Algebraic Properties of Z-Numbers Under Additive Arithmetic Operations

被引：2

作者：

Alizadeh, Akif V. ^{[1
]}

Aliyev, Rashad R. ^{[2
]}

Huseynov, Oleg H. ^{[3
]}

机构：

[1] Azerbaijan State Oil & Ind Univ, Dept Control & Syst Engn, 20 Azadlig Ave, AZ-1010 Baku, Azerbaijan

[2] Eastern Mediterranean Univ, Dept Math, Famagusta, North Cyprus, Turkey

[3] Azerbaijan State Oil & Ind Univ, Res Lab Intelligent Control & Decis Making Syst I, 20 Azadlig Ave, AZ-1010 Baku, Azerbaijan

来源：

13TH INTERNATIONAL CONFERENCE ON THEORY AND APPLICATION OF FUZZY SYSTEMS AND SOFT COMPUTING - ICAFS-2018 | 2019年 / 896卷

关键词：

Fuzzy arithmetic; Probabilistic arithmetic; Associativity law; Commutativity law; Z-number;

D O I：

10.1007/978-3-030-04164-9_118

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Prof. L. A. Zadeh introduced the concept of a Z-number for description of real-world information. A Z-number is an ordered pair Z = (A, B) of fuzzy numbers A and B used to describe a value of a random variable X. A is an imprecise estimation of a value of X and B is an imprecise estimation of reliability of A. A series of important works on computations with Z-numbers and applications were published. However, no study exists on properties of operation of Z-numbers. Such theoretical study is necessary to formulate the basics of the theory of Z-numbers. In this paper we prove that Z-numbers exhibit fundamental properties under additive arithmetic operations.

引用

页码：893 / 900

页数：8

共 50 条

[31] Data Envelopment Analysis with Z-Numbers - An Application to Project Selection
Kuchta, Dorota
Gladysz, Barbara
INTELLIGENT AND FUZZY SYSTEMS: DIGITAL ACCELERATION AND THE NEW NORMAL, INFUS 2022, VOL 1, 2022, 504 : 460 - 467
[32] Ranking of Z-Numbers Based on the Developed Golden Rule Representative Value
Cheng, Ruolan
Zhang, Jianfeng
Kang, Bingyi
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2022, 30 (12) : 5196 - 5210
[33] Eigensolutions of Partially Reliable Decision Preferences Described by Matrices of Z-Numbers
Aliev, Rafik A.
Pedrycz, Witold
Huseynov, Oleg H.
Aliyev, Rafig R.
INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING, 2020, 19 (06) : 1429 - 1450
[34] A Novel Z-TOPSIS Method Based on Improved Distance Measure of Z-Numbers
Ruolan Cheng
Jianfeng Zhang
Bingyi Kang
International Journal of Fuzzy Systems, 2022, 24 : 2813 - 2830
[35] A Novel Z-TOPSIS Method Based on Improved Distance Measure of Z-Numbers
Cheng, Ruolan
Zhang, Jianfeng
Kang, Bingyi
INTERNATIONAL JOURNAL OF FUZZY SYSTEMS, 2022, 24 (06) : 2813 - 2830
[36] Z-Numbers and Type-2 Fuzzy Sets: A Representation Result
Aliev, R. A.
Kreinovich, Vladik
INTELLIGENT AUTOMATION AND SOFT COMPUTING, 2018, 24 (01) : 205 - 209
[37] Momentum Ranking Function of Z-Numbers and its Application to Game Theory
Parameswari, K.
Velammal, G.
BAGHDAD SCIENCE JOURNAL, 2023, 20 (01) : 305 - 310
[38] Solving Differential Equations with Z-Numbers by Utilizing Fuzzy Sumudu Transform
Jafari, Raheleh
Razvarz, Sina
Gegov, Alexander
INTELLIGENT SYSTEMS AND APPLICATIONS, INTELLISYS, VOL 2, 2019, 869 : 1125 - 1138
[39] Multicriteria decision makingmodel with z-numbers based on fucom and mabac model
Božanic D.
Tešic D.
Milic A.
Decision Making: Applications in Management and Engineering, 2020, 3 (02): : 19 - 36
[40] Sensor Data Fusion with Z-Numbers and Its Application in Fault Diagnosis
Jiang, Wen
Xie, Chunhe
Zhuang, Miaoyan
Shou, Yehang
Tang, Yongchuan
SENSORS, 2016, 16 (09)

← 1 2 3 4 5 →