Fuzzy Truth Values Research Articles

Truth values on generalizations of some commutative fuzzy structures

Hájek introduced the logic BL vt enriching the logic BL by a unary connective vt which is a formalization of Zadeh's fuzzy truth value “very true”. BL vt -algebras, i.e. BL -algebras with unary operations, called vt -operators, which are among others subdiagonal, are an algebraic counterpart of BL vt . Residuated lattice ordered monoids ( R ℓ -monoids) are common generalizations of BL -algebras and Heyting algebras. In the paper, we study algebraic properties of R ℓ vt -algebras (and consequently of BL vt -algebras) and of those that are enriched by derived superdiagonal operators which in the case of MV-algebras are the duals to vt -operators.

E-Commerce and supply chains: Modelling of dynamics through fuzzy enhanced high level petri net

Although information plays a major role in effective functioning of supply chain networks (SCNs), studies that deal specifically with the dynamics of supply chains are few. This problem is relatively new since fast communications and the means to employ it for effective management of supply chains did not exist till recently. In order to provide a vehicle for dynamic modelling and analysis of supply chain operations in vague and uncertain environments, we propose a fuzzy enhanced high level petri net (FEHLPN) model. The proposed model captures the capability of petri nets for graphical and analytical representation of dynamic SCNs with the management of uncertain information provided by fuzzy logic. The dynamics associated with two production planning and control policies are modelled, viz. make-to-stock and assemble-to-order in vague and ambiguous situations in electronic commerce environment. A fuzzy set and fuzzy truth-values are attached to an uncertain fuzzy token to model imprecision and uncertainty. The proposed FEHLPN incorporates essential aspects of rule-based systems, such as conservation of facts, refraction, and closed-world assumption.

The algebra of fuzzy truth values

The purpose of this paper is to give a straightforward mathematical treatment of algebras of fuzzy truth values for type-2 fuzzy sets.

Properties of Interval Truth Values with Certainty Factor

Until now some truth values in fuzzy logic were suggested such as numerical truth value, interval truth value, fuzzy truth value and etc. Fuzzy truth value is considered as the most generalized truth values in fuzzy logic. Truth values except fuzzy truth value were suggested to clarify the properties of fuzzy truth values. However it is not sufficient to clarify the properties of fuzzy truth values from the properties of other truth values, because fuzzy truth value may not be convex or normal. On the other hand, the other truth values do have to be convex and normal. In this paper, we consider subnormal truth value and propose interval truth value with certainty factor. Then, we clarify the properties of interval truth value with certainty factor.

On very true

The fuzzy truth value “very true” is formalized as a unary connective (hedge). A complete axiomatization is presented.

HIGH-LEVEL FUZZY PETRI NETS AS A BASIS FOR MANAGING SYMBOLIC AND NUMERICAL INFORMATION

The focus of this paper is on an attempt towards a unified formalism to manage both symbolic and numerical information based on high-level fuzzy Petri nets (HLFPN). Fuzzy functions, fuzzy reasoning, and fuzzy neural networks are integrated in HLFPN In HLFPN model, a fuzzy place carries information to describe the fuzzy variable and the fuzzy set of a fuzzy condition. An arc is labeled with a fuzzy weight to represent the strength of connection between places and transitions. A fuzzy set and a fuzzy truth-value are attached to an uncertain fuzzy token to model imprecision and uncertainty. We have identified six types of uncertain transition: calculation transitions to compute functions with uncertain fuzzy inputs; inference transitions to perform fuzzy reasoning; neuron transitions to execute computations in neural networks; duplication transitions to duplicate an uncertain fuzzy token to several tokens carrying the same fuzzy sets and fuzzy truth values; aggregation transitions to combine several uncertain fuzzy tokens with the same fuzzy variable; and aggregation-duplication transitions to amalgamate aggregation transitions and duplication transitions. To guide the computation inside the HLFPN, an algorithm is developed and an example is used to illustrate the proposed approach.

