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: A novel ‘cognitive’ computational mind framework for text comprehension in terms of Minsky’s ‘Society of Mind’ and ‘Emotion Machine’ theories is described, envisioned to be strategic in the design of intelligent plagiarism checkers, literature genre-cataloguers, differential diagnosis systems, and educational aids for children with reading disorders.
Abstract: Guided by a polymath approach--encompassing neuroscience, philosophy, psychology and computer science, this article describes a novel `cognitive' computational mind framework for text comprehension in terms of Minsky's `Society of Mind' and `Emotion Machine' theories. Observing a top-down design method, we enumerate here the macrocosmic elements of the model--the `agencies' and memory constructs, followed by an elucidation on the working principles and synthesis concerns. Besides corroboration of results of a dry-run test by thoughts generated by random human subjects; the completeness of the conceptualized framework has been validated as a consequence of its total representation of `text understanding' functions of the human brain, types of human memory and emulation of the layers of the mind. A brief conceptual comparison, between the architecture and existing `conscious' agents, has been included as well. The framework, though observed here in its capacity as a text comprehender, is capable of understanding in general. A cognitive model of text comprehension, besides contributing to the `thinking machines' research enterprise, is envisioned to be strategic in the design of intelligent plagiarism checkers, literature genre-cataloguers, differential diagnosis systems, and educational aids for children with reading disorders. Turing's landmark 1950 article on computational intelligence is the principal motivator behind our research initiative.
13 citations
Cites background from "An Insight Into The Z-number Approa..."
...Delacorte Press, NY Banerjee R, Pal SK (2013) The Z-number enigma: a study through an experiment....
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...Soft Comput 2:23–25 Zadeh LA (2011) A note on Z-numbers....
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...Theor Comput Sci 448:2–14 Pal SK, Banerjee R, Dutta S, Sen Sarma S (2013) An insight into the Z-number approach to CWW. Fundam Inform 124(1–2): 197–229 Payne SJ, Reader WR (2006) Constructing structure maps of multiple on-line texts....
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...terminal slots are filled with ‘default (intuitive)’ or ‘most likely [high-certainty (Banerjee and Pal. 2013; Pal et al. 2013)]’ values for the terminal....
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...…Statistical Institute, Kolkata, India e-mail: rm.banerjee@gmail.com S. K. Pal e-mail: sankar@isical.ac.in comprehension in Banerjee and Pal (2013), Pal et al. (2013) that questions on how does the human mind recall, visualize, granulate and associate perceptions—despite information insufficiency…...
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TL;DR: A new DEA (abbreviated as Z-DEA) is introduced for working out CCR in which the input and/or output are Z-number variables and is converted to classical fuzzy model on the base of a fuzzy expectation of the fuzzy sets.
Abstract: Data envelopment analysis (DEA) is an effective technique for measuring the efficiency of decision-making units (DMUs) with several inputs and various outputs. Traditional DEA requires crisp data. However, the data in real applications are often imprecise. In order to dominate this restriction, the fuzzy sets may be utilized with the classical DEA to permit expert to integrate ambiguous data into the model. However, fuzzy sets encounter the limitation of not considering the estimation of reliability of information. In view of this, Z-number has been extended to model fuzzy numbers with a degree of confidence. In this paper, we introduce a new DEA (abbreviated as Z-DEA) for working out CCR in which the input and/or output are Z-number variables. We do this task by converting the Z-DEA to classical fuzzy model on the base of a fuzzy expectation of the fuzzy sets. In our study, the expert utilizes the linguistic terms for expressing judgment and an estimation of reliability. To the best of our knowledge, compared with the traditional DEA frameworks, The DEA with Z-data can more practically handle real-world problems.
13 citations
Cites background from "An Insight Into The Z-number Approa..."
...Z-number extends the idea of computing with words (CWW) [19]....
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12 citations
TL;DR: A novel group decision making framework based on Z-numbers and the TODIM method to synthesise the opinions of the experts and assist them in selecting an optimal HCW treatment technology.
Abstract: Health-care waste (HCW) management has been regarded as an increasingly important issue in environmental protection. The evaluation and selection of HCW treatment technologies are essential in HCW ...
12 citations
TL;DR: The theory of Z-number is investigated in portfolio selection problem using the utility function and a practical method for obtaining the utility of assets in shape of the Z-numbers is introduced.
Abstract: The Z-number theory is a new concept in fuzzy logic. This theory describes the uncertainty of information where any Z-number is displayed by a pair of fuzzy numbers. The first component of the Z-number creates a restriction on the uncertain variable through a fuzzy number, while the second component of the Z-number explains the reliability of the first component through another fuzzy number. Because there is no any accurate image of the future of financial markets, the Z-number theory can be widely used in the financial markets widely. In this paper, the theory of Z-number is investigated in portfolio selection problem using the utility function. The Z-number is almost always converted to classical fuzzy number in the existing literature. Although this approach reduces the computational complexity, converting Z-number to classical fuzzy number causes the loss of significant information. Hence, we propose two practical models with Z-number approach and optimize them both with and without converting Z-number to classical fuzzy number. Optimization without converting Z-number causes the information about utility of assets and their reliability to be available in each stage. However, optimization with converting Z-number causes portfolio selection model to be transformed into a linear programming model. Furthermore, a practical method for obtaining the utility of assets in shape of the Z-numbers is introduced. In addition, liquidity constraint and the maximal fraction of the capital allocated constraint are considered in portfolio selection models. Eventually, two numerical examples from NYSE and NASDAQ Stock Market are provided, and the results are compared with each other.
11 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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