Get Fuzzy Set Theory: Basic Concepts, Techniques and PDF

By R. Lowen

ISBN-10: 9048147069

ISBN-13: 9789048147069

ISBN-10: 9401587418

ISBN-13: 9789401587419

The function of this e-book is to supply the reader who's drawn to purposes of fuzzy set thought, within the first position with a textual content to which she or he can refer for the elemental theoretical principles, ideas and methods during this box and within the moment position with an unlimited and recent account of the literature. even though there at the moment are many books approximately fuzzy set thought, and regularly approximately its functions, e. g. up to the mark concept, there isn't particularly a e-book on hand which introduces the simple thought of fuzzy units, in what i need to name "a reliable measure of generality". to jot down a booklet which might deal with the whole variety of effects in regards to the simple theoretical innovations in nice element and which might additionally take care of all attainable versions and choices of the idea, corresponding to e. g. tough units and L-fuzzy units for arbitrary lattices L, with the possibility-probability theories and interpretations, with the basis of fuzzy set concept through multi-valued good judgment or through express tools etc, may were an altogether diversified venture. This booklet is much extra modest in its mathematical content material and in its scope.

Show description

Read or Download Fuzzy Set Theory: Basic Concepts, Techniques and Bibliography PDF

Best operations research books

Read e-book online Complex Scheduling (GOR-Publications) PDF

This publication provides versions and algorithms for complicated scheduling difficulties. along with resource-constrained venture scheduling issues of purposes additionally job-shop issues of versatile machines, transportation or constrained buffers are mentioned. Discrete optimization equipment like linear and integer programming, constraint propagation options, shortest course and community move algorithms, branch-and-bound equipment, neighborhood seek and genetic algorithms, and dynamic programming are provided.

Patrick Bangert's Optimization for Industrial Problems PDF

Commercial optimization lies at the crossroads among arithmetic, desktop technology, engineering and administration. This ebook offers those fields in interdependence as a talk among theoretical features of arithmetic and laptop technology and the mathematical box of optimization thought at a pragmatic point.

Get Fuzzy Set Theory — and Its Applications PDF

Considering the fact that its inception twenty years in the past the idea of fuzzy units has complex in various methods and in lots of disciplines. functions of this conception are available in synthetic intelligence, machine technology, keep an eye on engineering, choice idea, specialist structures, common sense, administration technology, operations study, development attractiveness, robotics and others.

New PDF release: Real Options Valuation: The Importance of Stochastic Process

The writer indicates that modelling the doubtful money movement dynamics of an funding venture merits cautious consciousness in genuine suggestions valuation. concentrating on the case of commodity rate uncertainty, a huge empirical research finds that, opposite to universal assumptions, costs are usually non-stationary and show non-normally dispensed returns.

Extra info for Fuzzy Set Theory: Basic Concepts, Techniques and Bibliography

Example text

All properties follow easily from the definitions. 4 Proposition lf X and Y are sets, I:X-Y is afunction, and arefamilies offuzzy sets on respectively X and Y, (/lj)jEJ' (Vj)jEJ then: 1. I (su p p,j) = sup I(p,j). JEJ 2. I 3. JEJ (j~} p,j) ~ j~} I(p,j). 1-1(SUP Vj) JEJ 4. ) JEJ J 1 =supl- (vj). JEJ = inf 1- 1(v·). JEJ J Proof. All properties follow at onee from the definitions. 0 At this point we would like to introduee what by many people working in fuzzy set theory is ealled the Extension Principle.

These are , intersection, union and complementation. These operations are important for set theory itself, but also because if one looks at the logical aspect of these operations, then they represent "and", "or" and "not". As is well known, from these basic logical connectives all other logical connectives are derived. We shall return to these aspects in detail in the chapter on fuzzy logic. For the moment it is sufficient to realize the importance of extending these three set theoretical operations to the setting of fuzzy sets.

Chapter 1. 6 Notes Set Theory There are many excellent textbooks on elementary set theory. One book in particular is worth mentioning since it is both interesting and pleasant to read, namely, "Naive Set Theory" by Paul R. Halmos [Van Nostrand 1960]. The reader should however be warned that the elementary set theory which we presented in this section is more elementary and naive than what is contained in the aforementioned book. We have not touched on matters such as axiomatics of set theory, or ordinals and cardinals since for our purposes this is not relevant.

Download PDF sample

Fuzzy Set Theory: Basic Concepts, Techniques and Bibliography by R. Lowen

by Charles

Rated 4.30 of 5 – based on 10 votes