scholarly journals Bipolar Hypersoft Sets

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1826
Author(s):  
Sagvan Y. Musa ◽  
Baravan A. Asaad
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Set Theory ◽  
Negative Information ◽  
The Other ◽  
Computer Memory ◽  
Mathematical Tool ◽  
Positive Information ◽  
Fundamental Properties ◽  
Null Set

Hypersoft set theory is an extension of soft set theory and is a new mathematical tool for dealing with fuzzy problems; however, it still suffers from the parametric tools’ inadequacies. In order to boost decision-making accuracy even more, a new mixed mathematical model called the bipolar hypersoft set is created by merging hypersoft sets and bipolarity. It is characterized by two hypersoft sets, one of which provides positive information and the other provides negative information. Moreover, some fundamental properties relative to it such as subset, superset, equal set, complement, difference, relative (absolute) null set and relative (absolute) whole set are defined. Furthermore, some set-theoretic operations such as the extended intersection, the restricted union, intersection, union, AND-operation and OR-operation of two bipolar hypersoft sets with their properties are discussed and supported by examples. Finally, tabular representations for the purposes of storing bipolar hypersoft sets in computer memory are used.

scholarly journals Bipolar Soft Topological Spaces

2020 ◽  
Vol 13 (2) ◽  
pp. 227-245
Author(s):  
Asmaa Fadel ◽  
Syahida Che Dzul-Kifli
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
The Other ◽  
Topological Spaces ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Positive Information ◽  
Soft Limit ◽  
Soft Point ◽  
Soft Topological Space

Bipolar soft set theory is a mathematical tool associates between bipolarity and soft set theory, it is defined by two soft sets one of them gives us the positive information where the other gives us the negative. The goal of our paper is to define the bipolar soft topological space on a bipolar soft set and study its basic notions and properties. We also investigate the definitions of: bipolar soft interior, bipolar soft closure, bipolar soft exterior, bipolar soft boundary and establish some important properties on them. Some relations between them are also discussed. Moreover, the notions of bipolar soft point, bipolar soft limit point and the derived set of a bipolar soft set are discussed. In additions, examples are presented to illustrate our work.

scholarly journals Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1498
Author(s):  
Shahbaz Ali ◽  
Muneeba Kousar ◽  
Qin Xin ◽  
Dragan Pamučar ◽  
Muhammad Shazib Hameed ◽  
...  
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Fundamental Properties ◽  
Research Article ◽  
Multi Attribute Decision Making ◽  
Algebraic Operations ◽  
Interval Valued

In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.

Does Performing Other Audit Tasks Affect Going-Concern Judgments?

1999 ◽  
Vol 74 (4) ◽  
pp. 493-508 ◽  
Author(s):  
Stephen E. Rau ◽  
Donald V. Moser
Keyword(s):  
Information Processing ◽  
Review Process ◽  
Negative Information ◽  
The Other ◽  
Positive Information ◽  
Going Concern ◽  
Staff Members

This study examines whether personally performing other audit tasks can bias supervising seniors' going-concern judgments. During an audit, the senior performs some audit tasks him/herself and delegates other tasks to staff members. When personally performing an audit task, the senior would focus on the evidence related to that task. We predict that such evidence will have greater influence on the senior's subsequent going-concern judgment. The results of our experiment are consistent with our predictions. When provided with an identical set of information, seniors who performed another audit task for which the underlying facts of the case reflected positively (negatively) on the company's viability, subsequently made going-concern judgments that were relatively more positive (negative). Our results also demonstrate that the well-documented tendency of auditors to attend more to negative information does not always dominate auditors' information processing. Subjects who performed the task for which the underlying facts reflected positively on the company's viability directed their attention to such positive information and, consequently, both their memory and judgments were more positive than those of subjects in the other conditions. Recent findings indicating that biases in seniors' going-concern judgments may not be fully offset in the review process are discussed along with other potential implications of our results.

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.

scholarly journals Fuzzy Soft Multiset Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Soft Set ◽  
Mathematical Tool ◽  
Basic Properties ◽  
Definition Of

In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh et al. in 2011 introduced the definition of a soft multiset as a generalization of Molodtsov's soft set. In this paper we give the definition of fuzzy soft multiset as a combination of soft multiset and fuzzy set and study its properties and operations. We give examples for these concepts. Basic properties of the operations are also given. An application of this theory in decision-making problems is shown.

scholarly journals Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematical Tool ◽  
Intuitionistic Fuzzy ◽  
Rough Approximation ◽  
Soft Rough Set

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical example is provided to illustrate the developed approach.

scholarly journals A new approach to bipolar soft sets and its applications

2015 ◽  
Vol 07 (04) ◽  
pp. 1550054 ◽  
Author(s):  
Faruk Karaaslan ◽  
Serkan Karataş
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Sets ◽  
New Approach ◽  
Basic Properties ◽  
Set Operations ◽  
First Results

Molodtsov [Soft set theory-first results, Comput. Math. App. 37 (1999) 19–31] proposed the concept of soft set theory in 1999, which can be used as a mathematical tool for dealing with problems that contain uncertainty. Shabir and Naz [On bipolar soft sets, preprint (2013), arXiv:1303.1344v1 [math.LO]] 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 Shabir and Naz’s definition and operations. Also we study on their basic properties and we present a decision making method with application.

scholarly journals Application of Average fs-Aggregate Algorithm for Multi-criteria Decision Making in Real Life Problem

2018 ◽  
pp. 1-11
Author(s):  
Rajesh Kumar Pal
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Accurate Result ◽  
Medical Science ◽  
Real Life ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Mathematical Methods ◽  
Real Life Problem ◽  
The Given

Generally in our day to day life we come across the real life situations when right decision making becomes difficult. In different fields like economics, social science, medical science, environment, where such complicacy arises and involves uncertainties. The conventional mathematical methods are unsuitable to solve such problems. To solve this problem, we are to find the various parameters related to the problem to use them to get the accurate result. So fuzzy soft set theory is the best mathematical tool for solving such problems using different techniques. In this research paper, we have taken a multi-criteria real life problem to select a suitable city which suits the best conditions as per the given parameters. For getting the solution, we used average fs-aggregation algorithm for using multi-criteria parameters.

scholarly journals Decision Making Using Rough Topology and Indiscernibility Matrix for Corona Virus Diagnosis

2020 ◽  
pp. 31-33
Author(s):  
Kanchana. M ◽  
Rekha. S
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Mathematical Tool ◽  
Virus Diagnosis ◽  
Corona Virus ◽  
Uncertain Knowledge

Rough set theory is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge. In recent years the research and applications on rough set theory have attracted more. In this paper, we have introduced and analyze the Rough set theory and also decide the factors for corona virus diagnosis by using Indiscernibility matrix.

scholarly journals Soft Expert Sets

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Mathematical Tool ◽  
Decision Making Problem

In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Many researchers have studied this theory, and they created some models to solve problems in decision making and medical diagnosis, but most of these models deal only with one expert. This causes a problem with the user, especially with those who use questionnaires in their work and studies. In our model, the user can know the opinion of all experts in one model. So, in this paper, we introduce the concept of a soft expert set, which will more effective and useful. We also define its basic operations, namely, complement, union intersection AND, and OR. Finally, we show an application of this concept in decision-making problem.

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