An Insight Into The Z-number Approach To CWW
TL;DR: A comprehensive investigation of the Z-number approach to CWW, which serves as a model of linguistic summarization of natural language statements, a technique to merge human-affective perspectives with C WW, and consequently can be envisaged to play a radical role in the domain of CWW-based system design and Natural Language Processing NLP.
Abstract: The Z-number is a new fuzzy-theoretic concept, proposed by Zadeh in 2011. It extends the basic philosophy of Computing With Words CWW to include the perception of uncertainty of the information conveyed by a natural language statement. The Z-number thus, serves as a model of linguistic summarization of natural language statements, a technique to merge human-affective perspectives with CWW, and consequently can be envisaged to play a radical role in the domain of CWW-based system design and Natural Language Processing NLP. This article presents a comprehensive investigation of the Z-number approach to CWW. We present here: a an outline of our understanding of the generic architecture, algorithm and challenges underlying CWW in general; b a detailed study of the Z-number methodology-where we propose an algorithm for CWW using Z-numbers, define a Z-number based operator for the evaluation of the level of requirement satisfaction, and describe simulation experiments of CWW utilizing Z-numbers; and c analyse the strengths and the challenges of the Z-numbers, and suggest possible solution strategies. We believe that this article would inspire research on the need for inclusion of human-behavioural aspects into CWW, as well as the integration of CWW and NLP.
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TL;DR: This paper applies the concept of distance of Z-numbers to the approximate reasoning with Z-number based IF-THEN rules and provides an example on solving problem related to psychological issues naturally characterized by imperfect information, which shows applicability and validity of the suggested approach.
Abstract: Decision making, reasoning, and analysis in real-world problems are complicated by imperfect information. Real-world imperfect information is mainly characterized by two features. In view of this, Professor Zadeh suggested the concept of a -number as an ordered pair of fuzzy numbers and , the first of which is a linguistic value of a variable of interest, and the second one is a linguistic value of probability measure of the first one, playing a role of its reliability. The concept of distance is one of the important concepts for handling imperfect information in decision making and reasoning. In this paper, we, for the first time, apply the concept of distance of -numbers to the approximate reasoning with -number based IF-THEN rules. We provide an example on solving problem related to psychological issues naturally characterized by imperfect information, which shows applicability and validity of the suggested approach.
10 citations
TL;DR: A corpus and entropy-based methodology that follows a subjectivist approach to granulate and identify statements of consequence in a natural language sample, all within the periphery of a particular context is proposed, which aims at reducing overall text-processing costs.
9 citations
Cites background or methods from "An Insight Into The Z-number Approa..."
...Considering the problem of ‘text-identification’ described in [4], the logic described in Section 4....
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...The research underlying this article, though is spurred by the need to reduce the computational complexities inherent in our algorithm [4] for the Z-number approach to computing with words (CWW), aims to achieve a lot more, thereby contributing to the field of CWW, natural language processing (NLP) and artificial intelligence in general....
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...The generic architecture of a system based on CWW [4]....
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...The ingenuity, algorithms and subsequent implementation challenges of the Z-number have been thoroughly investigated in [4]....
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...After being trained by 30 works of fiction (genre: mystery), the machine (M) possessed a vocabulary of 165 basic keywords [4] (not considering their differentmorphological forms) lyingunder twobroad subcontexts: ‘murdermysteries’ and ‘others’....
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TL;DR: A review of the development in the theory and application of the Z-numbers since its inception in 2011 is presented in this paper , which covers the formalization of Z-number-based mathematical operators, the role of Znumbers in computing with words, decision-making, and trust modeling, application of Z numbers in real-world problems such as multisensor data fusion, dynamic controller design, safety analytics, and natural language understanding, and some potential areas of future investigation.
