Top Research Papers on Fuzzy Set Theory

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.

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.

The following concepts are covered for standard fuzzy sets: ?

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.

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.

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 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 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.

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.

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 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 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 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.

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.

All possible involutions in fuzzy set theory are completely described.

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 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.

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...

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 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 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.

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 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.

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 ↔.

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.

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."

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.

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.

The definition of fuzzy variable sets which is expressed by relative membership function and the model of variable fuzzy clustering iteration, variable fuzzy pattern recognition, and variable fuzzy opposite recognition are given are given.

New measures of entropy for fuzzy sets in continuous reference set are introduced and a brief history of development of the fuzzy entropy is given.

A system to plan a color arrangement in interior space such as rooms and offices based on three main processes: a determination process of dominant colors, a determined process of harmony colors, and an adjustment process of the resultant colors.

The mathematical framework allows us a generalized method for `indexing' predicates, which corresponds to `fuzzification' of properties, in an intuitive sense, and it can be established a relationship between this indexed mathematics and fuzzy mathematics.

This paper proposes a possibility of developing an axiomatic set theory, as first-order theory within the framework of fuzzy logic in the style of Hajek's Basic fuzzy logic BL, and shows the nontriviality of the theory.

The Archimedean axiom in fuzzy set theory is critically discussed and brought into perspective within a measurement theoretic framework and then its validity for fuzzy set theories is questioned.

A new and natural interpretation of fuzzy set theory is presented in a cumulative Heyting valued model for intuitionistic set theory that can consistently get various notions and properties of fuzzy sets, fuzzy relations and fuzzy mappings.

Abstract : Dual automorphisms, involutions and intuitionistic negations on the lattice F(X) of Fuzzy Sets taking values on a complete distributive lattice L are characterized. All Symmetric, De Morgan and Intuitionistic Algebras on F(X) and their isomorphisms are described. Finally, negation functions and their conjugated classes are characterized.

The aim of this paper is to sketch some connections between concepts and results of the classical mathematics and, respectively the mathematics of fuzzy sets.

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 trials performed with the medical expert system CADIAG-2 suggest that it might be a suitable basis for the development of a computerized diagnosis system.

Fuzzy set theory is applied to three areas of economic modeling, economic forecasting and economic policy and offers a range of optimum policies depending on a risk parameter and leaves the final policy choice to the decision maker.