Pawlak, mainly focused on the approximation of sets characterized by a single equivalence relation (ER) over the universe. However, most of the current single granulation structure models cannot meet the user demand or the target of solving problems. Multi-granulation rough sets (MGRS) can better deal with the problems where data might be spread over various locations. In this article, based on modified rough bipolar soft sets (MRBSs), the concept of multi-granulation MRBSs (MGMRBSs) is introduced. A finite collection of bipolar soft sets (BSs) has been used for this purpose. Several important structural properties and results of the suggested model are carefully analyzed. Meanwhile, to measure the uncertainty of MGMRBSs, some important measures associated with MGMRBSs are presented in MGMRBS-approximation space, and some of their interesting properties are examined. In the framework of multi-granulation, we developed optimistic MGMRBSs (OMGMRBSs) and pessimistic MGMRBSs (PMGMRBSs). The relationships among the MGMRBSs, OMGMRBSs, and PMGMRBSs are also established. After that, a novel multi-criteria group decisionmaking (MCGDM) approach based on OMGMRBSs is developed to solve some problems in decisionmaking (DM). The basic principles and the detailed steps of the DM model are presented in detail. To demonstrate the applicability and potentiality of the developed model, we give a practical example of a medical diagnosis. Finally, we conduct a comparative study of the proposed MCGDM approach with some existing techniques to endorse the advantages of the proposed model.INDEX TERMS MGRS, MRBSs, MGMRBS-approximations, MCGDM.

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“…By embedding the ideas of fuzzy sets, intuitionistic fuzzy sets and interval-valued fuzzy sets, many interesting applications of soft set theory have been expanded [7,8,9,11,12,16,17,18,21,31,32,33,34,36]. In 2013, Sabir and Naz [30] defined bipolar soft sets and basic operations of union, intersection and complementation for bipolar soft sets. They gave examples of bipolar soft sets and an application of bipolar soft sets in a decision making problem.…”

Section: Introductionmentioning

confidence: 99%

A new approach to bipolar soft sets and its applications

Karaaslan

Karataş

2015

Discrete Math. Algorithm. Appl.

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Molodtsov [25] proposed the concept of soft set theory in 1999, which can be used as a mathematical tool for dealing with problems that contain uncertainty. Sabir and Naz [30] defined notion of bipolar soft set in 2013. In this paper, we redefine concept of bipolar soft set and bipolar soft set operations as more functional than former. Also we study on their basic properties and we present a decision making method with application.

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On Bipolar Soft Sets

Cited by 16 publications

References 11 publications

A Comparison of Promethee and TOPSIS Techniques Based on Bipolar Soft Covering-Based Rough Sets

A Comparison of Promethee and TOPSIS Techniques Based on Bipolar Soft Covering-Based Rough Sets

Multigranulation Modified Rough Bipolar Soft Sets and Their Applications in Decision-Making

A new approach to bipolar soft sets and its applications

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