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An interval type-2 fuzzy model of computing with words

INFORMATION SCIENCES 2014年 281卷 418-442页

作者： Jiang, Yuncheng Tang, Yong S China Normal Univ Sch Comp Sci Guangzhou 510631 Guangdong Peoples R China

As a methodology, computing with words allows the use of words, instead of numbers or symbols, in the process of computing and reasoning and thus conforms more to humans' inference when it is used to describe real-world problems. Motivated by Zadeh's paradigm of computing with words, the literature has proposed a kind of type-1 fuzzy automata as a formal model of computing with words, which takes type-1 fuzzy subsets of symbols as input. However, type-1 fuzzy representation provides a limited platform for approximating the meaning of words since it is not able to capture linguistic uncertainty. In this paper, we develop a formal interval type-2 fuzzy model of computing with words by generalizing the existing type-1 fuzzy sets-based model to an interval type-2 fuzzy environment. Concretely, we take interval type-2 fuzzy automata (i.e., interval type-2 fuzzy finite automata and interval type-2 fuzzy pushdown automata), which combine interval type-2 fuzzy set theory and automaton theory, as a computational model of computing with words. Furthermore, we develop the extension principles to extend from computing with values to computing with words and show that computing with words can be implemented with computing with values in the interval type-2 fuzzy setting at an extra computational cost. (C) 2014 Elsevier Inc. All rights reserved.

关键词： computing with word Interval type-2 fuzzy set Finite automata Interval type-2 fuzzy automata Pushdown automata

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A reconstruction decoder for computing with words

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INFORMATION SCIENCES 2014年 255卷 1-15页

作者： Wu, Dongrui GE Global Res Machine Learning Lab Niskayuna NY 12309 USA

The word decoder is a very important approach for decoding in the Perceptual Computer. It maps the computing with words (CWWs) engine output, which is a fuzzy set, into a word in a codebook so that it can be understood. However, the word decoder suffers from significant information loss, i.e., the fuzzy set model of the mapped word may be quite different from the fuzzy set output by the CWW engine, especially when the codebook is small. In this paper we propose a Reconstruction decoder, which represents the CWW engine output as a combination of two successive codebook words with minimum information loss by solving a constrained optimization problem. The Reconstruction decoder preserves the shape information of the CWW engine output in a simple form without sacrificing much accuracy. It can be viewed as a generalized word decoder and is also implicitly a Rank decoder. Moreover, it is equivalent to the 2-tuple representation under certain conditions. The effectiveness of the Reconstruction decoder is verified by three experiments. (C) 2013 Elsevier Inc. All rights reserved.

关键词： computing with word Perceptual Computer Decoder 2-Tuple representation Type-1 fuzzy sets Interval type-2 fuzzy sets

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A linguistic multi-criteria decision making approach based on logical reasoning

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INFORMATION SCIENCES 2014年 258卷 266-276页

作者： Chen, Shuwei Liu, Jun Wang, Hui Xu, Yang Augusto, Juan Carlos Univ Ulster Sch Comp & Math Newtownabbey BT37 0QB North Ireland Southwest Jiaotong Univ Sch Math Chengdu 610031 Peoples R China Middlesex Univ Sch Sci & Technol Dept Comp Sci London N17 8HR England

In real decision making problems, it is always more natural for decision makers to use linguistic terms to express their preferences/opinions in a qualitative way among alternatives than to provide quantitative values. Additionally, many of these decision making problems are under uncertain environments with vague and imprecise information involved. Following the idea of computing with words (CWW) methodology, we propose in this paper a linguistic valued qualitative aggregation and reasoning framework for multi-criteria decision making problems, where a linguistic valued algebraic structure is constructed for modelling the linguistic information involved in multi-criteria decision making problems, and a linguistic valued logic based approximate reasoning method is developed to infer the final decision making result. This method takes the advantage of handling the linguistic information, no matter totally ordered or partially ordered, directly without numerical approximation, and having a non-classical logic as its formal foundation for decision making process. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Decision making Linguistic information computing with word Lattice-valued logic Approximate reasoning Lattice implication algebra

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A LINGUISTIC AGGREGATION OPERATOR INCLUDING WEIGHTS FOR LINGUISTIC VALUES AND EXPERTS IN GROUP DECISION MAKING

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INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 2013年第6期21卷 927-943页

