Vague Soft Multiset Theory

2018

Symmetry

Neutrosophic triplet structure yields a symmetric property of truth membership on the left, indeterminacy membership in the centre and false membership on the right, as do points of object, centre and image of reflection. As an extension of a neutrosophic set, the Q-neutrosophic set was introduced to handle two-dimensional uncertain and inconsistent situations. We extend the soft expert set to generalized Q-neutrosophic soft expert set by incorporating the idea of soft expert set to the concept of Q-neutrosophic set and attaching the parameter of fuzzy set while defining a Q-neutrosophic soft expert set. This pattern carries the benefits of Q-neutrosophic sets and soft sets, enabling decision makers to recognize the views of specialists with no requirement for extra lumbering tasks, thus making it exceedingly reasonable for use in decision-making issues that include imprecise, indeterminate and inconsistent two-dimensional data. Some essential operations namely subset, equal, complement, union, intersection, AND and OR operations and additionally several properties relating to the notion of generalized Q-neutrosophic soft expert set are characterized. Finally, an algorithm on generalized Q-neutrosophic soft expert set is proposed and applied to a real-life example to show the efficiency of this notion in handling such problems.

Section: Introductionmentioning

confidence: 99%

Generalized Q-Neutrosophic Soft Expert Set for Decision under Uncertainty

Qamar

2018

Symmetry

“…Fuzzy set theory generalised the range values of classical set theory from the integer 0 and 1 to the interval [0, 1]. It was henceforth extended to various forms of fuzzy sets [2]- [5] and has proven to be very useful in many different fields [6]- [9]. However, there are many problems like complete colour characterization of colour images, taste recognition of food items and decision making problems with multi aspects which cannot be characterized by a single membership function of Zadeh's fuzzy sets.…”

Section: Introductionmentioning

confidence: 99%

Complex Multi-Fuzzy Relation for Decision Making using Uncertain Periodic Data

Al-Qudah

2018

IJET

We introduce a new type of relations called complex multi-fuzzy relation (CMFR). The novelty of CMFR lies in the ability of complex multi-membership functions to achieve more range of values while handling uncertainty of data that is periodic in nature. The application of complex multi-fuzzy sets is then discussed in determining: the influence of modern methods of education on student performance, and the time required for the former to affect the latter. A comparison between different existing relations and CMFR to show the ascendancy of our proposed CMFR is provided. Thereafter, a few related concepts such as complement, union, intersection and inverse along with several propositions are discussed, followed by the composition of CMFR along with some related theorems. Finally the notions of symmetric, transitive, reflexive, and equivalence complex multi-fuzzy relations are established in our work.

“…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

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.