Top Research Papers on Fuzzy Set Theory

It is proven that the basic constructions in the theories of fuzzy sets, fuzzy soft sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories, and this common background makes it possible to transform these basic concepts from one theory to another.

A model of analysis of successful strategies in academic influence is proposed and important recommendations for academics and journal editors are offered, allowing them to guide and advise academic production in the scholarly debate of the future.

The article provides information about fuzzy sets: its history, definitions, operations, and review of set theory, which provides a solution to one of the options.

A description of fuzzy indexing procedures defined to represent the varying significance of terms in synthesizing the documents’ contents and some applications to model flexible information retrieval systems are presented.

Fuzzy set theory was introduced in 1965 by Dr. Lotfi Zadeh to represent/manipulate data and information possessing nonstatistical uncertainties and allows for much more realistic models of real-world situations.

A quick overview of developing fuzzy sets methodologies in actuarial science, and the basic mathematics of fuzzy sets is provided.

In this review, the basic mathematical framework of fuzzy set theory will be described, as well as the most important applications of this theory to other theories and techniques.

A quick overview of developing fuzzy sets methodologies in actuarial science, and the basic mathematics of fuzzy sets is provided.

The following concepts are covered for standard fuzzy sets: ?

This paper defines the concept of interval probability distribution and discusses its properties, and an illustrative example related to the decision-making process is employed to illustrate the application of the presented work.

The new C*-fuzzy set considers the relationship between fuzzy sets and represents the relationship with relativity, and overcomes all the errors and shortcomings of Zadeh's fuzzy set theory.

Handbook

This paper focuses on the study of different methods to classify new objects, which are not considered in the starting data set, in order to determine the best possible decision for them.

It is shown that if the notion of fuzzy sets is further fuzzified by making equality (as well as membership) fuzzy, the resultant categories are indeed toposes.

Fuzzy sets could be an agreeable tool when no probabilities are accessible for states of nature and decisions are given under incompleteness, and usage of fuzzy sets gives better solutions in vagueness.

In the Classical Logic, the ‘Law of the Excluded Middle’ states that out of two contradictory propositions (where one proposition is the negation of the other) one must be true, and the other false, or that every proposition must either be true or false: it will not be possible to be and not to be the same thing; these truth values with a sharp demarcation may be represented by ‘1’ for ‘true’ and ‘0’ for ‘false’ and form the basis of the traditional set theory. Thus it cannot consider cases of vagueness. However, there are many concepts and predicates that are surrounded by vagueness or uncert...

The main objective of this paper is to present another variant of the neutrosophic set called T-spherical fuzzy-valued neutrosophic set (T-SFVNS), a generalization of the aforementioned combinations that allows for the representation of indeterminacy and inconsistency in a more nuanced manner.

This paper introduces the concept of effective fuzzy soft set and its operation and study some of its properties and gives an application of this theory to medical diagnosis (MD) and exhibits the technique with a hypothetical case study.

The purpose of this paper is to introduce fuzzy set theory which has a number of properties that makes it suitable for formalizing the uncertain information in dealing with systems comprising a very large number of interacting elements or involving aLarge number of variables in their decision trees.

Fuzzy Sets and Fuzzy Logic is a true magnum opus; it addresses practically every significant topic in the broad expanse of the union of fuzzy set theory and fuzzy logic.

Fuzzy set theory and fuzzy logic provide a different way to view the problem of modeling uncertainty and offer a wide range of computational tools to aid decision making.

Fuzzy set theory and fuzzy logic are a highly suitable and applicable basis for developing knowledgebased systems in medicine for tasks such as the interpretation of sets of medical findings, the single or differential diagnosis of diseases from various areas of medicine, the optimal selection of medical treatments, and for real-time monitoring of patient data.

All the negations of PL(X) satisfying the extension principle and the generalized extension principle are fully described through the negation of L. Necessary and sufficient conditions are given for n to be an ortho or u-complementation and for n to satisfy the DeMorgan laws.

Fuzzy linguistic variables and fuzzy algorithms offer an effective, more flexible way to describe a system's behavior too complex for a classical mathematical model and are very successful in economics, management science, artificial intelligence, information retrieval systems, pattern recognition, image processing, psychology, biology, and other fields rendered inherently fuzzy.

Fuzzy set theory has a number of properties that make it suitable for formalizing the uncertain information upon which medical diagnosis and treatment is usually based, and it provides a linguistic approach with an excellent approximation to texts.

An introduction to fuzzy set theory is described. Topics covered include: neural networks and fuzzy systems; the dynamical systems approach to machine intelligence; intelligent behavior as adaptive model-free estimation; fuzziness versus probability; fuzzy sets; the entropy-subsethood theorem; adaptive fuzzy systems for backing up a truck-and-trailer; product-space clustering with differential competitive learning; and adaptive fuzzy system for target tracking.

