Intuitionistic fuzzy sets theory is the modification or extension of fuzzy sets theory by incorporating two additional functions to the membership function. We studied the mathematics of intuitionistic fuzzy sets in collaboration with fuzzy sets. In terms of application, intuitionistic fuzzy sets theory is awesome because of its ability to cope with uncertainties in decision making especially in difficult cases we elaborated in this study. In a nutshell, intuitionistic fuzzy sets theory is a suitable and reliable tool in decision science.

This book deals with a concise study of convergence in intuitionistic fuzzy n-normed linear spaces. This book mainly contains the author's own research work in the area of lacunary ideal convergence. Fuzzy normed spaces have been an increasingly popular area of mathematical research in recent times, both in terms of theory and applications. But the availability of books in the area of fuzzy normed spaces is very rare. This book provides a good discussion on the development of both fuzzy and intuitionistic fuzzy set theory. The transition from fuzzy normed linear spaces to intuitionistic fuzzy n-normed linear spaces has been presented systematically. Anybody interested in the theory or application of fuzzy or intuitionistic fuzzy normed spaces will find this book more than useful. The book is written in such a way that mathematical prerequisites are minimum. Since the main subject of study in this book is a generalisaton of the concept of usual convergence, so all the related results in convergence have been incorporated in the book. This book may be used as a ready reference for an up to date account of results in the theory of fuzzy/intuitionistic fuzzy normed linear spaces.

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.

This book is intended mainly to make an understanding about the applications of intuitionistic fuzzy sets. Various operators on intuitionistic fuzzy sets are defined and their properties are also studied with suitable examples. Though no prior knowledge of IFSs is required, the reader is expected to be familiar with the basic notions of fuzzy sets and the operators defined on them.This is only a beginning of the applications of ‘intuitionistic fuzzy’ logic and it will give further elegance in logical computing.

Efficiency evaluation is an important part of decision making in many areas particularly in management and manufacturing sectors. Uncertainty and fuzziness of the real world problems have increased utilization of fuzzy sets theory in many research areas and data envelopment analysis is one of them. Utilizing data envelopment analysis to evaluate efficiency scores of decision making units in fuzzy environment requires fuzzy models and mathematical methods for solving fuzzy models with minimum calculation and maximum precision. This book provides latest theoretical developments in fuzzy DEA and can be considered as a basic reference for new researchers in fuzzy DEA.

Decision making by the aircrafts services of the international airport, which provides for intensive traffic of aircraft and their ground handling, becomes a very topical issue. If earlier it was believed that the intensity is provided only by the number of runways, nowadays a large accumulation of aircraft on the airport platform-field creates equally complex difficulties in comparison with aircraft take-offs and landings. Solving such problems with the use of «crisp methods» of queuing theory gives little. This article deals with modern «fuzzy methods» based on simulation modeling and fuzzy logic.

Linear programming is one of the most frequently applied operations research techniques. The classical tool for solving the linear programming problem in practice is the class of simplex algorithm which was proposed and developed by Dantzig. A lot of real world decision problems are described by linear programming models and sometimes it is necessary to formulate them with elements of imprecision or uncertainty. This imprecise nature has long been studied with the help of the probability theory. However, the probability theory might not provide the correct interpretation to solve some practical decision making problems. In these cases, the fuzzy set theory might be more helpful. In this book, the limitations and shortcomings of existing methods for solving linear programming problems with fuzzy sets are pointed out. Some new ranking approaches for the ordering of fuzzy sets and vague sets are developed and also new methods to find the unique optimal solutions of linear programming problems under fuzzy environment and vague environment are presented.

Any modern industrial manufacturing unit inevitably faces problems of vagueness in various aspects such as raw material availability, human resource availability, processing capability and constraints and limitations imposed by marketing department. This problem has to be solved by a methodology which takes care of such fuzzy information. As the analyst solves this problem, the decision maker and the implementer have to coordinate with the analyst for taking up a decision on a successful strategy for implementation. Such a complex problem of vagueness and uncertainty can be handled by the theory of fuzzy logic.In this book, a new fuzzy logic based methodology using a specific membership function, named as modified S-curve membership function is proposed. The modified S-curve membership function is first formulated and its flexibility in taking up vagueness in parameters is established by an analytical approach.The usefulness of this modified S-curve membership function is further established using a real life industrial production planning of a chocolate manufacturing unit.

