Цена: 4839 RUR

ПодробнееSolution of Fuzzy Linear and Non-linear Equations

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31903771

Fuzzy sets are sets whose elements have degrees of membership. Fuzzy set theory was formalized by Professor Lotfi Zadeh at the University of California in 1965 as an extension of the classical notion of set. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition an element either belongs or does not belong to the set. Fuzzy sets generalize classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values 0 or 1. Classical bivalent sets are in fuzzy set theory usually called crisp sets. On the other hand fuzzy set is more specified than crisp set. It can take a decision between membership grade 0 to 1, i.e. unit interval [0, 1]. This book attempts to fill the needs of the algorithms of Newton’s method, Fixed-Point Iteration method and Bisection method which are used to solve fuzzy non-linear equations for the linear fuzzy real number. The procedures to obtain solutions of different types of fuzzy linear equations have also been discussed. The book has been outlined into four chapters.

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Цена: 3549 RUR

ПодробнееFuzzy Logic Unveiled

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31966331

The concept of fuzzy logic is based on the fuzzy set theory which tries to represent the vagueness. Due to ambiguity, real word problems are very complex in nature. We cannot solve multifaceted vagueness using classical set theory. The reason behind that is, in classical set theory element either belongs to or does not belong to a set. Solution to real world problems can be given using human expertise and knowledge and classical logic failed to do so. Fuzzy logic provide solution to such problems as it supports to multivalued propositions. Thus fuzzy logic is widely used for application development in many areas. In this book we tried to unveil the fuzzy logic concept. We have discussed various concepts like the difference between classical set theory and fuzzy logic, fuzzy set, membership function and its type, fuzzification, fuzzy rules, method of defuzzification, etc. Then we elaborate the concept of fuzzy inference system and its implementation using MATLAB Fuzzy Logic Toolbox.

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Цена: 9716 RUR

ПодробнееTheory of Fuzzy Structures and Applications

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31903033

This book is an exposition of some fundamental concepts of Fuzzy Algebra, Fuzzy Topology along with applications of Fuzzy Set Theory in diverse field of scientific knowledge. Today in almost all disciplines of science, engineering and technology, the theory of Fuzzy Sets has become an indispensable part of the curriculum. In fact, Fuzzy Set Theory (FST) provides language for almost all disciplines in contemporary mathematics in much the same way as mathematics does for many sciences. The book first provides exposure to the concepts of fuzzy subgroupoids, fuzzy subgroups, fuzzy level subgroups, fuzzy normal subgroups, fuzzy ring, fuzzy ideal, fuzzy field, fuzzy linear spaces, geometrical sets in a linear space, fuzzy module. Secondly, topological & algebraic topological linear spaces has been dealt with. Finally, the applicational aspects of Fuzzy Set Theory (FST) to two different areas of human knowledge such as sports (Cricket scores) and medicine (detection of blood sugar in human beings) are in-corporated.

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Цена: 8190 RUR

ПодробнееFuzzy Algebra

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31902912

A classical subset of a universal set X is identified by its corresponding characteristic function which is a function from X to {0,1}. This can be generalized by considering a function from X to [0,1]. The corresponding subset is called a fuzzy subset and the function is called a membership function. This generalization helps in fuzzifying different theories involving sets. Algebra is an important field in which fuzzification is done. In this book an attempt has been made to deal with the study of some types of algebraic structures in different fuzzy setting. Homomorphism of different types in fuzzy setting are dealt with in group structures. A fuzzy set called translational invariant fuzzy set is introduced and with respect to it different algebraic structures are constructed. Lattice structure in fuzzy setting is considered and product of different fuzzy structures are studied.No previous knowledge of fuzzy set is assumed and so all basics of fuzzy set theory is discussed here. It is expected that post graduate students and researchers in fuzzy algebra will be benefited from this monograph.

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Цена: 4139 RUR

ПодробнееTheory of Fuzzy Soft Sets

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31904031

Fuzzy set theory proposed by Professor L. A. Zadeh is assumed to be generalization of classical or crisp sets. In case of fuzzy sets, it has been accepted that neither the intersection of a fuzzy set with its complement is the null set, nor the union of a fuzzy set with its complement is the universal set. In this regard H. K. Baruah has forwarded an extended definition of fuzzy sets which enables us to define complement of fuzzy set in a way that the axioms of exclusion and contradiction are satisfied by the fuzzy sets also. The sole motivation of this book is to study the notion of fuzzy soft sets in the light of extended definition of fuzzy sets initiated by H. K. Baruah and hence to formulate the fuzziness and softness occurring within the frame work of a number of mathematical avenues. In our work, an attempt has been made to formulate some soft mathematical theories along with a few extensions to some existing frameworks.

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Цена: 3549 RUR

ПодробнееFuzzy B-double star Opensets and fuzzy chi-double star Closed Sets

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31903732

The concept of fuzzy set was introduced by Zadeh in his classical paper (Zadeh, 1965). Balasubramaniam and Sundaram defined generalized fuzzy closed sets in a fuzzy topological space and introduced certain types of fuzzy continuous functions between fuzzy topological spaces.(X, T) and (Y, S) denotes a fuzzy topological spaces.Also in this book I introduced different types of open sets and closed sets in fuzzy topological spaces.I think it will be very useful to co higher research in this field.

