In this paper, the authors propose the concept of expert complex fuzzy soft sets as an extension to the classical complex fuzzy set model. Instead of being concerned with the study of the basic set theoretic operations for this model, which are essentially generalizations of the corresponding operations of the complex fuzzy set model, we extend the study of this model through the establishment of the mappings on classes of expert complex fuzzy soft sets. Through these mappings, we introduce the image and inverse image of an expert complex fuzzy soft set, which have immense applications in real-life applications. In addition to presenting the properties of the images and inverse images of this model, we present two numerical examples to demonstrate the utility of these concepts.

This paper examines the generalized intuitionistic fuzzy soft set (GIFSS) model which is an intuitively straightforward extension of the intuitionistic fuzzy soft set (IFSS) model. This concept which arises from IFSSs, is generalized by including a moderator's opinion regarding the validity of the information at hand, thus making it highly suitable for use in decision-making problems that involve uncertain, vague and/or unreliable data. In this paper, we introduce the tools that measure the distance, similarity and the degree of fuzziness of GIFSSs. The axiomatic definitions of the distance measure is introduced and subsequently used to define the similarity measure and intuitionistic entropy induced by this distance measure. Some of the algebraic properties of these measures are also verified. The well-known Hamming, normalized Hamming, Euclidean and normalized Euclidean distances are generalized to make them compatible with the concept of GIFSSs. Subsequently, some relations among these information measures are proposed and verified. These results indicate how these measures are related and how they can be deduced from one another. Finally, we demonstrate the application of the information measure between GIFSSs by applying it to a case study related to the moderation of school-based assessment components of students in externally accredited academic programs.

In this paper, we propose the concept of complex vague soft sets which are vague soft sets defined in a complex setting. 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. We introduce the axiomatic definition of the distance function between two complex vague soft sets and subsequently define several distance measures between complex vague soft sets. Finally some of the algebraic properties of these distance measures are verified.

Complex vague soft sets are essentially vague soft sets characterized by an additional parameter called the phase term which is defined over the set of complex numbers. In this study, we introduce and discuss the relations between complex vague soft sets. We present the definitions of the Cartesian product of complex vague soft sets and subsequently that of complex vague soft relations. The definition of the composition of complex vague soft sets is also provided. The notions of symmetric, transitive, reflexive and equivalence complex vague soft relations are then proposed and the algebraic properties of these concepts are verified. The relation between complex vague soft sets is then discussed in the context of a real-life problem: the relation between the financial indicators of the Chinese economy which are characterized by their degrees of influence on the financial indicators of the Malaysian economy, and the time required for the former to affect the latter. Interpretations of the results obtained from this example are then proposed by relating them to recent significant real-life events in the Chinese and Malaysian economies. (C) 2016 Elsevier B.V. All rights reserved.

The importance of decision making problem in an imprecise environment is growing very significantly in recent years. An object recognition from an imprecise multiobserver data has been presented here. We apply the concept of intuitionistic fuzzy soft sets in a decision making problem. We solve the problem with the help of `similarity measurement' technique.

Spectroscopic determinations of Fe, Zn, Mn, Cu, Co and Ni were carried out in 23 organisms including seaweeds, zooplankters, molluscs and fishes from Hooghly estuary at the confluence of Bay of Bengal. Seaweeds and gastropods were more efficient in accumulating levels while zooplankters bivalves and fishes showed intermediate levels. Analyses were performed on the sediment, water and on the individual dissected organs of a mussel, oyster and teleost fish. Bioaccumulation of Fe, Zn, Mn and Cu in the soft body parts (gills, mantle, liver etc.) of the three species showed a high degree of organ specificity in some cases. Major sources of the micropollutants include natural weathering, catchment runoff, urban and industrial discharges that may pose an ecological risk to the local estuarine ecosystem.

The problem of decision making in an imprecise environment has found paramount importance in recent years. A novel method of object recognition from an imprecise multiobserver data has been presented here. The method involves construction of a Comparison Table from a fuzzy soft set in a parametric sense for decision making.

In this paper, the authors study the theory of soft sets initiated by Molodtsov. The authors define equality of two soft sets, subset and super set of a soft set, complement of a soft set, null soft set, and absolute soft set with examples. Soft binary operations like AND, OR and also the operations of union, intersection are defined. De Morgan's laws and a number of results are verified in soft set theory.

In this paper, we apply the theory of soft sets to solve a decision making problem using rough mathematics.