The book contains elementary ideas of different Intuitionistic fuzzy algebraic structures viz. Intuitionistic fuzzy ideals and Intuitionistic fuzzy submodules. Some interesting relationships between images of Intuitionistic fuzzy ideal and Noetherian & Artinian rings are established. The notion of Intuitionistic fuzzy essential submodules, Intuitionistic fuzzy closed submodules, finite dimensional Intuitionistic fuzzy submodules, Intuitionistic fuzzy uniform submodules, Intuitionistic fuzzy submodules of IF Goldie dimension, Intuitionistic fuzzy projective and injective submodules are introduced and many of their important properties are discussed. Hope this book will provide necessary prerequisites for researchers in this field.

The book deals with the problems regarding IFMs and IVIFMs. Three new operations viz., direct product, Kronecker product and Kronecker sum on IFMs are defined and studied some interesting properties. Some conditions are discussed for which a GIFM will be a generalized intuitionistic fuzzy nilpotent matrix. Also, by using the concept of relative pseudocomplement relation on intuitionistic fuzzy distributive lattice, the intuitionistic fuzzy eigenvalue and eigenvector of IFM A are defined. An application of GIFM in multicriteria decision making problem are presented. It is also proved that the set of IVIFMs form a semiring.

A very convenient mechanism for exploitation of uncertainty and vagueness in decision making is fuzzy logic. This paper shows practical application of fuzzy logic in the Armed Forces of Serbia through an example of selecting the location for setting a bridge for crossing a water obstacle. By the fuzzy logic system inexperience of the decision maker is minimized. This demonstration is even more significant considering experience of some experts gained during combat activities. The criteria relevant for the choice of a bridge crossing point, as well as their influence on the choice of the alternatives, have the values displayed in numerical values or fuzzy linguistic descriptors. By analyzing the results obtained, we can conclude that the developed fuzzy system can successfully evaluate the chosen locations and formulate the strategy of decision-making in the choice of the location. This book should hlep shed some light on modelling of fuzzy logic system to support decision making process, and should be especially useful to students who have interest in fuzzy logic modelling, or anyone else who have interest in operational researchs.

Multi-Fuzzy Sets is an introductory text on multi-fuzzy sets written with minimal prerequisites. It is a study of multi-fuzzification of crisp sets, multi-level fuzziness and multi-dimensional fuzziness. The concept of multi-fuzzy sets is a generalization of Zadeh’s fuzzy sets and Atanassov’s intuitionistic fuzzy sets. The book offers a concise account of various topics such as multi-fuzzy sets, multi-fuzzy topology, multi-fuzzy subgroups, multi-fuzzy logic, Atanassov intuitionistic fuzzy sets generating maps, strong L-fuzzy sets, etc. It covers multi-dimensional characterization problems in image processing, taste recognition and uncertainty.

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.

In this book, we study the lattice valued intuitionistic fuzzy topological spaces, lattice valued intuitionistic fuzzy syntopogenous structures, lattice valued intuitionistic proximity and lattice valued intuitionistic fuzzy uniformity in Entourag approach. Also, we construct stratified intuitionistic L-topological structures from a given intuitionistic L-topological structures. Finally, we introduce a new intuitionistic LC-uniformity in term of covering approach

In accordance with advancements of fuzzy set theory and its applications in decision making problems, there is a recent trend to provide versatile decision support systems for different Inventory Management problems. Again, managing inventory in a real organizations provides an understanding that gives the managers’ new insights and capabilities to determine better solutions in problems like production management, supply chain management, project management, etc. Inventories are kept so that demands may be met, orders filled, requirements satisfied, etc. So the problem of analyzing inventory problems in a real environment is an eternal task. It has been argued in a large body of recent literature that fuzzy sets theory could provide an appropriate framework for dealing with uncertainties in areas where intuition and subjective judgment play an important role. In such cases uncertainty is caused by the imprecision of natural language description rather than the existence of statistical frequency of the occurrence of events. To our consideration modeling and analysis of inventory systems using fuzzy logic deserve a good platform in generating some realistic fuzzy inventory problems.

## intuitionistic fuzzy sets theory in decision making в наличии / купить интернет-магазине

## Intuitionistic fuzzy sets theory in decision making

Intuitionistic fuzzy sets theory is the modification or extension of fuzzy sets theory by incorporating two additional functions to the membership function. We studied the mathematics of intuitionistic fuzzy sets in collaboration with fuzzy sets. In terms of application, intuitionistic fuzzy sets theory is awesome because of its ability to cope with uncertainties in decision making especially in difficult cases we elaborated in this study. In a nutshell, intuitionistic fuzzy sets theory is a suitable and reliable tool in decision science.