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Цена: 7890 RUR

ПодробнееSome Aspects of Fuzzy Algebraic Structures

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31904973

This book deals with a comprehensive study of fuzzy algebraic structures. The objective of this book is to investigate fuzzy aspects of some algebraic structures. We attempt to study algebraic structures like modules, rings, hemirings in fuzzy and intuitionistic fuzzy setting. Small submodules of modules play a vital role in structure theorem. Study of fuzzy aspects of small submodules motivates us to study the concepts like fuzzy small epimorphism, fuzzy co-essential extension, Jacobson L-radical, fuzzy hollow submodules. The introduction of fuzzy point and neighbourhood relations leads to a new direction of research on fuzzy algebraic structure generalizing the conventional notion of studies. t - norms play a crucial role in several areas of mathematics and computer science. These studies motivate us to define fuzzy submodule with respect a t-norm which is based on neighbourhood relation. As an immediate consequence of degree of belongs to in fuzzy set, degree of not belongs to arises. This concept generalizes the concept of fuzzy set to intuitionistic fuzzy sets. These concepts inspire us to study about fuzzy modules, fuzzy rings and ideals, fuzzy hemirings intuitionistically.

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Цена: 3549 RUR

ПодробнееLinear Programming Problems with Fuzzy Technical Coefficients

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31904528

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming (LP) with fuzzy variables. This book contains an approximate but convenient method, without using the ranking functions, for solving these problems with fuzzy non-negative technical coefficients. The method has been illustrated with numerical examples.

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Цена: 6026 RUR

ПодробнееTHE MATHEMATICS OF FUZZINESS: MYTHS AND REALITIES

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31901647

Two things we are aiming to discuss. First, it has been accepted that intersection of a fuzzy set and its complement is not the void set. Similarly it has also been accepted that the union of a fuzzy set and its complement is not the universal set.Accordingly, the fuzzy sets have been accepted not to form a field. However, can the intersection of anything, a fuzzy set or whatever else, and its complement be non-null? Secondly, when it was seen that the fuzzy sets do not allow the additivity postulate for a measure to hold, a new definition of fuzzy measure was formalized. Can it not be so that possibility can be expressed in terms of something that is measure theoretic? Here in this monograph, we are going to show that the fuzzy sets do form a field. For that, we need to extend the definition of fuzziness just to define the complement of a fuzzy set. We are further going to establish that not one but two probability spaces are necessary and sufficient to define a possibility space. Hence in terms of two probability measures, possibility can be studied. We assure the readers that what we are proposing is absolutely mathematical. There is nothing fuzzy about it.

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Цена: 5790 RUR

ПодробнееA Study On Fuzzy Topological Spaces In Sostak's Sence

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31905253

Zadeh (1965), introduced the basic idea of a fuzzy set as an extension of classical set theory. In 1968, Chang was the first to introduce the concept of a fuzzy topology. Kubiak and Sostak (1985) introduced the fundamental concept of a fuzzy topological structure, as an extension of both crisp topology and fuzzy topology, in the sense that not only the objects are fuzzified, but also the axiomatics. Also, Sostak gave some rules and showed how such an extension can be realized. The purpose of this book is to introduce and study some new definitions of fuzzy sets, continuous mappings and separation axioms On Fuzzy Topological Spaces In Sostak's Sence.

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Цена: 5790 RUR

ПодробнееSome Approximation Methods in Fuzzy Logic

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31903268

In this book we define some new methods to approximate a fuzzy function by fuzzy polynomials. Also by introducing some new distances we define the nearest approximations of a fuzzy number. ?In his book?, the ?definition of fuzzy linear programming with fuzzy variables and a? ?method for solving it according to a special class of ranking which is used ?to find the approximating polynomials as well as? ?definition of the problem of approximation?, ??are discussed?. Then the approximation problem on triangular fuzzy numbers ?leads us to an approximating polynomial name e?-approximation? ?and on the set of all fuzzy numbers?, ?the approximation problem gives ?us the D-approximation and we present a method to find it?, ? also ?the universal and SAF-approximations which are special cases of D-approximation are found in this book?. ?Also two best ?approximations of a triangular valued fuzzy function on a set of? ?points are defined and are computed?. ?Furthermore a chapter contains an idea for ?computing the nearest approximation of a fuzzy number out of a? ?particular subset of all fuzzy numbers.

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Цена: 7790 RUR

ПодробнееA Study on Intuitionistic Fuzzy Matrices

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31903778

This monogram is so written that it is self contained for independent study as well and hope it very much useful for cognition of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy set, generalized intuitionistic fuzzy sets, generalized interval-valued intuitionistic fuzzy sets, generalized intuitionistic fuzzy matrices, generalized interval-valued intuitionistic fuzzy matrices and neutrosophic intuitionistic fuzzy sets. The arrangement and presentation is simple. The chapters are arranged in logical order. The theorems and propositions have been stated carefully and whenever necessary complete proofs of the theorems and propositions have been given. Also numerical examples are given for concretization of the theorems and propositions. It is hope that the readers will benefit immensely from this monogram.