Abstract: In this article, we present a study on the development in the theory and application of the Z-numbers since its inception in 2011. The review covers the formalization of Z-number-based mathematical operators, the role of Z-numbers in computing with words, decision-making, and trust modeling, application of Z-numbers in real-world problems such as multisensor data fusion, dynamic controller design, safety analytics, and natural language understanding, a brief comparison with conceptually similar paradigms, and some potential areas of future investigation. The paradigm currently has at least four extensions to its definition: multidimensional Z-numbers, parametric Z-numbers, hesitant-uncertain linguistic Z-numbers, and Z*-numbers. The Z-numbers have also been used in conjunction with rough sets and granular computing for enhanced uncertainty handling. While this decade has seen a plethora of theoretical initiatives toward its growth, there remains a major work scope in the direction of practical realization of the paradigm. Some challenges yet unresolved are automated translation of (imprecise, sarcastic, and metaphorical) linguistic expressions to their Z-number forms, discernment of probability–possibility distributions to map real-world situations under consideration, analysis of linguistic equivalents of Z-operator results to intuitive human responses, the endogenous arousal of belief in intelligent agents, and analysis of biases embedded in expert-belief values that are primary inputs to Z-number-based expert systems. After a decade of the Z-numbers, the paradigm has proved to be of use in expert-input-based decision-making systems and initial value problems. Its applicability in high-risk, high-precision areas, such as deep-sea exploration and space science, remains unexplored.
9 citations
8 citations
TL;DR: Zadeh introduced the concept of Z-numbers in 2011 to deal with imprecise information and many research works have been published in an attempt to introduce some basic theoretical conce...
Abstract: Zadeh introduced the concept of Z-numbers in 2011 to deal with imprecise information. In this regard, many research works have been published in an attempt to introduce some basic theoretical conce...
7 citations
References
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TL;DR: WordNet1 provides a more effective combination of traditional lexicographic information and modern computing, and is an online lexical database designed for use under program control.
Abstract: Because meaningful sentences are composed of meaningful words, any system that hopes to process natural languages as people do must have information about words and their meanings. This information is traditionally provided through dictionaries, and machine-readable dictionaries are now widely available. But dictionary entries evolved for the convenience of human readers, not for machines. WordNet1 provides a more effective combination of traditional lexicographic information and modern computing. WordNet is an online lexical database designed for use under program control. English nouns, verbs, adjectives, and adverbs are organized into sets of synonyms, each representing a lexicalized concept. Semantic relations link the synonym sets [4].
15,068 citations
"An Insight Into The Z-number Approa..." refers background in this paper
...(ii) The 'FrameNet' [3], 'WordNet' [14, 5] and 'ConceptNet' [6] projects could come to the aide of the creation of the semantic nets, synonym clusters and common-sense semantic nets, respectively....
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TL;DR: The lexical database: nouns in WordNet, Katherine J. Miller a semantic network of English verbs, and applications of WordNet: building semantic concordances are presented.
Abstract: Part 1 The lexical database: nouns in WordNet, George A. Miller modifiers in WordNet, Katherine J. Miller a semantic network of English verbs, Christiane Fellbaum design and implementation of the WordNet lexical database and searching software, Randee I. Tengi. Part 2: automated discovery of WordNet relations, Marti A. Hearst representing verb alterations in WordNet, Karen T. Kohl et al the formalization of WordNet by methods of relational concept analysis, Uta E. Priss. Part 3 Applications of WordNet: building semantic concordances, Shari Landes et al performance and confidence in a semantic annotation task, Christiane Fellbaum et al WordNet and class-based probabilities, Philip Resnik combining local context and WordNet similarity for word sense identification, Claudia Leacock and Martin Chodorow using WordNet for text retrieval, Ellen M. Voorhees lexical chains as representations of context for the detection and correction of malapropisms, Graeme Hirst and David St-Onge temporal indexing through lexical chaining, Reem Al-Halimi and Rick Kazman COLOR-X - using knowledge from WordNet for conceptual modelling, J.F.M. Burg and R.P. van de Riet knowledge processing on an extended WordNet, Sanda M. Harabagiu and Dan I Moldovan appendix - obtaining and using WordNet.
