The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. It is pr...
A comparison between type-1 fuzzy sets (T1FSs) and intuitionistic fuzzy sets (IFSs) is made. The operators defined over IFSs that do not have analogues in T1FSs are shown, and such analogues are introduced whenever possible.
The conventional concept of α-level sets of fuzzy sets will be treated as the upper α-level sets. In this paper, the concept of lower α-level sets of fuzzy sets will be introduced, which can also be regarded as a dual concept of upp...
Two important basic inference models of fuzzy reasoning are Fuzzy Modus Ponens (FMP) and Fuzzy Modus Tollens (FMT). In order to solve FMP and FMT problems, the full implication triple I algorithm, the reverse triple I algorithm and the Subsethood Inf...
This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of...
A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set...
This paper addresses uncertainty modelling of shorelines by comparing fuzzy sets and random sets. Both methods quantify extensional uncertainty of shorelines extracted from remote sensing images. Two datasets were tested: pan-sharpened Pleiades with...
Hesitant fuzzy sets extend fuzzy sets by considering many-valued sets of membership degrees. Real applications validate this model and decision making approaches of various forms permit to act in a flexible manner. If we can avail ourselves of hesita...
Complex fuzzy sets (CFSs) are a suitable tool to manage spatial directional information which includes distance and direction. However, spatial directional information is given by linguistic values. It is very awkward for the CFS to describe this typ...
Recently, the notion of a three-way fuzzy set is presented, inspired by the basic ideas of three-way decision and various generalized fuzzy sets, including lattice-valued fuzzy sets, partial fuzzy sets, intuitionistic fuzzy sets, etc. As the new theo...
The arithmetic operations of fuzzy sets are completely different from the arithmetic operations of vectors of fuzzy sets. In this paper, the arithmetic operations of vectors of fuzzy intervals are studied by using the extension principle and a form o...
Many of the new fuzzy structures with complete
In this article, we introduce two new rough set models based on the concept of double fuzzy relations. These models are called optimistic and pessimistic multi-granulation double fuzzy rough sets. We discuss their properties and explore the relations...
We lay the theoretical foundations of a novel model, termed picture hesitant fuzzy rough sets, based on picture hesitant fuzzy relations. We also combine this notion with the ideas of multi-granulation rough sets. As a consequence, a new multi-granul...
The research of incomplete fuzzy soft sets is of paramount importance in fuzzy soft sets, where the combination of incomplete fuzzy soft set and decision-making problem is of great significance. Incomplete information in fuzzy soft sets leads to more...
Considering a fuzzy graph G is simple and can be connected and considered as a subset
The following paper presents deductive theories of n-Pythagorean fuzzy sets (n-PFS). N-PFS objects are a generalization of the intuitionistic fuzzy sets (IFSs) and the Yager Pythagorean fuzzy sets (PFSs). Until now, the values of membership and non-m...
In the paper, for the first time, four distances for Circular Intuitionistic Fuzzy Sets (C-IFSs) are defined. These sets are extensions of the standard IFS that are extensions of Zadeh’s fuzzy sets. As it is shown, the distances for the C-IFS are dif...
The goal of this paper is to introduce a novel soft hyperstructure called multi-fuzzy soft hyperstructure. We investigate the notion of multi-fuzzy soft hypermodules and some of their structural properties are discussed. We discuss the behavior image...
In a real-life scenario, it is undoable and unmanageable to solve a decision-making problem with the single stand-alone decision-aid method, expert assessment methodology or deterministic approaches. Such problems are often based on the suggestions o...
Intuitionistic Fuzzy Sets (
In this manuscript, two generalizations of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets, known as spherical fuzzy sets and T-spherical fuzzy sets, are discussed and a numerical and geometrical comparison among them is established. A T...
A well-researched field is the development of Computer Aided Diagnosis (CADx) Systems for the benign-malignant classification of abnormalities detected by mammography. Due to the nature of the breast parenchyma, there are significant uncertainties ab...
Measuring the similarity between two objects and classifying them on the basis of their resemblance level has been a fundamental tool of the human mind. In an intuitionistic fuzzy environment, we find researchers that have attempted to generalize the...
