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 new weighted Z-similarity measure is proposed, which is able to retain the original information provided by experts in linguistic terms, which takes care of the directional aspect of reliability of information by leveraging the Hausdorff distance.
Abstract: In this article, we propose a new weighted Z -similarity measure between two Z -numbers, which is able to retain the original information provided by experts in linguistic terms. This measure takes care of the directional aspect of reliability of information by leveraging the Hausdorff distance. Probabilistic-approach-based statistical distance measure is used to characterize the internal relationship between two parts of a Z -number. Some properties of the Z -similarity measure are proved. The measure is capable of quantifying the probability of basic events in bow-tie analysis. It is experimentally shown that the Z -similarity measure is able to overcome the lacuna of the available techniques. Sensitivity analysis is done to verify its feasibility and applicability. We further propose another measure, called Z -similarity-based basic event contribution ( Z -BEC), to quantify the contribution of basic events to the occurrence of different accidents. The performance of the Z -BEC measure is compared with that of Fussell–Vesely index and Birnbaum's structural index.
20 citations
Cites background from "An Insight Into The Z-number Approa..."
...Definition 11 (see [42] and [43]): Let X be a random variable with pdf p(x) and Z = (A,B), where A is a discrete fuzzy number representing the fuzzy constraint on values of X and B plays the role of the fuzzy constraint on the probability measure of A....
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DOI•
01 Jun 2017TL;DR: It is concluded that future energy hub models need to realistic scheduling and modeling of MES to be able to achieve a realistic and comprehensive model of future sustainable energy systems.
Abstract: Energy Hub is an appropriate framework for modeling and optimal scheduling of multi-energy systems (MES). However, the optimal scheduling problem in the energy hub models is fed by various technical, economic, social and environmental parameters. Many of these parameters are mainly subject to uncertainties. Fluctuating nature of renewable energy sources (RES), energy prices in deregulated markets, the behavior of consumers, simplifications and approximations in modeling, linguistic terms of experts, etc. are just a few examples of uncertainty sources in the optimal scheduling problem of energy hub. Ignoring such uncertainties in the process of modeling and optimization of energy hub results in unrealistic models and inaccurate results. On the other hand addressing these uncertainties leads to increased complexity of modeling and optimization. Therefore, identifying appropriate methods to address uncertainties is essential to achieve a realistic model of MES in the framework of energy hub. This paper reviews the different uncertainty modeling methods in optimal scheduling of energy hub. In this paper, different modeling and optimization methods of energy hub are discussed and strengths and weaknesses of these methods are demonstrated. A classification and review of the various uncertainty modeling methods implemented in the most recent research on MES are done to identify efficient methods for using in energy hub models. This paper concludes that future energy hub models need to realistic scheduling and modeling of MES to be able to achieve a realistic and comprehensive model of future sustainable energy systems.
19 citations
TL;DR: The fuzzy interpolative reasoning is proposed for construction of inference mechanism of a Z-number-based fuzzy system for estimation of food security risk level and prediction periods of the food supply.
Abstract: Fuzzy logic systems based on If-Then rules are widely used for modelling of the systems characterizing imprecise and uncertain information. These systems are basically based on type-1 fuzzy sets and allow handling the uncertain and imprecise information to some degree in the developed models. Zadeh extended the concept of fuzzy sets and proposed Z-number characterized by two components, constraint and reliability parameters, which are an ordered pair of fuzzy numbers. Here, the first component is used to represent uncertain information, and the second component is used to evaluate the reliability or the confidence in truth. Z-number is an effective approach to solving uncertain problems. In this paper, Z-number-based fuzzy system is proposed for estimation of food security risk level. To construct fuzzy If-Then rules, the basic parameters cereal yield, cereal production, and economic growth affecting food security are selected, and the relationship between these input parameters and risk level are determined through If-Then fuzzy rules. The fuzzy interpolative reasoning is proposed for construction of inference mechanism of a Z-number-based fuzzy system. The designed system is tested using Turkey cereal data for assessing food security risk level and prediction periods of the food supply.
19 citations
Cites methods from "An Insight Into The Z-number Approa..."
...Z-numbers are used to solve the problems related to computing with words [27] and decision-making [28] problems....
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TL;DR: A new method of ranking Z‐numbers based on the concept of value and ambiguity at levels of decision‐making has been proposed and seems to deliver a reasonable decision and proper ranking of Z‐Numbers of various types.
Abstract: The concept of Z‐number, is very new in the literature, proposed by Zadeh in 2011. The Z‐number Z = ( A , B ) is a pair of fuzzy numbers where the first component represents the restriction and the second component represents the certainty of the first component. Further, its application is evident in decision‐making problems, risk assessment, linear programming problems, and so forth. Hence, under such circumstances ranking of Z‐numbers need an utmost attention, as such, a few methods of ranking Z‐numbers are proposed by various researcher. However, in many situations the existing methods depict drawbacks and limitations as discussed in this paper. Hence, a new method of ranking Z‐numbers is essential for an appropriate decision‐making. In this paper, a new method of ranking Z‐numbers based on the concept of value and ambiguity at levels of decision‐making have been proposed. The method seems to deliver a reasonable decision and proper ranking of Z‐numbers of various types. A few numerical examples are discussed which show the out‐performance of the proposed method.
17 citations
DOI•
01 Jul 2015
TL;DR: The computational technique is explained and examples how sum and product of Z-valuations can be computed are illustrated with examples.
Abstract: Zadeh defined a Z-number associated with an uncertain variable X as an ordered pair of fuzzy numbers,(A,B). The first component represents the value of the variable while the second component gives a measure of certainty. Computations with Z-numbers is a topic which is both interesting and useful. In this paper we explain the computational technique and illustrate with examples how sum and product of Z-valuations can be computed. Keyword: Fuzzy event probability ,Restriction, Zadeh's Z-numbers ,Z-valuation
16 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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