13,049 citations
"An Insight Into The Z-number Approa..." refers background in this paper
...(ii) The 'FrameNet' [3], 'WordNet' [14, 5] and 'ConceptNet' [6] projects could come to the aide of the creation of the semantic nets, synonym clusters and common-sense semantic nets, respectively....
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01 Jan 1973
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.
Abstract: The approach described in this paper represents a substantive departure from the conventional quantitative techniques of system analysis. It has three main distinguishing features: 1) use of so-called ``linguistic'' variables in place of or in addition to numerical variables; 2) characterization of simple relations between variables by fuzzy conditional statements; and 3) characterization of complex relations by fuzzy algorithms. A linguistic variable is defined as a variable whose values are sentences in a natural or artificial language. Thus, if tall, not tall, very tall, very very tall, etc. are values of height, then height is a linguistic variable. Fuzzy conditional statements are expressions of the form IF A THEN B, where A and B have fuzzy meaning, e.g., IF x is small THEN y is large, where small and large are viewed as labels of fuzzy sets. A fuzzy algorithm is an ordered sequence of instructions which may contain fuzzy assignment and conditional statements, e.g., x = very small, IF x is small THEN Y is large. The execution of such instructions is governed by the compositional rule of inference and the rule of the preponderant alternative. 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.
8,547 citations
"An Insight Into The Z-number Approa..." refers background in this paper
...The Z-number draws on the concepts in [24], [21], [22], [23] and [27], and is subtly inspired by [7]....
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...The concepts of CWW are essentially rooted in [24], [21], [22] and [23], [27], where Zadeh equates the concepts of fuzzy logic to CWW, describes the rationale underlying fuzzy linguistics and information granulation, elucidates the concept of the test-score semantics that associates all natural language statements to degrees of constraint satisfaction, explains the precisiation of natural language, and illustrates the computational theory of perceptions, respectively....
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Book•
01 Jan 1950TL;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.
Abstract: I propose to consider the question, “Can machines think?”♣ This should begin with definitions of the meaning of the terms “machine” and “think”. The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous. 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.
6,137 citations
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.
Abstract: As its name suggests, computing with words (CW) is a methodology in which words are used in place of numbers for computing and reasoning. The point of this note is that fuzzy logic plays a pivotal role in CW and vice-versa. Thus, as an approximation, fuzzy logic may be equated to CW. There are two major imperatives for computing with words. First, computing with words is a necessity when the available information is too imprecise to justify the use of numbers, and second, when there is a tolerance for imprecision which can be exploited to achieve tractability, robustness, low solution cost, and better rapport with reality. Exploitation of the tolerance for imprecision is an issue of central importance in CW. In CW, a word is viewed as a label of a granule; that is, a fuzzy set of points drawn together by similarity, with the fuzzy set playing the role of a fuzzy constraint on a variable. The premises are assumed to be expressed as propositions in a natural language. In coming years, computing with words is likely to evolve into a basic methodology in its own right with wide-ranging ramifications on both basic and applied levels.
3,093 citations
"An Insight Into The Z-number Approa..." refers background in this paper
...The concepts of CWW are essentially rooted in [24], [21], [22] and [23], [27], where Zadeh equates the concepts of fuzzy logic to CWW, describes the rationale underlying fuzzy linguistics and information granulation, elucidates the concept of the test-score semantics that associates all natural language statements to degrees of constraint satisfaction, explains the precisiation of natural language, and illustrates the computational theory of perceptions, respectively....
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...The Z-number draws on the concepts in [24], [21], [22], [23] and [27], and is subtly inspired by [7]....
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...[24] and [26] assert that CWW is imperative when:...
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...The human brain, possesses an amazing decision-making ability, based on 'perceptions' encoded in the 'words' and 'phrases' in natural language sentences - giving rise to the “Computing with Words (CWW) [24]” paradigm....
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...Computing with Words (CWW), however, refers to an entire “paradigm shift”, where the elements of manipulation are no longer numbers but 'words' and 'phrases' in natural language statements [24], [26]....
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