T-spherical fuzzy power aggregation operators and their applications in multi-attribute decision making.

The paper aims to present the concept of power aggregation operators for the T-spherical fuzzy sets (T-SFSs). T-SFS is a powerful concept, with four membership functions denoting membership, abstinence, non-membership and refusal degree, to deal with the uncertain information as compared to other existing fuzzy sets. On the other hand, the relationship between the different pairs of the attributes are well recorded in terms of power operators. Thus, keeping these advantages of T-SFSs and power operator, the objective of this work is to define several weighted averaging and geometric power aggregation operators. The stated operators named as T-spherical fuzzy weighted, ordered weighted, hybrid averaging and geometric operators for the collection of the T-SFSs. The various properties and the special cases of them are also derived. Further, the consequences of proposed new power aggregation operators are studied in view of some constraints. Finally, a multiple attribute decision making algorithm, based on the proposed operators, is established to solve the problems with uncertain information and illustrate with numerical examples. A comparative study, superiority analysis and discussion of the proposed approach are furnished to confirm the approach.

Cubic Vague Set and its Application in Decision Making.

From the hybrid nature of cubic sets, we develop a new generalized hybrid structure of cubic sets known as cubic vague sets (CVSs). We also define the concept of internal cubic vague sets (ICVSs) and external cubic vague sets (ECVSs) with examples and discuss their interesting properties, including ICVSs and ECVSs under both P and R-Order. Moreover, we prove that the R and R-intersection of ICVSs (or ECVSs) need not be an ICVS (or ECVS). We also derive the different conditions for P-union (P-intersection, R and R-intersection) operations of both ICVSs (ECVSs) to become an ICVS (ECVS). Finally, we introduce a decision-making based on the proposed similarity measure of the CVSs domain and a numerical example is given to elucidate that the proposed similarity measure of CVSs is an important concept for measuring entropy in the information/data. It will be shown that the cubic vague set has the novelty to accurately represent and model two-dimensional information for real-life phenomena that are periodic in nature.

The Complex Neutrosophic Soft Expert Relation and Its Multiple Attribute Decision-Making Method.

This paper introduces a novel soft computing technique, called the complex neutrosophic soft expert relation (CNSER), to evaluate the degree of interaction between two hybrid models called complex neutrosophic soft expert sets (CNSESs). CNSESs are used to represent two-dimensional data that are imprecise, uncertain, incomplete and indeterminate. Moreover, it has a mechanism to incorporate the parameter set and the opinions of all experts in one model, thus making it highly suitable for use in decision-making problems where the time factor plays a key role in determining the final decision. The complex neutrosophic soft expert set and complex neutrosophic soft expert relation are both defined. Utilizing the properties of CNSER introduced, an empirical study is conducted on the relationship between the variability of the currency exchange rate and Malaysian exports and the time frame (phase) of the interaction between these two variables. This study is supported further by an algorithm to determine the type and the degree of this relationship. A comparison between different existing relations and CNSER to show the ascendancy of our proposed CNSER is provided. Then, the notion of the inverse, complement and composition of CNSERs along with some related theorems and properties are introduced. Finally, we define the symmetry, transitivity and reflexivity of CNSERs, as well as the equivalence relation and equivalence classes on CNSESs. Some interesting properties are also obtained.

Q-Neutrosophic Soft Relation and Its Application in Decision Making.

Q-neutrosophic soft sets are essentially neutrosophic soft sets characterized by three independent two-dimensional membership functions which stand for uncertainty, indeterminacy and falsity. Thus, it can be applied to two-dimensional imprecise, indeterminate and inconsistent data which appear in most real life problems. Relations are a suitable tool for describing correspondences between objects. In this study we introduce and discuss Q-neutrosophic soft relations, which can be discussed as a generalization of fuzzy soft relations, intuitionistic fuzzy soft relations, and neutrosophic soft relations. Q-neutrosophic soft relation is a sub Q-neutrosophic soft set of the Cartesian product of the Q-neutrosophic soft sets, in other words Q-neutrosophic soft relation is Q-neutrosophic soft sets in a Cartesian product of universes. We also present the notions of inverse, composition of Q-neutrosophic soft relations and functions along with some related theorems and properties. Reflexivity, symmetry, transitivity as well as equivalence relations and equivalence classes of Q-neutrosophic soft relations are also defined. Some properties of these concepts are presented and supported by real life examples. Finally, an algorithm to solve decision making problems using Q-neutrosophic soft relations is developed and verified by an example to show the efficiency of this method.

Entropy, Measures of Distance and Similarity of Q-Neutrosophic Soft Sets and Some Applications.

The idea of the Q-neutrosophic soft set emerges from the neutrosophic soft set by upgrading the membership functions to a two-dimensional entity which indicate uncertainty, indeterminacy and falsity. Hence, it is able to deal with two-dimensional inconsistent, imprecise, and indeterminate information appearing in real life situations. In this study, the tools that measure the similarity, distance and the degree of fuzziness of Q-neutrosophic soft sets are presented. The definitions of distance, similarity and measures of entropy are introduced. Some formulas for Q-neutrosophic soft entropy were presented. The known Hamming, Euclidean and their normalized distances are generalized to make them well matched with the idea of Q-neutrosophic soft set. The distance measure is subsequently used to define the measure of similarity. Lastly, we expound three applications of the measures of Q-neutrosophic soft sets by applying entropy and the similarity measure to a medical diagnosis and decision making problems.