Book ChapterDOI
The Z-Number Enigma: A Study through an Experiment
Romi Banerjee,Sankar K. Pal +1 more
- pp 71-88
TLDR
The probable contributions of the Z-number to CWW are enlisted, the algorithm for CWW is presented, the interpretation of the set-theoretic intersection operator is extended to evaluate the intersection of perceptions, and some of the challenges underlying the implementation of theZ-number are discovered.Abstract:
The Z-number, proposed by Zadeh in the year 2011, is a new fuzzy-theoretic approach to the Computing With Words (CWW) paradigm. It aspires to capture the uncertainty of information conveyed by a sentence, and serve as a model for the precisiation and linguistic summarization of a natural language statement. The Z-number thereby, lends a new dimension to CWW – uniting CWW with Natural Language Processing (NLP). This article is an illumination upon our exploration of the Z-number approach to CWW. Here, we enlist the probable contributions of the Z-number to CWW, present our algorithm for CWW using the Z-number, and describe a simulation of the technique with respect to a real-life example of CWW. In the course of the simulation, we extend the interpretation of the set-theoretic intersection operator to evaluate the intersection of perceptions and discover some of the challenges underlying the implementation of the Z-number in the area of CWW.read more
Citations
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Journal ArticleDOI
The arithmetic of discrete Z-numbers
TL;DR: In this article, the main critical problem that naturally arises in processing Z-number-based information is computation with Z-numbers, which is a more adequate concept for description of real-world information.
Journal ArticleDOI
Multi-Criteria Decision-Making Method Based on Distance Measure and Choquet Integral for Linguistic Z-Numbers
TL;DR: An extended TODIM method based on the Choquet integral for multi-criteria decision-making (MCDM) problems with linguistic Z-numbers is developed, which is a more comprehensive reflection of the decision-makers’ cognition but also is more in line with expression habits.
Journal ArticleDOI
The arithmetic of continuous Z-numbers
TL;DR: This work developed basic arithmetic operations such as addition, subtraction, multiplication and division, and some algebraic operations as maximum, minimum, square and square root of continuous Z-numbers.
Journal ArticleDOI
Approximate Reasoning on a Basis of Z -Number-Valued If–Then Rules
TL;DR: A new approach is developed to study approximate reasoning with Zadeh rules on a basis of linear interpolation to provide an application of the approach to job satisfaction evaluation and to students’ educational achievement evaluation problems related to psychological and perceptual issues naturally characterized by imperfect information.
Journal ArticleDOI
On computing generalized Hukuhara differences of Z-numbers
Dong Qiu,Haihuan Jiang,Yan Yu +2 more
References
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Journal ArticleDOI
Outline of a New Approach to the Analysis of Complex Systems and Decision Processes
TL;DR: By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
Book
Computing Machinery and Intelligence
TL;DR: If the meaning of the words “machine” and “think” are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to the question, “Can machines think?” is to be sought in a statistical survey such as a Gallup poll.
Journal ArticleDOI
Fuzzy logic = computing with words
TL;DR: The point of this note is that fuzzy logic plays a pivotal role in CW and vice-versa and, as an approximation, fuzzy logic may be equated to CW.
Journal ArticleDOI
A Note on Z-numbers
TL;DR: The concept of a Z-number has a potential for many applications, especially in the realms of economics, decision analysis, risk assessment, prediction, anticipation and rule-based characterization of imprecise functions and relations.