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.
Citations
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TL;DR: A novel Technique for Order of Preference by Similarity to Ideal Solution based on the Z-Numbers (Z-TOPSIS) method, which directly calculates Z-numbers instead of converting them to fuzzy numbers.
16 citations
01 Jan 2015
TL;DR: What challenges ACWW encounters given the current trend of data abundance and widespread use of Internet for dealing with questions posed in natural languages is explained and a syllogistic approach to solving ACWW problems is proposed that uses the Extension Principle but in a different way.
Abstract: In this chapter, we focus on the status of Advanced Computing with Words (ACWW) and the challenges that it may encounter in the future. First, we elaborate on the notion of Computing with Words (CWW) and its various subareas. Then we present some non-engineering ACWW problems and connect them to more realistic engineering problems, after which we provide a roadmap for solving ACWW problems, and show how the Generalized Extension Principle (GEP) can be used to formulate their solutions. We also propose a syllogistic approach to solving ACWW problems that also uses the Extension Principle but in a different way. Finally, we discuss present and future challenges to ACWW, i.e. we explain what challenges ACWW encounters given the current trend of data abundance and widespread use of Internet for dealing with questions posed in natural languages.
16 citations
Cites methods from "An Insight Into The Z-number Approa..."
...Because the GEP is the main tool for manipulating Z-numbers [2, 42, 43, 76, 126, 151], the connections between ACWW and computing with Z-numbers is also an interesting topic for future research....
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Journal Article•
TL;DR: Z-numbers is applied to express the relative weights of criteria and the fuzzy TOPSIS is used to rank the alternatives and the basic benefit of the proposed method is its low computational intricacy.
Abstract: The technique for order preference by similarity to ideal solution (TOPSIS) is one of the most popular approaches for multiple criteria decision making (MCDM). The main limitation of the traditional TOPSIS lies in the inability to handle the ambiguity in the decision making process. Several researchers have introduced various fuzzy TOPSIS models. However, there is the key shortcoming in all previous approaches. When dealing with real information, fuzziness is not adequate and a degree of reliability of the information is very critical. In view of this, Prof. Zadeh introduced a Z-number for a more efficient explanation of real-life information. Compared with the usual fuzzy number, Z-number has extra capacity to depict the imperfect information. In this paper, Z-numbers is applied to express the relative weights of criteria and the fuzzy TOPSIS is used to rank the alternatives. The basic benefit of the proposed method is its low computational intricacy.
15 citations
Cites background from "An Insight Into The Z-number Approa..."
...Studies about Z-numbers and its applications can be found in Aliev et al. (2015), Azadeh et al. (2013), Kang et al. (2012a, 2012b), Salari et al. (2014), Yager (2012), Pal et al. (2013), and Tadayon and Tadayon (2012)....
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TL;DR: Fuzzy rule interpolation is presented for designing of an inference engine of fuzzy rule-based system based on interpolative mechanism and the obtained comparative results demonstrate the suitability of designed system in control of dynamic plants.
Abstract: Frequently the reliabilities of the linguistic values of the variables in the rule base are becoming important in the modeling of fuzzy systems. Taking into consideration the reliability degree of the fuzzy values of variables of the rules the design of inference mechanism acquires importance. For this purpose, Z number based fuzzy rules that include constraint and reliability degrees of information are constructed. Fuzzy rule interpolation is presented for designing of an inference engine of fuzzy rule-based system. The mathematical background of the fuzzy inference system based on interpolative mechanism is developed. Based on interpolative inference process Z number based fuzzy controller for control of dynamic plant has been designed. The transient response characteristic of designed controller is compared with the transient response characteristic of the conventional fuzzy controller. The obtained comparative results demonstrate the suitability of designed system in control of dynamic plants.
14 citations
Cites background from "An Insight Into The Z-number Approa..."
...The paper [7] suggests the use of Z number in the perception of the uncertainty of the information conveyed by a natural language statement and to merge human-affective perspectiveswithComputingwithWords (CWW)....
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01 Jan 2015
TL;DR: The extension of Zadeh's basic Z-numbers into a tool for level-2 Computing With Words (CWW) and consequently subjective natural language understanding and the design of a, Minsky’s Society of Mind based, natural language comprehending machine-mind architecture are described.
Abstract: This article is centred on two themes. The first is the extension of Zadeh’s basic Z-numbers into a tool for level-2 Computing With Words (CWW) and consequently subjective natural language understanding. We describe an algorithm and new operators (leading to complex or spectral Z-numbers), use them to simulate differential diagnosis, and highlight the inherent strengths and challenges of the Z-numbers. The second theme deals with the design of a, Minsky’s Society of Mind based, natural language comprehending machine-mind architecture. We enumerate its macro-components (function modules and memory units) and illustrate its working mechanism through simulation of metaphor understanding; validating system outputs against human-comprehension responses. The framework uses the aforementioned new Z-number paradigm to precisiate knowledge-frames. The completeness of the conceptualized architecture is analyzed through its coverage of mind-layers (Minsky) and cerebral cortex regions. The research described here draws from multiple disciplines and seeks to contribute to the cognitive-systems design initiatives for man-machine symbiosis.
14 citations
Cites background from "An Insight Into The Z-number Approa..."
...Refer to [27, 28] for a discussion on the generic architecture and algorithm for CWW....
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...1 Z-Number Based Algorithm for CWW [27, 28]...
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...3 [refer to [27, 28] for other simulation examples]....
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...Let S1 and S2 be two natural language statements, and Z1 = <X1, A1, B1> and Z2 = <X2, A2, B2> be the Z-valuations of S1 and S2 respectively • Operator for the intersection of perceptions ð∩ PÞ [27, 28]...
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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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