The fuzzification of k-ideals (also r-ideal) of inclines is considered, and then it is proved the notion of fuzzy ideal and fuzzy k-Ideal coincide, and some properties on fuzzy r-Ideals are investigated.

This edited book is a compilation of the papers presented at a symposium held in Acapulco, Mexico, in December 1980 and aims to provide the reader with an up-to-date view of the development in the theory of fuzzy sets.

It is demonstrated that fuzzy set theory is applicable to a wide range of practical problems and that simple fuzzy control algorithms do give good results.

An emerging group of successful parties in Central and Eastern "Concept Structures and Fuzzy Set Theory: A Proposal for Concept" and an in-depth understanding of rough set theory is discussed.

The paper shows, in particular, that these theories do always verify the Kleene's law, as well as the Non-Contradiction and Excluded-Middle principles when these are understood as in ancient logic.

All possible involutions in fuzzy set theory are completely described.

It is found that the existing definition of complementation as well as the probability - possibility consistency principles is not well defined and the results obtained would be inappropriate fro m the standpoint of the Randomness-Fuzziness consistency principles.

La teoria clasica de conjuntos precisa en sus construcciones logicas y en sus reglas deductivas no recoge aquellos fenomenos reales cuyas caracteristicas son "imprecisas" o "difusas". En la esfera de los predicados subjetivos, y por tanto imprecisos, la teoria de conjuntos se enfrenta a un obstaculo dificil de superar. ?Como podriamos definir el conjunto formado por las personas "altas" de una determinada reunion? ?Desde que altura se empieza a ser "alto"? La teoria de subconjuntos difusos pretende eliminar los obstaculos habituales para la teoria de conjuntos y reclama para si un cuerpo de do...

An interpretation of lattice-valued logic, defined by Titani, in basic fuzzy logic,defined by Hajek, is presented and its axioms are interpreted in fuzzy set theory, under slight modifications of the fuzzy set theories axiomatics.

This section of HSM will also put forward some concerns regarding present attitudes towards the theory of fuzzy sets and its applicability III management-oriented fields of research.

This paper presents the author's personal views on the descriptive and prescriptive power of Fuzzy set Theory in letting informational and intrinsic imprecision be taken into account in an Optimization model.

This paper studies about the higher order fuzzy sets specially about intuitionistic fuzzy sets (or vague sets) and some examples of these sets are studied.

A way in which quantum computing can be used to extend the class of fuzzy sets is investigated, to see states of a quantum register as characteristic functions of quantum fuzzy subsets of a given set.

The notion of a fuzzy set provides a convenient point of departure for the construction of a conceptual framework which parallels in many respects the framework used in the case of ordinary sets, but is more general than the latter and may prove to have a much wider scope of applicability, particularly in the fields of pattern classification and information processing.

This study proves that fuzzy soft sets also give rise to a powerset theory, which is also defined by a monad, and describes the construction of fuzzy soft relations as an example of the use of monads in fuzzysoft sets.

This paper investigated α-sets, operations of fuzzy numbers, on interval fuzzy sets and also on fuzzy mappings, and introduced S.Bs.

This paper presents a simplified way of application of rough set data analysis in decision-making process concerning the use of real estates. The results will be presented based on the example of real estates at the disposal of local communal government.In the second part of this paper an object of research was the area of the fringe area of the city and the village and parameters characterizing it, definite on the ground analyses of current forms of the land use with the utilization of foundations of the fuzzy sets theory.

Qualitative & Multi-Method Research, Spring 2014 puter Is Changing The authors' Analytic Habits, finds that the relationship between Software Development, Theory, and Education in Structural Equation Modeling and the Goals of QCA is changing.

From a logical standpoint, each logic has its corresponding set theory in which each logical operation is translated into a basic operation for set theory; namely, the relation ⊆ and = on sets are translation of the logical operations → and ↔.

Initial analysis indicates that such three types of nice Zadeh sets seem to have captured the correct concept of fuzziness, and mathematically speaking, the theory forms naturally, behaves smoothly and three categories of nice Y2K sets are concrete categories, so Z adeh set theory is "perfect."

This paper comments on the results that B. K. McDaniel had achieved by having applied fuzzy set theory in analyzing the interdependences and coalescences of basic color categories, reveals the great importance that fuzzy set Theory holds in the study of semantic fuzziness of categories, and points out the problems existing in the studies.

A fundamental set of arithmetic operations for (a, b) $-FSSs is established and their main characteristics are explored, and a multi-criteria decision-making strategy is designed that operates in this novel framework.

Using fuzzy type theory, basic concepts of rough set theory and the topological concepts of AST are generalized to become the concepts of the fuzzy set theory.

This paper introduces the unification of these four cut sets as one cut set with parameters, and establishes the appropriate decomposition theorem and representation theorem of fuzzy sets.