Towards a linear general type-2 fuzzy logic based approach for computing with words

Within the last two decades, the paradigm of Computing With Words (CWW) has been gaining more attention. Mainly, CWW has an exciting vision which tries to tackle the problem of human intelligence by taking the human mind as a role model. The human intelligence has been investigated by various disciplines including psychology, philosophy, neuroscience, linguistics, computer science, and cognitive sciences. Notably, it is not a straightforward task to map the human’s brain reasoning into computer processes. In this paper, we propose to facilitate such mapping by investigating a key element, which is to identify the step-by-step formation of perceptual judgments. Herein, we first introduce an approach that employs general type-2 fuzzy logic to dynamically model the human perceptions based on the human experience. This approach can be regarded as a step to enable the CWW vision. We have deployed the proposed approach in real-world settings and we will present two sets of real-world experiments which were conducted in the intelligent apartment (iSpace) in the University of Essex. The first set of experiments demonstrates the results of the proposed approach for the adaptive modeling of ambient luminance perception. In the second set of experiments, we show that our approach performs better in the rule base evaluation processing time and in output accuracy with comparison to an interval type-2 fuzzy logic system.     

Data compactification and computing with words

The underlying objective of this study is to show how fuzzy sets (and information granules in general) and grammatical inference play an interdependent role in information granularization and knowledge-based problem characterization. The bottom-up organization of the material starts with a concept and selected techniques of data compactification which involves information granulation and gives rise to higher-order constructs (type-2 fuzzy sets). The detailed algorithmic investigations are provided.In the sequel, we focus on Computing with Words (CW), which in this context is treated as a general paradigm of processing information granules. We elaborate on a role of randomization and offer a detailed example illustrating the essence of the granular constructs along with the grammatical aspects of the processing.     

Fuzzy logic with biomolecules

 The uncertain and inexact nature of the chemical reactions used to implement DNA computations can be turned into an advantage for implementing robust soft computing systems. The key feature of DNA hybridization that makes it appropriate for fuzzy computing is the uncertainty and incompleteness in the formation of a double-stranded duplex from single-stranded oligonucleotides. To implement fuzzy computing, a set of encoding DNA molecules is given that reproduces a specific membership function in the energetics of the DNA duplex. In addition, a fuzzy inference system implemented with DNA hybridization on solid supports is discussed. The ultimate success of this idea as a general technique, however, is dependent on the actual geometry of the Gibbs free-energy landscapes in the space of all duplex formations. Elucidating this problem is undoubtedly of great importance for biomolecular implementation of soft-computing because it may, in particular, shed light on the true import of fuzzy models in biological processes fundamental to life.     

A formal model of computing with words

Classical automata are formal models of computing with values. Fuzzy automata are generalizations of classical automata where the knowledge about the system's next state is vague or uncertain. It is worth noting that like classical automata, fuzzy automata can only process strings of input symbols. Therefore, such fuzzy automata are still (abstract) devices for computing with values, although a certain vagueness or uncertainty are involved in the process of computation. We introduce a new kind of fuzzy automata whose inputs are instead strings of fuzzy subsets of the input alphabet. These new fuzzy automata may serve as formal models of computing with words. We establish an extension principle from computing with values to computing with words. This principle indicates that computing with words can be implemented with computing with values with the price of a big amount of extra computations.     

On computing logic programs

In this paper we present and compare some classical problem-solving methods for computing the stable models of logic programs with negation. Using a graph theoretic representation of logic programs and their stable models, we discuss and compare linear programming, propositional satisfiability, constraint satisfaction, and graph methods.     

Fuzzy logic

The author presents a condensed exposition of some basic ideas underlying fuzzy logic and describes some representative applications. He covers basic principles; meaning representation and inference; basic rules of inference; and the linguistic variable and its application to fuzzy control     

On forming joint variables in computing with words

Abstract

We discuss Zadeh’s idea of computing with words and emphasize its perspective that information provides a restriction on the values variables can assume. We describe the role that the constraint-based semantics plays in translating natural language statements into formal mathematical objects. One task that arises in using this approach is the formulation of joint restrictions on multiple variables from individual information about each of the variables. Our interest here is to extend the capability of the framework of computing with words in the task of forming joint variables with the introduction of the idea of perceived relatedness between variables, a concept closely related to the idea of correlation. We are particularly interested in role that knowledge about perceived relatedness between variables can play in further restricting the possible values of joint then that simple provided by the individual constraints. We look at the problem of joining various types of uncertain variables, possibilistic, probabilistic and Dempster-Shafer belief structures.     