作者： Pei, Zheng Zou, Li Yi, Liangzhong Xihua Univ Ctr Radio Adm & Technol Dev Chengdu 610039 Sichuan Peoples R China Liaoning Normal Univ Sch Comp & Informat Technol Dalian 116029 Peoples R China Nanjing Univ State Key Lab Novel Software Technol Nanjing 210093 Jiangsu Peoples R China Sichuan Police Coll Luzhou 646000 Sichuan Peoples R China

Different linguistic aggregation methods have been proposed and applied in the linguistic decision making problems. Generally, weights for experts or criteria are considered in linguistic aggregation processes. In this paper, we provide a method to discovery new forms to compute weights and new interpretations in the linguistic ordered weighted averaging operator. In linguistic decision analysis, it can be noticed that some of initial linguistic values used by experts have priority over others linguistic values in evaluation processes. We formalize the priority over initial linguistic values as weights for linguistic values, by considering weights for linguistic values as well as weights for experts, we provide an alternative method to discovery weights information of the linguistic ordered weighted averaging operator, its properties show that such linguistic aggregation operator is extensions of the 2-tuple arithmetic mean, the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator. By an illustrative example, we compare the linguistic aggregation operator with the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator in a decision making problem. From the practical point of view, we provide an optimization model to obtain such weights information in linguistic aggregation processes, examples show the linguistic aggregation operator as an alternative linguistic ordered weighted averaging operator in practice.

关键词： computing with word linguistic group decision making the 2-tuple fuzzy linguistic representation model

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FAST: A Fuzzy Semantic Sentence Similarity Measure

FAST: A Fuzzy Semantic Sentence Similarity Measure

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IEEE International Conference on Fuzzy Systems (FUZZ)

作者： Chandran, David Crockett, Keeley Mclean, David Bandar, Zuhair Manchester Metropolitan Univ Intelligent Syst Grp Sch Comp Math & Digital Technol Chester St Manchester M1 5GD Lancs England

ISBN: (纸本)9781479900206

A problem in the field of semantic sentence similarity is the inability of sentence similarity measures to accurately represent perception based (fuzzy) words that are commonly used in natural language. This paper presents a new sentence similarity measure that attempts to solve this problem. The new measure, Fuzzy Algorithm for Similarity Testing (FAST) is an ontology based similarity measure that uses concepts of fuzzy and computing with words to allow for the accurate representation of fuzzy based words. Through human experimentation fuzzy sets were created for six categories of words based on their levels of association with particular concepts. These fuzzy sets were then defuzzified and the results used to create new ontological relations between the words. Using these relationships allows for the creation of a new ontology based semantic text similarity algorithm that is able to show the effect of fuzzy words on computing sentence similarity as well as the effect that fuzzy words have on non-fuzzy words within a sentence. Experiments on FAST were conducted using a new fuzzy dataset, the creation of which is described in this paper. The results of the evaluation showed that there was an improved level of correlation between FAST and human test results over two existing sentence similarity measures.

关键词： semantic similarity measures computing with word ontology FAST

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ON CONCEPT ALGEBRA FOR computing with wordS (CWW)

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INTERNATIONAL JOURNAL OF SEMANTIC computing 2010年第3期4卷 331-356页

作者： Wang, Yingxu Univ Calgary Dept Elect & Comp Engn 2500 Univ Dr NW Calgary AB T2N 1N4 Canada

computing with words (CWW) is an intelligent computing methodology for processing words, linguistic variables, and their semantics, which mimics the natural-language-based reasoning mechanisms of human beings in soft computing, semantic computing, and cognitive computing. The central objects in CWW techniques are words and linguistic variables, which may be formally modeled by abstract concepts that are a basic cognitive unit to identify and model a concrete entity in the real world and an abstract object in the perceived world. Therefore, concepts are the most fundamental linguistic entities that carries certain meanings in expression, thinking, reasoning, and system modeling, which may be formally modeled as an abstract and dynamic mathematical structure in denotational mathematics. This paper presents a formal theory for concept and knowledge manipulations in CWW known as concept algebra. The mathematical models of abstract and concrete concepts are developed based on the object-attributerelation (OAR) theory. The formal methodology for manipulating knowledge as a concept network is described. Case studies demonstrate that concept algebra provides a generic and formal knowledge manipulation means, which is capable of dealing with complex knowledge and their algebraic operations in CWW.

