Robert Fuller

Christer Carlsson

Mario Fedrizzi

This book shows how the application of fuzzy logic can benefit management, group decision making, strategic planning, supply chain management and other business imperatives. The theoretical analysis is fully supported by real-life case studies. The book develops themes that businesses can use to master effectiveness and quality, work with flexibility, and support continuous learning in the organization and the individual.

Fuzzy Logic in Management

This book contains introductory material to neuro-fuzzy systems. Its main purpose is to explain the information processing in mostly-used fuzzy inference systems, neural networks and neuro-fuzzy systems. More than 180 figures and a large number of (numerical) exercises (with solutions) have been inserted to explain the principles of fuzzy, neural and neuro-fuzzy systems. Also the mathematics applied in the models is carefully explained, and in many cases exact computational formulas have been derived for the rules in error correction learning procedures. Numerous models treated in the book will help the reader to design his own neuro-fuzzy system for his specific (managerial, industrial, financial) problem. The book can serve as a textbook for students in computer and management sciences who are interested in adaptive technologies.

Introduction to Neuro-Fuzzy Systems

Two baffling concepts have always confronted Christianity: the doctrine of the trinity and the subject of Christology. Both subjects deal with the inexplicable mysteries of how God became incarnate in Jesus Christ, and when did Jesus know He was God? The author believes the subject of the trinity is actually simple and easily understood from a scriptural perspective. This book is for anyone who wants to know about the preexistence of Jesus Christ, for believers who might be unsure about their personal salvation, and for all Christians who want the entire message of how and why Jesus is the Son of God. Robert Fuller is an ordained minister having received his B.A. degree in the Biblical Field from Abilene Christian University and a M.Ed. degree from the University of North Texas. Mr. Fuller states: "I was raised a Trinitarian as defined by the Nicene Counsel of 325 A.D., and was taught Chalcedonian Christology; yet, it was not until later in life that I have come to understand the scriptures concerning why and how God the Son emptied Himself, not of divinity, but of equality with Very God to become the Son of God and eventually the man Jesus Christ. Jesus was the Son of God in human form, and fulfilled God's perfect will so that God the Father gave Him the authoritative name of Jesus." Jesus was aware of His divinity at His barmitzvah, when He demonstrated to the temple priest His divine wisdom about the Torah. Catholics have always been right about Mary being the Mother of God. She knew Jesus was God in the flesh and no doubt informed Him early on about His miraculous conception. Jesus' virgin birth was something Mary just couldn't keep to herself! (Luke 1:46-56)

When God the Son Became the Son of God

Fuzzy sets were introduced by Zadeh (1965) as a means of representing and manipulating data that was not precise, but rather fuzzy. Fuzzy logic pro vides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems. The theory of fuzzy logic provides a mathematical strength to capture the uncertainties associ ated with human cognitive processes, such as thinking and reasoning. The conventional approaches to knowledge representation lack the means for rep resentating the meaning of fuzzy concepts. As a consequence, the approaches based on first order logic and classical probablity theory do not provide an appropriate conceptual framework for dealing with the representation of com monsense knowledge, since such knowledge is by its nature both lexically imprecise and noncategorical. The developement of fuzzy logic was motivated in large measure by the need for a conceptual framework which can address the issue of uncertainty and lexical imprecision. Some of the essential characteristics of fuzzy logic relate to the following [242]. • In fuzzy logic, exact reasoning is viewed as a limiting case of ap proximate reasoning. • In fuzzy logic, everything is a matter of degree. • In fuzzy logic, knowledge is interpreted a collection of elastic or, equivalently, fuzzy constraint on a collection of variables. • Inference is viewed as a process of propagation of elastic con straints. • Any logical system can be fuzzified. There are two main characteristics of fuzzy systems that give them better performance für specific applications.

Robert Fuller

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