Complexity of computing with extended propositional logic programs

In this paper we introduce the notion of anF-program, whereF is a collection of formulas. We then study the complexity of computing withF-programs.F-programs can be regarded as a generalization of standard logic programs. Clauses (or rules) ofF-programs are built of formulas fromF. In particular, formulas other than atoms are allowed as building blocks ofF-program rules. Typical examples ofF are the set of all atoms (in which case the class of ordinary logic programs is obtained), the set of all literals (in this case, we get the class of logic programs with classical negation [9]), the set of all Horn clauses, the set of all clauses, the set of all clauses with at most two literals, the set of all clauses with at least three literals, etc. The notions of minimal and stable models [16, 1, 7] of a logic program have natural generalizations to the case ofF-programs. The resulting notions are called in this paperminimal andstable answer sets. We study the complexity of reasoning involving these notions. In particular, we establish the complexity of determining the existence of a stable answer set, and the complexity of determining the membership of a formula in some (or all) stable answer sets. We study the complexity of the existence of minimal answer sets, and that of determining the membership of a formula in all minimal answer sets. We also list several open problems.This work was partially supported by National Science Foundation under grant IRI-9012902.This work was partially supported by National Science Foundation under grant CCR-9110721.     

Fuzzy logic deduction with crisp observations

This paper presents an approach to approximate reasoning over a set of IF-THEN rules called fuzzy logic deduction. It understands IF-THEN rules as linguistically expressed logical implications and interprets them inside formal logical theory. Methodology and some properties are presented. This paper has been supported by the Grant A1187901/99 of the GA AV R and project W-00-016 of the Cz-US scientific cooperation.     

Soft computing and fuzzy logic

What is soft computing? What is fuzzy computing? What is the relationship between them? This paper intends to provide clear answers to these questions. We focus on exploring the notions of the fuzzy coordinate system and the related transformations between qualitative and quantitative information. These notions are considered to be the core ideas of fuzzy computing. Then the three novel theories of fuzzy computing and soft computing developed by the first author of this paper, namely, the Falling Shadow Representation of fuzzy theory, the Factors Space theory and the Truth Value Flow Inference theory are introduced.     

Soft computing and fuzzy logic

Discusses soft computing, a collection of methodologies that aim to exploit the tolerance for imprecision and uncertainty to achieve tractability, robustness, and low solution cost. Its principal constituents are fuzzy logic, neurocomputing, and probabilistic reasoning. Soft computing is likely to play an increasingly important role in many application areas, including software engineering. The role model for soft computing is the human mind     

An evaluation of retranslation methods in computing with words

To represent output fuzzy values of a computing with words (CW) system in natural language, a retranslation unit is required. In this work, retranslation methods applicable to a CW system are explored. Several methods that employ similarity measures of fuzzy sets, linguistic modifiers, or linguistic quantifiers have been applied to three real-world case studies. Performances of the applied methods have been evaluated through degree of validity, and comparison of characteristics of fuzzy sets such as fuzziness and specificity. Results show that invalid linguistic terms might be used in the retranslation process which also cause incomprehensible phrases in natural language.     

An arithmetic approach for the computing with words paradigm

Computing with words applications are mostly built using rule‐based systems, which have some important deficits: First, it is not easy to deal with high dimension problems because the size of the rule base increases exponentially; second, it is not possible to concatenate two or more systems without losing information; and third, there are no ways to compute inputs from outputs. In this article we show an alternative kind of system that remedies those deficits in many applications. It is based on fuzzy arithmetic rather than fuzzy logic. We also show application examples. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 121–142, 2006.     

Fuzzy logic microcontroller

We propose an architecture dedicated mainly to medium-range applications that demand computational power combined with low cost for the resulting hardware system (chip and board). Our architecture is a 16-bit processor with dedicated instructions and hardware for efficient support of fuzzy logic. To make the architecture effective for control applications developed with a traditional approach or with fuzzy logic, we equipped the processor with a microcontroller's general features. Our design accounts for application characteristics to provide efficient hardware support for fuzzy logic. To achieve this we first analyzed fuzzy control algorithms and derived a general model for fuzzy computation. In defining the model, we considered the large spectrum of possible inference methods, fuzzification and defuzzification mechanisms, and the operators used in control applications. On this basis, we defined the instruction set that supports this computational model and a proper architectural solution. We tested the system (composed of the software model and its hardware support) by simulating different sets of general-purpose and fuzzy control benchmarks     

Meta-linguistic axioms as a foundation for computing with words

Meta-linguistic axioms are proposed in analogy to the axioms of classical theory as a foundation for Computing With Words. Consequences of these meta-linguistic expressions are explored in the light of Interval-valued Type-2 Fuzzy Sets. The mapping of meta-linguistic axioms to Fuzzy Disjunctive and Conjunctive Canonical forms generate two set theoretic axioms for each meta-linguistic axiom that is composed of two elements such as commutativity and four set theoretic axioms for each meta-linguistic axiom that is composed of three elements such as associativity as opposed to one axiom that is generated in the classical theory. The set theoretic axioms double or quadruple because the basic equivalences of the classical theory break down in fuzzy theory. In this setting, we become aware that first, these new axioms hold as a matter of degree, and secondly there is an upper and lower limit with which they hold as a matter of degree.     

Fuzzy evolutionary computing

 This paper elaborates on a new paradigm of computing embracing fuzzy sets and evolutionary methods (specially genetic algorithms). We discuss conceptual and algorithmic enhancements to the individual methods. Fuzzy sets are geared toward granular information processing. Evolutionary computing are population-based optimization methods. In this way, as being components of any hybrid structure, they naturally complement each other. The study reveals a number of representative symbiotic links between fuzzy and genetic computing and provides with relevant illustrative examples.