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: 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.
234 citations
Cites background from "An Insight Into The Z-number Approa..."
...In [24] the authors of [6] suggest an outline of the general principles, challenges and perspectives of CWW in light of the Z-number concept and consider issues of integration of CWW and Natural Language Processing technology....
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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.
Abstract: Z-numbers are a new concept considering both the description of cognitive information and the reliability of information. Linguistic terms are useful tools to adequately and effectively model real-life cognitive information, as well as to characterize the randomness of events. However, a form of Z-numbers, in which their two components are in the form of linguistic terms, is rarely studied, although it is common in decision-making problems. In terms of Z-numbers and linguistic term sets, we provided the definition of linguistic Z-numbers as a form of Z-numbers or a subclass of Z-numbers. Then, we defined some operations of linguistic Z-numbers and proposed a comparison method based on the score and accuracy functions of linguistic Z-numbers. We also presented the distance measure of linguistic Z-numbers. Next, we developed an extended TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method based on the Choquet integral for multi-criteria decision-making (MCDM) problems with linguistic Z-numbers. Finally, we provided an example concerning the selection of medical inquiry applications to demonstrate the feasibility of our proposed approach. We then verified the applicability and superiority of our approach through comparative analyses with other existing methods. Illustrative and comparative analyses indicated that the proposed approach was valid and feasible for different decision-makers and cognitive environments. Furthermore, the final ranking results of the proposed approach were closer to real decision-making processes. Linguistic Z-numbers can flexibly characterize real cognitive information as well as describe the reliability of information. This method not only is a more comprehensive reflection of the decision-makers’ cognition but also is more in line with expression habits. The proposed method inherited the merits of the classical TODIM method and considers the interactivity of criteria; therefore, the proposed method was effective for dealing with real-life MCDM problems. Consideration about bounded rational and the interactivity of criteria made final outcomes convincing and consistent with real decision-making.
144 citations
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.
135 citations
TL;DR: Results show that the proposed framework can improve the previous methods with comparability considering the reliability of information using Z-numbers and is more flexible comparing with previous work.
Abstract: Environmental assessment and decision making is complex leading to uncertainty due to multiple criteria involved with uncertain information. Uncertainty is an unavoidable and inevitable element of any environmental evaluation process. The published literatures rarely include the studies on uncertain data with variable fuzzy reliabilities. This research has proposed an environmental evaluation framework based on Dempster–Shafer theory and Z-numbers. Of which a new notion of the utility of fuzzy number is proposed to generate the basic probability assignment of Z-numbers. The framework can effectively aggregate uncertain data with different fuzzy reliabilities to obtain a comprehensive evaluation measure. The proposed model has been applied to two case studies to illustrate the proposed framework and show its effectiveness in environmental evaluations. Results show that the proposed framework can improve the previous methods with comparability considering the reliability of information using Z-numbers. The proposed method is more flexible comparing with previous work.
133 citations
TL;DR: An innovative method for addressing multicriteria group decision-making (MCGDM) problems with Z-numbers under the condition that the weight information is completely unknown is developed.
Abstract: Z -number is the general representation of real-life information with reliability, and it has adequate description power from the point of view of human perception. This study develops an innovative method for addressing multicriteria group decision-making (MCGDM) problems with Z -numbers under the condition that the weight information is completely unknown. Processing Z -numbers requires effective support of reliable tools. Then, the normal cloud model can be employed to analyze the Z -number construct. First, the potential information involved in Z -numbers is invoked, and a novel concept of normal Z +-value is proposed with the aid of the normal cloud model. The operations, distance measurement, and power aggregation operators of normal Z +-values are defined. Moreover, an MCGDM method is developed by incorporating the defined distance measurement and power aggregation operators into the MultiObjective Optimization by Ratio Analysis plus the Full Multiplicative Form. Finally, an illustrative example concerning air pollution potential evaluation is provided to demonstrate the proposed method. Its feasibility and validity are further verified by a sensitivity analysis and comparison with other existing methods.
129 citations
Cites methods from "An Insight Into The Z-number Approa..."
...Applying the Z-number method to CWW was investigated in [16]....
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References
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10 Aug 1998
TL;DR: This report will present the project's goals and workflow, and information about the computational tools that have been adapted or created in-house for this work.
