Group Generalized q-Rung Orthopair Fuzzy Soft Sets: New Aggregation Operators and Their Applications

In recent years, q-rung orthopair fuzzy sets have been appeared to deal with an increase in the value of q > 1 , which allows obtaining membership and nonmembership grades from a larger area. Practically, it covers those membership and nonmembership grades, which are not in the range of intuitionistic fuzzy sets. The hybrid form of q-rung orthopair fuzzy sets with soft sets have emerged as a useful framework in fuzzy mathematics and decision-makings. In this paper, we presented group generalized q-rung orthopair fuzzy soft sets (GGq-ROFSSs) by using the combination of q-rung orthopair fuzzy soft sets and q-rung orthopair fuzzy sets. We investigated some basic operations on GGq-ROFSSs. Notably, we initiated new averaging and geometric aggregation operators on GGq-ROFSSs and investigated their underlying properties. A multicriteria decision-making (MCDM) framework is presented and validated through a numerical example. Finally, we showed the interconnection of our methodology with other existing methods.

On Interval-Valued Fuzzy Soft Preordered Sets and Associated Applications in Decision-Making

Recently, using interval-valued fuzzy soft sets to rank alternatives has become an important research area in decision-making because it provides decision-makers with the best option in a vague and uncertain environment. The present study aims to give an extensive insight into decision-making processes relying on a preference relationship of interval-valued fuzzy soft sets. Firstly, interval-valued fuzzy soft preorderings and an interval-valued fuzzy soft equivalence are established based on the interval-valued fuzzy soft topology. Then, two crisp preordering sets, namely lower crisp and upper crisp preordering sets, are proposed. Next, a score function depending on comparison matrices is expressed in solving multi-group decision-making problems. Finally, a numerical example is given to illustrate the validity and efficacy of the proposed method.

Semiring-Valued Fuzzy Sets and F-Transform

The notion of a semiring-valued fuzzy set is introduced for special commutative partially pre-ordered semirings, including basic operations with these fuzzy structures. It is showed that many standard MV-algebra-valued fuzzy type structures with standard operations, such as hesitant, intuitionistic, neutrosophic or fuzzy soft sets are, for appropriate semirings, isomorphic to semiring-valued fuzzy sets with operations defined. F-transform and inverse F-transform are introduced for semiring-valued fuzzy sets and properties of these transformations are investigated. Using the transformation of MV-algebra-valued fuzzy type structures to semiring-valued fuzzy sets, the F-transforms for these fuzzy type structures is introduced. The advantage of this procedure is, among other things, that the properties of this F-transform are analogous to the properties of the classical F-transform and because these properties are proven for any semiring-valued fuzzy sets, it is not necessary to prove them for individual fuzzy type structures.

Fuzzy Soft Topology Based on Generalized Intersection and Generalized Union of Fuzzy Soft Sets

In this study, the generalized intersection and union operations of fuzzy soft set (FSS) are established on the basis of traditional FSS operations, which overcome the shortcomings of traditional FSS operations that do not meet De Morgan’s law, and a series of properties of generalized intersection and union operations of FSS are obtained. The fuzzy soft topology under generalized intersection and generalized union operation of FSSs is established. Finally, the topological construction of weak FSS and strong FSS is discussed, and the relationship between them and the topological construction of traditional FSS is obtained.

Observation of a Change in Human Attitude in a Decision Making Process Equipped with an Interference of a Third Party

In this paper, the attitudes of experts are observed for the possible changes after taking a certain decision. The decision is taken by two persons with different fields of expertise. There is also an annotation of such changes due to the interference of a third person, which is main idea of this paper. These observations are done by developing fuzzy soft differential equations with the help of optimum fuzzy soft constants (OFSCs), which are obtained through the ranking coefficients. The ranking of alternatives is based on the coefficients, which are obtained through a decision-making process. Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is exploited to rank the alternatives, and the attitudes of resource persons are examined through phase portraits and line graphs of the respective system of differential equations. The utilization of TOPSIS is a practice of multi-criteria decision-making in the analysis of human behaviours. Dual hesitant fuzzy soft sets are taken to represent the initial data.

Fuzzy Transforms for Hesitant, Soft or Intuitionistic Fuzzy Sets

Classical F-transform for lattice-valued fuzzy sets can be defined using monadic relation in Zadeh’s monad or, equivalently, as a special semimodule homomorphism. In this paper, we use an analogical approach and by choosing suitable monads and semimodule homomorphisms, we define F-transform for hesitant, intuitionistic or fuzzy soft sets. We prove that these F-transforms naturally extend classical lattice-valued F-transform for lattice-valued fuzzy sets.

Decision-Making with Fuzzy Soft Matrix Using a Revised Method: A Case of Medical Diagnosis of Diseases

In this paper, we study the matrix representation of fuzzy soft sets, complement of fuzzy soft sets, product of fuzzy soft matrices and the application of fuzzy soft matrices in medical diagnosis presented by Lavanya and Akila. Additionally, a new method (max-min average) based on fuzzy reference function is introduced instead of the max-product method by Lavanya and Akila to extend Sanchez’s technique for decision making problems in medical diagnosis. Using the same data by Lavanya and Akila, the result shows that the new method gives more information about the medical status of the patients being considered in relation to a set of diseases.