关键词： computing with word concept algebra semantic computing denotational mathematics cognitive informatics concept network knowledge representation OAR model soft computing cognitive computing computational intelligence case studies

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LINGUISTIC INVENTORY PROBLEMS

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NEW MATHEMATICS AND NATURAL COMPUTATION 2011年第1期7卷 1-49页

作者： Hsieh, Chih Hsun Aletheia Univ Dept Informat Management 32Chen Li St Taipei 251 Taiwan

The work presented in this paper has been motivated primarily by Zadeh's idea of linguistic variables intended to provide rigorous mathematical modeling of natural language and CWW, computing with words. This paper reports some modeling of the linguistic inventory problems where CWW have been implemented: linguistic production inventory, linguistic inventory models under linguistic demand and linguistic lead time, linguistic production inventory models based on the preference of a decision maker, and linguistic inventory model for fuzzy reorder point and fuzzy safety stock. Only studies that focus on CWW, two linguistic inventory models and two linguistic backorder inventory models, which each model is combined by the heuristic fuzzy total inventory cost based on the preference of a decision maker, are proposed in this paper. The heuristic fuzzy total inventory cost of each model is modeled by linguistic values in natural language, fuzzy numbers, and crisp real numbers. It is also computed and defuzzified by using some fuzzy arithmetical operations by Function Principle and Graded k-preference integration representation method, respectively. In addition, Extension of the LaGrangean method is used for solving inequality constrain problem in the proposed linguistic inventory environments. Furthermore, we find that our heuristic optimal solutions of the new introduced modeling the linguistic inventory problems can also be specified to meet the classical inventory models, when all linguistic variables are crisp real numbers, such as the previous proposed linguistic inventory models.

关键词： Linguistic computing with word fuzzy inventory

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Relationship among basic concepts in covering-based rough sets

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INFORMATION SCIENCES 2009年第14期179卷 2478-2486页

作者： Zhu, William Univ Elect Sci & Technol China Sch Engn & Comp Sci Chengdu 610054 Peoples R China Chinese Acad Sci Inst Automat Key Lab Complex Syst & Intelligence Sci Beijing Peoples R China

Uncertainty and incompleteness of knowledge are widespread phenomena in information systems. Rough set theory is a tool for dealing with granularity and vagueness in data analysis. Rough set method has already been applied to various fields such as process control, economics, medical diagnosis, biochemistry, environmental science, biology, chemistry, psychology, and conflict analysis. Covering-based rough set theory is an extension to classical rough sets. In covering-based rough sets, there exist several basic concepts such as reducible elements of a covering, minimal descriptions, unary coverings. and the property that the intersection of any two elements is the union of finite elements in this covering. These concepts appeared in the literature of covering-based rough sets separately. In this paper we study the relationships between them. In particular, we establish the equivalence of the unary covering and the covering with the property that the intersection of any two elements is the union of finite elements in this covering. We also investigate the relationship between the covering lower approximation operation and the interior operator. A characterization of the interior operator by the covering lower approximation operation is presented in this paper. Correspondingly, we study the relationship between the covering upper approximation operation and the closure operator. In addition, we explore the conditions under which the covering upper approximation operation is monotone. The study of the relationships between these concepts will help us have a better understanding of covering-based rough sets. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Rough set Covering Granular computing Fuzzy set computing with word

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Properties of the third type of covering-based rough sets

Properties of the third type of covering-based rough sets

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6th International Conference on Machine Learning and Cybernetics

作者： Zhu, William Wang, Fei-Yue Chinese Acad Sci Inst Automat Beijing 100080 Peoples R China

ISBN: (纸本)9781424409723

Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information systems. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations, or partitions. This paper studies covering-based generalized rough sets. In this setting, a covering can generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a covering under which these properties hold for the third type of covering-based lower and upper approximation operations.

关键词： rough set covering granular computing fuzzy set computing with word

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PROPERTIES OF THE THIRD TYPE OF COVERING-BASED ROUGH SETS

PROPERTIES OF THE THIRD TYPE OF COVERING-BASED ROUGH SETS

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2007 International Conference on Machine Learning and Cybernetics(IEEE第六届机器学习与控制论国际会议)

作者： WILLIAM ZHU FEI-YUE WANG The Institute of Automation The Chinese Academy of Sciences Beijing 100080 China The Department o The Institute of Automation The Chinese Academy of Sciences Beijing 100080 China The Systems and

Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information *** core concepts of classical rough sets are lower and upper approximations based on equivalence relations, or *** paper studies covering-based generalized rough *** this setting, a covering can generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer *** investigate conditions for a covering under which these properties hold for the third type of covering-based lower and upper approximation operations.

关键词： Rough set Covering Granular computing Fuzzy set computing with word

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