In this paper, we consider the family of parameterized Mandelbrot-like sets generated as any point
In this paper, we open up more possibilities to define higher types of fuzzy sets in a mixed way. In doing so, we show that there are essentially two alternative definitions for fuzzy sets of higher types, one of which is widely adopted in the litera...
A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership ve...
Consider a simple connected fuzzy graph (FG) G and consider an ordered fuzzy subset H = {(u1, σ(u1)), (u2, σ(u2)), …(uk, σ(uk))}, |H| ≥ 2 of a fuzzy graph; then, the representation of σ − H is an ordered k-tupl...
This article introduces the notion of bipolar complex fuzzy soft set as a generalization of bipolar complex fuzzy set and soft set. Furthermore, this article contains elementary operations for bipolar complex fuzzy soft sets such as complement, union...
Orthopairs (pairs of disjoint sets) have points in common with many approaches to managing vaguness/uncertainty such as fuzzy sets, rough sets, soft sets, etc. Indeed, they are successfully employed to address partial knowledge, consensus, and border...
We review several generalizations of the concept of fuzzy sets with two- or three-dimensional lattices of truth values and study their relationship. It turns out that, in the two-dimensional case, several of the lattices of truth values considered he...
In this work, we consider De Luca and Termini’s notion of non-probabilistic entropy, and we extend some entropy-like measures of the degree of fuzziness to type-2 fuzzy sets. With this aim, we first study different entropy measures proposed in...
In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notio...
In this paper, a generalized picture fuzzy soft set is proposed, which is an extension of the picture fuzzy soft sets. We investigate the basic properties of picture fuzzy soft sets and define an F-subset, M-subset, extended union, extended intersect...
This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prosta...
This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: two disjoint union fuzzy sets, two disjoint fuzzy sets and two gener...
Recently, the new operation ∆ was introduced over intuitionistic fuzzy sets and some of its properties were studied. Here, new additional properties of this operations are formulated and checked, providing an analogue to the De Morgan’s Law (Theorem...
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
Interval type-2 fuzzy sets (IT2 FS) play an important part in dealing with uncertain applications. However, how to measure the uncertainty of IT2 FS is still an open issue. The specific objective of this study is to present a new entropy named fuzzy...
Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture...
The combination of two elements in a group structure is an element, while, in a hypergroup, the combination of two elements is a non-empty set. The use of hypergroups appears mainly in certain subclasses. For instance, polygroups, which are a special...
In support of reasoning with sparse rule bases, fuzzy rule interpolation (FRI) offers a helpful inference mechanism for deriving an approximate conclusion when a given observation has no overlap with any rule in the existing rule base. One of the rec...
The publication opportunities in science require knowing the existing gaps in the academic debate. In recent decades, scholars specializing in fuzzy theory and applied methodologies have experienced an unprecedented evolution of the field. The Sustai...
This article presents a pioneering mathematical model, fuzzy bipolar hypersoft (FBHS) sets, which combines the bipolarity of parameters with the fuzziness of data. Motivated by the need for a comprehensive framework capable of addressing uncertainty...
In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the fuzzy set (FS) coined by Yager in 2017, have been used to manage inexplicit and indefinite information in daily life with a high precision and greater...
Recent trends in modern information processing have focused on polarizing information, and and bipolar fuzzy sets can be useful. Bipolar fuzzy sets are one of the important tools that can be used to distinguish between positive information and negati...
This paper presents the novel concept of rough intuitionistic fuzzy ideals within the realm of BCK-algebras and investigates their fundamental properties. Furthermore, we introduce a set-valued homomorphism over a BCK-algebra, laying the foundation f...
The concept of Multi Q-Fermatean hesitant fuzzy soft sets (MQFHFSS), derived from the integration of multi-Q fuzzy soft sets and Fermatean hesitant fuzzy sets, can be applied in practice to optimise the resolution of complex multi-criteria decision-m...
The Open Geospatial Consortium (OGC) Geography Markup Language (GML) explicitly represents geographical spatial knowledge in text mode. All kinds of fuzzy problems will inevitably be encountered in spatial knowledge expression. Especially for those e...
Overlap function (which has symmetry and continuity) is widely used in image processing, data classification, and multi-attribute decision making problems. In recent years, theoretical research on overlap function has been extended to interval valued...
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