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Цена: 6690 RUR

ПодробнееFuzzy Logistic Regression models with their application in Medicine

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31903601

This book points out to logistic regression analysis in fuzzy environment. In this regard, three clinical situations are considered with a proposed method for each one. First and second methods model fuzzy diagnosis based on a set of non fuzzy (crisp) variables by using a real number and a fuzzy number for the possibility of being ill, respectively. The third model is proposed for a situation of no ambiguities in diagnosis but in the relations among the variables.

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Цена: 4839 RUR

ПодробнееFuzzy R0 and R1 Properties

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31904410

In 1965, L.A. Zadeh introduced the concept of Fuzzy Set as an attempt to mathematically handle those situations which are inherently vogue, imprecise or fuzzy in nature. The advent of Fuzzy Set Theory has led to the development of many areas of Mathematics and Sciences. It has become a concern and a new tool for mathematicians working in many different disciplines of Mathematics. After the introduction of "Fuzzy Topology" by Chang C.L. many concepts of "General Topology" have been fuzzified successfully by many researchers. The present book entitled "Fuzzy R0 and R1 Properties" is devoted to finding out some new R1-concepts for fuzzy topological spaces. Besides some existing concepts of fuzzy R0, R1, T0, T1, T2 and regular topological spaces are recalled, and studied in detail. Interrelations among various separation axioms of fuzzy topological spaces are discussed. This book will be helpful for the undergraduate and graduate students, particularity for those who are studying Fuzzy Mathematics.

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Цена: 7256 RUR

ПодробнееFuzzy Sets and Information

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31901293

Fuzzy set theory has capability to describe the uncertain situations, containing ambiguity and vagueness. Fuzziness is found in our decision, in our thinking, in the way we process information, and particularly in our language.The objective of the book is to study fuzzy mathematics with applications and to characterize new measures of fuzzy information with their various generalizations. The fuzzy information measure deals with vague and ambiguous uncertainties. Large number of measures of entropy, directed divergence and symmetric divergence for probability distributions are known. Analogously, there is a set of variety of measures for fuzzy sets available. Cross-entropy measure is also known as the information discrepancy between two probability distributions. Derived from cross-entropy, fuzzy directed divergence measures the dissimilarity between two fuzzy sets. Various generalized measures of fuzzy information have been introduced. The concept of ''useful'' fuzzy information by attaching utility to the uncertainties of fuzziness and probabilities of randomness has been introduced.

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Цена: 7790 RUR

ПодробнееL-Fuzzy Subgroups, L-Vague Ideals and Boolean Vague Sets. Dr.T.Eswarlal

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31848333

The concept of Fuzzy set was opened up a new horizon in Mathematical Sciences.In fuzzy set theory, a fuzzy set which assigns to each object a grade of membership ranking between 0 and 1. This single value combines both evidence and nonevidence without indicating howmuch there is of each. But it is felt by several decission makers and researchers that proper decission making the evidence and non evidence both necessary.To counter this problem, the vague set theory is introduced which it has both the grade of membership and grade of nonmembership functions and these are generalization of fuzzy sets. The object of thesis, author is to generalize the fuzzy algebra in terms of L-fuzzy and vague algebra with complete version.The author introduced and studied Boolean vague sets and its algebra, this type of Booleanisation of vague sets has the advantages of representing such Boolean vague sets as a pair of arrays where each array consists of 0,s & 1's, in view of famous Stone theorem that any Boolean algebra is a subalgebra of direct product of two element Boolean algebra. Further, the author introduced and studied L-vague sets and its algebra, where L is a complete Brouwerian lattice.

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This book deals with a comprehensive study of fuzzy algebraic structures. The objective of this book is to investigate fuzzy aspects of some algebraic structures. We attempt to study algebraic structures like modules, rings, hemirings in fuzzy and intuitionistic fuzzy setting. Small submodules of modules play a vital role in structure theorem. Study of fuzzy aspects of small submodules motivates us to study the concepts like fuzzy small epimorphism, fuzzy co-essential extension, Jacobson L-radical, fuzzy hollow submodules. The introduction of fuzzy point and neighbourhood relations leads to a new direction of research on fuzzy algebraic structure generalizing the conventional notion of studies. t - norms play a crucial role in several areas of mathematics and computer science. These studies motivate us to define fuzzy submodule with respect a t-norm which is based on neighbourhood relation. As an immediate consequence of degree of belongs to in fuzzy set, degree of not belongs to arises. This concept generalizes the concept of fuzzy set to intuitionistic fuzzy sets. These concepts inspire us to study about fuzzy modules, fuzzy rings and ideals, fuzzy hemirings intuitionistically.