## On Lacunary Ideal Convergence in Intuitionistic Fuzzy n-Normed Spaces

This book deals with a concise study of convergence in intuitionistic fuzzy n-normed linear spaces. This book mainly contains the author's own research work in the area of lacunary ideal convergence. Fuzzy normed spaces have been an increasingly popular area of mathematical research in recent times, both in terms of theory and applications. But the availability of books in the area of fuzzy normed spaces is very rare. This book provides a good discussion on the development of both fuzzy and intuitionistic fuzzy set theory. The transition from fuzzy normed linear spaces to intuitionistic fuzzy n-normed linear spaces has been presented systematically. Anybody interested in the theory or application of fuzzy or intuitionistic fuzzy normed spaces will find this book more than useful. The book is written in such a way that mathematical prerequisites are minimum. Since the main subject of study in this book is a generalisaton of the concept of usual convergence, so all the related results in convergence have been incorporated in the book. This book may be used as a ready reference for an up to date account of results in the theory of fuzzy/intuitionistic fuzzy normed linear spaces.

## A Study on Intuitionistic Fuzzy Matrices

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.

## Operators on Intuitionistic Fuzzy Sets

This book is intended mainly to make an understanding about the applications of intuitionistic fuzzy sets. Various operators on intuitionistic fuzzy sets are defined and their properties are also studied with suitable examples. Though no prior knowledge of IFSs is required, the reader is expected to be familiar with the basic notions of fuzzy sets and the operators defined on them.This is only a beginning of the applications of ‘intuitionistic fuzzy’ logic and it will give further elegance in logical computing.

## Uncertainty & Fuzziness in Performance Evaluation Using DEA

Efficiency evaluation is an important part of decision making in many areas particularly in management and manufacturing sectors. Uncertainty and fuzziness of the real world problems have increased utilization of fuzzy sets theory in many research areas and data envelopment analysis is one of them. Utilizing data envelopment analysis to evaluate efficiency scores of decision making units in fuzzy environment requires fuzzy models and mathematical methods for solving fuzzy models with minimum calculation and maximum precision. This book provides latest theoretical developments in fuzzy DEA and can be considered as a basic reference for new researchers in fuzzy DEA.

## Н. З. Емельянова Simulation modeling and fuzzy logic in real-time decision-making of airport services

Decision making by the aircrafts services of the international airport, which provides for intensive traffic of aircraft and their ground handling, becomes a very topical issue. If earlier it was believed that the intensity is provided only by the number of runways, nowadays a large accumulation of aircraft on the airport platform-field creates equally complex difficulties in comparison with aircraft take-offs and landings. Solving such problems with the use of «crisp methods» of queuing theory gives little. This article deals with modern «fuzzy methods» based on simulation modeling and fuzzy logic.

## Ranking Approach to Solve Linear Programming Problems with Fuzzy Sets

Linear programming is one of the most frequently applied operations research techniques. The classical tool for solving the linear programming problem in practice is the class of simplex algorithm which was proposed and developed by Dantzig. A lot of real world decision problems are described by linear programming models and sometimes it is necessary to formulate them with elements of imprecision or uncertainty. This imprecise nature has long been studied with the help of the probability theory. However, the probability theory might not provide the correct interpretation to solve some practical decision making problems. In these cases, the fuzzy set theory might be more helpful. In this book, the limitations and shortcomings of existing methods for solving linear programming problems with fuzzy sets are pointed out. Some new ranking approaches for the ordering of fuzzy sets and vague sets are developed and also new methods to find the unique optimal solutions of linear programming problems under fuzzy environment and vague environment are presented.

## Intelligent Fuzzy Decision Making for Industrial Production Planning

Any modern industrial manufacturing unit inevitably faces problems of vagueness in various aspects such as raw material availability, human resource availability, processing capability and constraints and limitations imposed by marketing department. This problem has to be solved by a methodology which takes care of such fuzzy information. As the analyst solves this problem, the decision maker and the implementer have to coordinate with the analyst for taking up a decision on a successful strategy for implementation. Such a complex problem of vagueness and uncertainty can be handled by the theory of fuzzy logic.In this book, a new fuzzy logic based methodology using a specific membership function, named as modified S-curve membership function is proposed. The modified S-curve membership function is first formulated and its flexibility in taking up vagueness in parameters is established by an analytical approach.The usefulness of this modified S-curve membership function is further established using a real life industrial production planning of a chocolate manufacturing unit.

