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Arithmetic Of Z-numbers, The: Theory And Applications [Kietas viršelis]

(Azerbaijan State Oil & Industry Univ, Azerbaijan), (Azerbaijan State Oil & Industry Univ, Azerbaijan), (Eastern Mediterranean Univ, Turkey), (Azerbaijan Univ, Azerbaijan)
  • Formatas: Hardback, 316 pages
  • Išleidimo metai: 26-Jun-2015
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9814675288
  • ISBN-13: 9789814675284
Kitos knygos pagal šią temą:
Arithmetic Of Z-numbers, The: Theory And ApplicationsDidesnis paveikslėlis
  • Formatas: Hardback, 316 pages
  • Išleidimo metai: 26-Jun-2015
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9814675288
  • ISBN-13: 9789814675284
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9789814675284.html
Real-world information is imperfect and is usually described in natural language (NL). Moreover, this information is often partially reliable and a degree of reliability is also expressed in NL. In view of this, the concept of a Z-number is a more adequate concept for the description of real-world information. The main critical problem that naturally arises in processing Z-numbers-based information is the computation with Z-numbers. Nowadays, there is no arithmetic of Z-numbers suggested in existing literature.This book is the first to present a comprehensive and self-contained theory of Z-arithmetic and its applications. Many of the concepts and techniques described in the book, with carefully worked-out examples, are original and appear in the literature for the first time.The book will be helpful for professionals, academics, managers and graduate students in fuzzy logic, decision sciences, artificial intelligence, mathematical economics, and computational economics.
Preface vii
1
1. The General Concept of a Restriction and Z-numbers
1(43)
1.1 Z-restriction
1(23)
1.1.1 Introduction
1(2)
1.1.2 The Concept of a Restriction---A Brief Exposition
3(7)
1.1.3 Truth and Meaning
10(14)
1.2 On Z-numbers
24(20)
1.2.1 Introduction
24(8)
1.2.2 Computation with Z-numbers
32(12)
2 Definitions and Main Properties of Z-numbers
44(48)
2.1 Generalization Levels of Uncertain Numbers
44(5)
2.2 Interval Arithmetic
49(2)
2.3 Operations on Random Variables
51(13)
2.4 Fuzzy Arithmetic
64(19)
2.4.1 Main Definitions
64(7)
2.4.2 Operations on Continuous Fuzzy Numbers
71(6)
2.4.3 Arithmetic Operations on Discrete Fuzzy Numbers
77(6)
2.5 Continuous Z-numbers, Properties
83(7)
2.6 Discrete Z-numbers, Properties
90(2)
3 Operations on Continuous Z-numbers
92(17)
3.1 Addition of Continuous Z-numbers
92(7)
3.2 Standard Subtraction of Continuous Z-numbers
99(3)
3.3 Multiplication of Continuous Z-numbers
102(2)
3.4 Standard Division of Continuous Z-numbers
104(2)
3.5 Square of a Continuous Z-number
106(1)
3.6 Square Root of a Continuous Z-number
107(2)
4 Operations on Discrete Z-numbers
109(58)
4.1 Arithmetic Operations
109(31)
4.1.1 Continuous and Discrete Z-numbers: Discussion
109(1)
4.1.2 A Z-number and a Z+number
110(2)
4.1.3 Addition of Discrete Z-numbers
112(8)
4.1.4 Standard Subtraction of Discrete Z-numbers
120(3)
4.1.5 Hukuhara Difference of Discrete Z-numbers
123(13)
4.1.6 Multiplication of Discrete Z-numbers
136(2)
4.1.7 Standard Division of Discrete Z-numbers
138(2)
4.2 Power of a Discrete Z-number
140(5)
4.2.1 Square of a Discrete Z-number
140(3)
4.2.2 Square Root of a Discrete Z-number
143(2)
4.3 Ranking of Discrete Z-numbers
145(5)
4.4 Minimum and Maximum of Discrete Z-numbers
150(14)
4.5 Comparison of Processing Pure Fuzzy and Z-information
164(3)
5 Algebraic System of Z-numbers
167(63)
5.1 Absolute Value of a Z-number
167(4)
5.2 Distance Between Two Z-numbers
171(10)
5.3 Functions of Discrete Z-numbers
181(15)
5.3.1 Main Definitions
181(3)
5.3.2 Typical Functions
184(1)
5.3.2.1 A Discrete Z-number Valued Exponential Function
184(3)
5.3.2.2 A Discrete Z-number Valued Natural Logarithm
187(3)
5.3.3 Approximation of an Unknown Discrete Z-number Valued Mappings
190(1)
5.3.3.1 Approximation by Using a Discrete Z-number Valued Polynomial
190(1)
5.3.3.2 Z-interpolation
190(6)
5.4 Equations with Z-numbers
196(6)
5.5 Derivative of Function of Z-numbers
202(11)
5.5.1 Discrete Derivative of a Discrete Z-number Valued Function at a Numerical Point
203(7)
5.5.2 Discrete Derivative of a Discrete Z-number Valued Function at a Z-point
210(3)
5.6 T-norm and T-conorm of Z-numbers
213(7)
5.7 Aggregation of Z-numbers
220(10)
6 Z-number Based Operation Research Problems
230(35)
6.1 Z-number Valued Linear Programming
230(10)
6.2 Z-number Based Regression Analysis
240(4)
6.3 Z-resrtiction Based Multicriteria Choice
244(8)
6.4 Decision Making under Z-information
252(8)
6.5 Computing with Words and Z-numbers
260(5)
7 Application of Z-numbers
265(22)
7.1 Business Behavioral Decision under Z-information
265(5)
7.2 Business Decision Making in Mix-product
270(2)
7.3 Marketing Decision Making under Z-information
272(8)
7.4 Optimal Planning of Company Production by Z-linear Programming
280(7)
Bibliography 287(11)
Index 298