Possibility interval-valued vague soft set

2019

Symmetry

Self Cite

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. soft sets [27], complex neutrosophic soft expert sets [28,29] and time-neutrosophic soft sets [30]. Many researchers [23,[31][32][33][34][35][36] have constructed several aggregation operators, such as simplified neutrosophic prioritized aggregation operators, single-valued neutrosophic Dombi weighted aggregation operators, simplified neutrosophic weighted aggregation operators, interval neutrosophic exponential weighted aggregation operators, and used them in decision-making issues. Aggregation operators perform a vital role in multicriteria decision making (MCDM) issues whose principle target is to aggregate a collection of inputs to a single number. Thus, aggregation operators give us effective tools to handle neutrosophic data in the decision process.For a two-dimensional universal set, Adam and Hassan [37,38] introduced the Q-fuzzy soft set (Q-FSS) and multi-Q-FSS, which includes a Q-fuzzy soft aggregation operator that allows constructing more efficient decision-making methods. Broumi [39] presented the notion of the Q-intuitionistic fuzzy soft set (Q-IFSS), and defined some basic properties and basic operations. Actually, these notions cannot handle indeterminate data that appear in two universal sets. Inspired by this, Abu Qamar and Hassan [40] initiated the concept of the Q-neutrosophic soft set (Q-NSS) by upgrading the membership functions of the NSS to a two-dimensional entity. As a result, Q-NSS is premium to these models with three two-dimensional independent membership functions. Hence, this concept serves indeterminacy and two-dimensionality at the same time. Moreover, the Q-neutrosophic set (Q-NS) is basically an NS defined over a two-dimensional set. Thus, it has added advantages to NS by treating a two-dimensional universal set, which makes it mor...

Section: Introductionmentioning

confidence: 99%

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

Qamar

2019

Symmetry

Self Cite

“…Soft set theory, on the other hand, was initiated by Molodtsov [27] as a general mathematical tool used to handle uncertainties, imprecision and vagueness. Since its inception, a lot of extensions of soft set model have been developed such as fuzzy soft sets [28], vague soft sets [29], interval-valued vague soft sets [30][31][32], soft expert sets [33], soft multiset theory [34] and neutrosophic soft set [35][36][37][38][39]. At present, soft set has allured wide attention and made many achievements [40][41][42].…”

Section: Introductionmentioning

confidence: 99%

The complex neutrosophic soft expert set and its application in decision making

Al-Quran

2018

IFS

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This paper presents a novel complex neutrosophic soft expert set (CNSES) concept. The range of values of CNSES is extended to the unit circle in the complex plane by adding an additional term called the phase term which describes CNSES's elements in terms of the time aspect. CNSES is a hybrid structure of soft sets and single-valued neutrosophic sets (SVNSs) defined in a complex setting where the experts' opinions are included, thus making it highly suitable for use in decision-making problems that involve uncertain and indeterminate data where the time factor plays a key role in determining the final decision. Based on this new concept we define some concepts related to this notion as well as some basic operations namely the complement, union, intersection, AND and OR. The basic properties and relevant laws pertaining to this concept such as the De Morgan's laws are also verified. Lastly, we propose an algorithm to solve complex neutrosophic soft expert decision-making problem by converting it from the complex state to the real state and subsequently provided the detailed decision steps. This study is supported by the comparison with other existing methods.

“…Later Maji and Roy [2,3] used soft set theory in decision making problems and defined some operations in soft set theory such as subset and the complement of soft set [4]. Moreover, soft set has been developed rapidly to fuzzy soft sets [5][6][7][8], intuitionistic fuzzy soft sets [9][10][11][12], vague soft set [13][14][15][16], vague soft multiset [17], generalised vague soft expert set [18][19][20][21], interval-valued fuzzy soft sets [22], interval-valued vague soft sets [23][24][25] and interval-valued intuitionstic fuzzy soft sets [26]. Fuzzy soft sets are further extended to neuro-fuzzy soft sets [27,28] and Q-fuzzy soft sets [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Vague soft set relations and functions

Alhazaymeh

Journal of Intelligent &Amp; Fuzzy Systems

2015

Self Cite

Molodtsov introduced the theory of soft sets as a generalized tool for modelling complex systems involving uncertain or not clearly defined objects. In this paper the concepts of vague soft set relations are introduced as a sub-vague soft set of the Cartesian product of the vague soft sets and related concepts such as equivalent vague soft set relation, partition, composition and function along with some properties and illustrative examples.