## TOPICS IN INTUITIONISTIC FUZZY ALGEBRA

The book contains elementary ideas of different Intuitionistic fuzzy algebraic structures viz. Intuitionistic fuzzy ideals and Intuitionistic fuzzy submodules. Some interesting relationships between images of Intuitionistic fuzzy ideal and Noetherian & Artinian rings are established. The notion of Intuitionistic fuzzy essential submodules, Intuitionistic fuzzy closed submodules, finite dimensional Intuitionistic fuzzy submodules, Intuitionistic fuzzy uniform submodules, Intuitionistic fuzzy submodules of IF Goldie dimension, Intuitionistic fuzzy projective and injective submodules are introduced and many of their important properties are discussed. Hope this book will provide necessary prerequisites for researchers in this field.

## A Study on Intuitionistic Fuzzy Matrices with Some Applications

The book deals with the problems regarding IFMs and IVIFMs. Three new operations viz., direct product, Kronecker product and Kronecker sum on IFMs are defined and studied some interesting properties. Some conditions are discussed for which a GIFM will be a generalized intuitionistic fuzzy nilpotent matrix. Also, by using the concept of relative pseudocomplement relation on intuitionistic fuzzy distributive lattice, the intuitionistic fuzzy eigenvalue and eigenvector of IFM A are defined. An application of GIFM in multicriteria decision making problem are presented. It is also proved that the set of IVIFMs form a semiring.

## Fuzzy Logic in Decision Making Process in the Armed Forces of Serbia

A very convenient mechanism for exploitation of uncertainty and vagueness in decision making is fuzzy logic. This paper shows practical application of fuzzy logic in the Armed Forces of Serbia through an example of selecting the location for setting a bridge for crossing a water obstacle. By the fuzzy logic system inexperience of the decision maker is minimized. This demonstration is even more significant considering experience of some experts gained during combat activities. The criteria relevant for the choice of a bridge crossing point, as well as their influence on the choice of the alternatives, have the values displayed in numerical values or fuzzy linguistic descriptors. By analyzing the results obtained, we can conclude that the developed fuzzy system can successfully evaluate the chosen locations and formulate the strategy of decision-making in the choice of the location. This book should hlep shed some light on modelling of fuzzy logic system to support decision making process, and should be especially useful to students who have interest in fuzzy logic modelling, or anyone else who have interest in operational researchs.

## Multi-Fuzzy Sets

Multi-Fuzzy Sets is an introductory text on multi-fuzzy sets written with minimal prerequisites. It is a study of multi-fuzzification of crisp sets, multi-level fuzziness and multi-dimensional fuzziness. The concept of multi-fuzzy sets is a generalization of Zadeh’s fuzzy sets and Atanassov’s intuitionistic fuzzy sets. The book offers a concise account of various topics such as multi-fuzzy sets, multi-fuzzy topology, multi-fuzzy subgroups, multi-fuzzy logic, Atanassov intuitionistic fuzzy sets generating maps, strong L-fuzzy sets, etc. It covers multi-dimensional characterization problems in image processing, taste recognition and uncertainty.

## Solution of Fuzzy Linear and Non-linear Equations

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.

## Lattice Valued Intuitionistic Fuzzy topological Structures

In this book, we study the lattice valued intuitionistic fuzzy topological spaces, lattice valued intuitionistic fuzzy syntopogenous structures, lattice valued intuitionistic proximity and lattice valued intuitionistic fuzzy uniformity in Entourag approach. Also, we construct stratified intuitionistic L-topological structures from a given intuitionistic L-topological structures. Finally, we introduce a new intuitionistic LC-uniformity in term of covering approach

## Modelling in Inventory Management under Fuzzy Environment

In accordance with advancements of fuzzy set theory and its applications in decision making problems, there is a recent trend to provide versatile decision support systems for different Inventory Management problems. Again, managing inventory in a real organizations provides an understanding that gives the managers’ new insights and capabilities to determine better solutions in problems like production management, supply chain management, project management, etc. Inventories are kept so that demands may be met, orders filled, requirements satisfied, etc. So the problem of analyzing inventory problems in a real environment is an eternal task. It has been argued in a large body of recent literature that fuzzy sets theory could provide an appropriate framework for dealing with uncertainties in areas where intuition and subjective judgment play an important role. In such cases uncertainty is caused by the imprecision of natural language description rather than the existence of statistical frequency of the occurrence of events. To our consideration modeling and analysis of inventory systems using fuzzy logic deserve a good platform in generating some realistic fuzzy inventory problems.