Abstract: FrameNet is a three-year NSF-supported project in corpus-based computational lexicography, now in its second year (NSF IRI-9618838, "Tools for Lexicon Building"). The project's key features are (a) a commitment to corpus evidence for semantic and syntactic generalizations, and (b) the representation of the valences of its target words (mostly nouns, adjectives, and verbs) in which the semantic portion makes use of frame semantics. The resulting database will contain (a) descriptions of the semantic frames underlying the meanings of the words described, and (b) the valence representation (semantic and syntactic) of several thousand words and phrases, each accompanied by (c) a representative collection of annotated corpus attestations, which jointly exemplify the observed linkings between "frame elements" and their syntactic realizations (e.g. grammatical function, phrase type, and other syntactic traits). This report will present the project's goals and workflow, and information about the computational tools that have been adapted or created in-house for this work.
2,900 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 computational theory of perceptions (CTP) as mentioned in this paper is a methodology for reasoning and computing with perceptions rather than measurements, where words play the role of labels of perceptions and, more generally, perceptions are expressed as propositions in a natural language.
Abstract: Discusses a methodology for reasoning and computing with perceptions rather than measurements. An outline of such a methodology-referred to as a computational theory of perceptions is presented in this paper. The computational theory of perceptions, or CTP for short, is based on the methodology of CW. In CTP, words play the role of labels of perceptions and, more generally, perceptions are expressed as propositions in a natural language. CW-based techniques are employed to translate propositions expressed in a natural language into what is called the Generalized Constraint Language (GCL). In this language, the meaning of a proposition is expressed as a generalized constraint, N is R, where N is the constrained variable, R is the constraining relation and isr is a variable copula in which r is a variable whose value defines the way in which R constrains S. Among the basic types of constraints are: possibilistic, veristic, probabilistic, random set, Pawlak set, fuzzy graph and usuality. The wide variety of constraints in GCL makes GCL a much more expressive language than the language of predicate logic. In CW, the initial and terminal data sets, IDS and TDS, are assumed to consist of propositions expressed in a natural language. These propositions are translated, respectively, into antecedent and consequent constraints. Consequent constraints are derived from antecedent constraints through the use of rules of constraint propagation. The principal constraint propagation rule is the generalized extension principle. The derived constraints are retranslated into a natural language, yielding the terminal data set (TDS). The rules of constraint propagation in CW coincide with the rules of inference in fuzzy logic. A basic problem in CW is that of explicitation of N, R, and r in a generalized constraint, X is R, which represents the meaning of a proposition, p, in a natural language.
1,453 citations
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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.
865 citations
"An Insight Into The Z-number Approa..." refers methods in this paper
...In the following section (Section 3) we present an overview of the Z-number, as is visualized by Zadeh in [29], and then describe our proposed methodology for CWW using the Z-numbers (Section 4)....
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...In 2011, Zadeh proposed the notion of the Z-number [29] - a technique to incorporate the concept of the reliability of information within CWW....
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...Preliminary rules of computation [29] using the Z-numbers are as follows: (i) For the purpose of computation, the values of A and B need to be precisiated through association with membership functions, μA, μB respectively....
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Book•
26 Apr 2010
TL;DR: Perceptual Computing explains how to implement CWW to aid in the important area of making subjective judgments, using a methodology that propagates random and linguistic uncertainties into the subjective judgment in a way that can be modeled and observed by the judgment maker.
Abstract: Explains for the first time how "computing with words" can aid in making subjective judgments Lotfi Zadeh, the father of fuzzy logic, coined the phrase "computing with words" (CWW) to describe a methodology in which the objects of computation are words and propositions drawn from a natural language. Perceptual Computing explains how to implement CWW to aid in the important area of making subjective judgments, using a methodology that leads to an interactive devicea "Perceptual Computer"that propagates random and linguistic uncertainties into the subjective judgment in a way that can be modeled and observed by the judgment maker. This book focuses on the three components of a Perceptual Computerencoder, CWW engines, and decoderand then provides detailed applications for each. It uses interval type-2 fuzzy sets (IT2 FSs) and fuzzy logic as the mathematical vehicle for perceptual computing, because such fuzzy sets can model first-order linguistic uncertainties whereas the usual kind of fuzzy sets cannot. Drawing upon the work on subjective judgments that Jerry Mendel and his students completed over the past decade, Perceptual Computing shows readers how to: Map word-data with its inherent uncertainties into an IT2 FS that captures these uncertainties Use uncertainty measures to quantify linguistic uncertainties Compare IT2 FSs by using similarity and rank Compute the subsethood of one IT2 FS in another such set Aggregate disparate data, ranging from numbers to uniformly weighted intervals to nonuniformly weighted intervals to words Aggregate multiple-fired IF-THEN rules so that the integrity of word IT2 FS models is preserved Free MATLAB-based software is also available online so readers can apply the methodology of perceptual computing immediately, and even try to improve upon it. Perceptual Computing is an important go-to for researchers and students in the fields of artificial intelligence and fuzzy logic, as well as for operations researchers, decision makers, psychologists, computer scientists, and computational intelligence experts.
