Implication functions in interval-valued fuzzy set theory

Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results pertaining to implications in interval-valued fuzzy set theory. In particular, we describe several possibilities to represent such implications using implications on the unit interval, we give a characterization of the implications in interval-valued fuzzy set theory which satisfy the Smets-Magrez axioms, we discuss the solutions of a particular distributivity equation involving strict t-norms, we extend monoidal logic to the interval-valued fuzzy case and we give a soundness and completeness theorem which is similar to the one existing for monoidal logic, and finally we discuss some other constructions of implications in interval-valued fuzzy set theory

Methodology for predicting and/or compensating the behavior of optical frequency comb

RESUMEN: Optical frequency comb spectrum can change its behavior due to temperature fluctuations, normal dispersion, and mechanical vibrations. Such limitations can affect the peak power and wavelength separation of comb lines. In the propagation through single−mode fiber, the linear and non−linear phenomena can modify spectral shape, phase shifts and flatness of spectrum. To find a strategy of compensation, the PhD thesis is focused on a prediction methodology based on fuzzy cellular automata, intuitionistic fuzzy sets and fuzzy entropy measures. The research work proposes a predictor called intuitionistic fuzzy cellular automata based on mean vector and a validation measure called general intuitionistic fuzzy entropy based on adequacy and non−adequacy. In the accomplished experiments, the method was used in three experiments: mode−locked lasers, cascaded intensity modulators−Mach Zehnder modulators, and microresonator ring. The obtained results showed that the power and phase distortions were reduced by using a pulse shaper, where the method was programmed. In addition, the stability and/or instability of spectrum were found for the microresonator ring

A multi-attribute framework for the selection of high-performance work systems: the hybrid DEMATEL-MABAC model

Research in strategic human resource management indicates that high performance work systems (HPWS) have a positive impact on the overall performance of an organization as a result of better human resource (HR) outcomes. Regarding the multi-dimensional and complex nature of these factors, common statistical models are not useful for examining the performance of HPWS. Using the capabilities of multi-attribute decision-making (MADM) methods to deal with various criteria that may be contradictory, this study proposes a MADM-based framework that provides the opportunity to prioritize HR practices. Based on this framework, high-performance HR practices and their related HR outcomes were identified after studying the theoretical literature and ascertaining the views of decision-makers and HR experts. Then, after looking at the interactions among HR outcomes, the weights of the criteria were calculated using the method of the decision making trial and evaluation laboratory (DEMATEL). Then, the alternatives were ranked using the multi-attributive border approximation area comparison (MABAC) method. Finally, the designed framework was implemented in an organization active in the banking industry. This framework can be used to improve employees’ performance and, consequently, the performance of the organization. Accordingly, taking into account the resource constraints organizations face, the priorities presented can be helpful in budgeting human-resource-management (HRM) improvement projects and making an appropriate resource allocation for this

Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists

This book introduces the concept of fuzzy super matrices and operations on them. This book will be highly useful to social scientists who wish to work with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational Maps, Bidirectional Associative Memories and Fuzzy Associative Memories are defined here. The authors introduce 13 multi-expert models using the notion of fuzzy supermatrices. These models are described with illustrative examples. This book has three chapters. In the first chaper, the basic concepts about super matrices and fuzzy super matrices are recalled. Chapter two introduces the notion of fuzzy super matrices adn their properties. The final chapter introduces many super fuzzy multi expert models.Comment: 280 page

Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps

As extension of Fuzzy Cognitive Maps are now introduced the Neutrosophic Cognitive Map

Fuzzy Interval Matrices, Neutrosophic Interval Matrices and their Applications

The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem. Further, the authors have introduced in this book multiexpert models using these three new types of interval matrices. The new multi expert models dealt in this book are FCIMs, FRIMs, FCInMs, FRInMs, IBAMs, IBBAMs, nIBAMs, FAIMs, FAnIMS, etc. Illustrative examples are given so that the reader can follow these concepts easily. This book has three chapters. The first chapter is introductory in nature and makes the book a self-contained one. Chapter two introduces the concept of fuzzy interval matrices. Also the notion of fuzzy interval matrices, neutrosophic interval matrices and fuzzy neutrosophic interval matrices, can find applications to Markov chains and Leontief economic models. Chapter three gives the application of fuzzy interval matrices and neutrosophic interval matrices to real-world problems by constructing the models already mentioned. Further these models are mainly useful when the data is an unsupervised one and when one needs a multi-expert model. The new concept of fuzzy interval matrices and neutrosophic interval matrices will find their applications in engineering, medical, industrial, social and psychological problems. We have given a long list of references to help the interested reader.Comment: 304 page

SPECIAL FUZZY MATRICES FOR SOCIAL SCIENTISTS

This book is a continuation of the book, Elementary fuzzy matrix and fuzzy models for socio-scientists by the same authors. This book is a little advanced because we introduce a multi-expert fuzzy and neutrosophic models. It mainly tries to help social scientists to analyze any problem in which they need multi-expert systems with multi-models. To cater to this need, we have introduced new classes of fuzzy and neutrosophic special matrices. The first chapter is essentially spent on introducing the new notion of different types of special fuzzy and neutrosophic matrices, and the simple operations on them which are needed in the working of these multi expert models. In the second chapter, new set of multi expert models are introduced; these special fuzzy models and special fuzzy neutrosophic models that can cater to adopt any number of experts. The working of the model is also explained by illustrative examples. However, these special fuzzy models can also be used by applied mathematicians to study social and psychological problems. These models can also be used by doctors, engineers, scientists and statisticians. The SFCM, SMFCM, SNCM, SMNCM, SFRM, SNRM, SMFRM, SMNRM, SFNCMs, SFNRMs, etc. can give the special hidden pattern for any given special input vector