435 citations
"An Insight Into The Z-number Approa..." refers background in this paper
...Notable works include: [4] where the authors attempt to break away from the traditional rule-based approach to formulate an arithmetic-based technique based on fuzzy numbers; [11] describes the application of the mass assignment theory to fuzzy sets to provide semantic interpretations for membership functions; [18] illustrates the concept of a fuzzy Finite State Machine (FSM) to generate linguistic descriptions of complex phenomenon, which is further extended in [20] to simulate emotions in such a system; [12] explains the relevance of the Interval Type-2 Fuzzy Set (IT2-FS) in mapping the different levels of ambiguities in word perceptions - crucial to the intended human-like responses of a system based on CWW; [17] coalesces the concepts of fuzzy sets and ontology; while [8] and [9] formalize the Generalized Constraint Language (GCL) into a tool for CWW....
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...(iv) The IT2-FS [12] has gained immense importance as one of the best fuzzy set models of word perceptions....
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...Since its coinage, the last decade has seen a surge in research on the concepts of CWW. Notable works include: [4] where the authors attempt to break away from the traditional rule-based approach to formulate an arithmetic-based technique based on fuzzy numbers; [11] describes the application of the mass assignment theory to fuzzy sets to provide semantic interpretations for membership functions; [18] illustrates the concept of a fuzzy Finite State Machine (FSM) to generate linguistic descriptions of complex phenomenon, which is further extended in [20] to simulate emotions in such a system; [12] explains the relevance of the Interval Type-2 Fuzzy Set (IT2-FS) in mapping the different levels of ambiguities in word perceptions - crucial to the intended human-like responses of a system based on CWW; [17] coalesces the concepts of fuzzy sets and ontology; while [8] and [9] formalize the Generalized Constraint Language (GCL) into a tool for CWW....
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TL;DR: Fast-forward (FF) as mentioned in this paper was the most successful automatic planner in the Fifth International Conference on Artificial Intelligence Planning and Scheduling (AIPS '00) planning systems competition, which relies on forward search in the state space guided by a heuristic that estimates goal distances by ignoring delete lists.
Abstract: Fast-forward (FF) was the most successful automatic planner in the Fifth International Conference on Artificial Intelligence Planning and Scheduling (AIPS '00) planning systems competition. Like the well-known hsp system, FF relies on forward search in the state space, guided by a heuristic that estimates goal distances by ignoring delete lists. It differs from HSP in a number of important details. This article describes the algorithmic techniques used in FF in comparison to hsp and evaluates their benefits in terms of run-time and solution-length behavior. Humans have a remarkable capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Familiar examples are parking a car, driving in city traffic, playing golf, cooking a meal, and summarizing a story. In performing such tasks, humans use perceptions of time, direction, speed, shape, possibility, likelihood, truth, and other attributes of physical and mental objects. Reflecting the bounded ability of the human brain to resolve detail, perceptions are intrinsically imprecise. In more concrete terms, perceptions are f-granular, meaning that (1) the boundaries of perceived classes are unsharp and (2) the values of attributes are granulated, with a granule being a clump of values (points, objects) drawn together by indistinguishability, similarity, proximity, and function. For example, the granules of age might be labeled very young, young, middle aged, old, very old, and so on. F-granularity of perceptions puts them well beyond the reach of traditional methods of analysis based on predicate logic or probability theory. The computational theory of perceptions (CTP), which is outlined in this article, adds to the armamentarium of AI a capability to compute and reason with perception-based information. The point of departure in CTP is the assumption that perceptions are described by propositions drawn from a natural language; for example, it is unlikely that there will be a significant increase in the price of oil in the near future. In CTP, a proposition, p, is viewed as an answer to a question, and the meaning of p is represented as a generalized constraint. To compute with perceptions, their descriptors are translated into what is called the generalized constraint language (GCL). Then, goal-directed constraint propagation is utilized to answer a given query. A concept that plays a key role in CTP is that of precisiated natural language (PNL). The computational theory of perceptions suggests a new direction in AI -- a direction that might enhance the ability of AI to deal with realworld problems in which decision-relevant information is a mixture of measurements and perceptions. What is not widely recognized is that many important problems in AI fall into this category.
399 citations