Fuzzy types: a framework for handling uncertainty about types of objects

Like other kinds of information, types of objects in the real world are often found to be filled with uncertainty and/or partial truth. It may be due to either the vague nature of a type itself or to incomplete information in the process determining it even if the type is crisp, i.e., clearly defined. This paper proposes a framework to deal with uncertainty and/or partial truth in automated reasoning systems with taxonomic information, and in particular type hierarchies. A fuzzy type is formulated as a pair combining a basic type and a fuzzy truth-value, where a basic type can be crisp or vague (in the intuitive sense). A structure for a class of fuzzy truth-value lattices is proposed for this construction. The fuzzy subtype relation satisfying intuition is defined as a partial order between two fuzzy types. As an object may belong to more than one (fuzzy) type, conjunctive fuzzy types are introduced and their lattice properties are studied. Then, for reasoning with fuzzy types, a mismatching degree of one (conjunctive) fuzzy type to another is defined as the complement of the relative necessity degree of the former to the latter. It is proved that the defined fuzzy type mismatching degree has properties similar to those of fuzzy set mismatching degree, which allow a unified treatment of fuzzy types and fuzzy sets in reasoning. The framework provides a formal basis for development of order-sorted fuzzy logic systems.

A possibilistic-logic-based approach to integrating imprecise and uncertain information

A reasoning mechanism capable of dealing with imprecise and uncertain information is essential for expert systems. In this paper, we propose the use of truth-qualified fuzzy propositions as the representation of imprecise and uncertain information, where the fuzzy sets embody the intended meaning of imprecise information and the fuzzy truth values serve as the representation of uncertainty for its capability to express the possibility of the degree of truth of a fuzzy proposition. An inference mechanism for fuzzy propositions with fuzzy truth values is developed to serve as a bridge that brings together the possibilistic reasoning and fuzzy reasoning into a hybrid approach to reasoning under uncertainty and imprecision. There are three steps involved. First, the fuzzy rules and fuzzy facts with fuzzy truth values are transformed into a set of uncertain classical propositions with necessity and possibility measures. Second, a possibilistic reasoning called possibilistic entailment is performed on the set of uncertain classical propositions. Third, we reverse the process in the first step to synthesize all the classical sets obtained in the second step into a fuzzy set, and to compose necessity and possibility pairs to form a fuzzy truth value.

A FUZZY MEASURE FOR EXPLANATORY COHERENCE

In a series of articles, Paul Thagard has developed a connectionist's model for the evaluation of explanatory coherence for competing systems of hypotheses. He has successfully applied it to various examples from the history of science and common language reasoning. However, I will argue that his formalism does not adequately represent explanatory relations between more than two propositions. In this paper, I develop a generalization of Thagard's approach. It is not subject to the connectionist paradigm of neural nets, but is based on fuzzy logic: Explanatory coherence increases with the fuzzy truth value of the conjunction of explanans and explanandum and decreases with the value of the conjunction of explanans and the negation of the explanandum.

NECESSARY AND SUFFICIENT CONDITIONS FOR FUZZY TRUTH VALUES TO FORM A DE MORGAN ALGEBRA

Different fuzzy logics were shown to be particular cases of many kinds of algebras, such as Lukasiewicz algebra, Heyting algebra, de Morgan algebra, Kleene algebra, etc. In this paper, following the original definitions of fuzzy set operations proposed by L. A. Zadeh, we consider the set of all possible fuzzy truth values, the set which contains linguistic truth values such as "true", "very true", "more or less true", etc. We show that if we impose some conditions on fuzzy truth values, then the resulting set of fuzzy truth vlues with naturally defined logical operations forms a de Morgan algebra.

Requirements specification and analysis of digital systems using fuzzy and marked Petri nets

Fuzzy information often appears in the system requirements. Fuzzy Petri nets (FPN) are Petri nets in which certain fuzzy truth values are assigned to its transitions. We show how the FPN model can be used for formal specification and verification of digital systems. The consistent FPN model is actually a state machine, from which we can obtain a consistent marked Petri net (MPN) model. Based on the consistent MPN model, the hardware prototype at register transfer level can be easily induced by using the optimization rules. Finally, main results are presented in the form of three theorems and are supported by some experiments.

A semantics for Fuzzy Logic

We present a semantics for certain Fuzzy Logics of vagueness by identifying the fuzzy truth value an agent gives to a proposition with the number of independent arguments that the agent can muster in favour of that proposition.

Derivation of substructures from infrared band shapes by fuzzy logic and partial cross correlation functions

For the analysis of infrared spectroscopic bands and complex patterns partial cross correlation functions of a sample spectrum with reference spectra are calculated. The chosen ranges of the spectra are based on empirical knowledge of infrared spectrum structure correlations. The normalised maxima of the partial cross correlation functions are interpreted as fuzzy truth values and are combined by fuzzy logical operators. By application of that procedure larger common substructures will be derived from the reference spectra than by a maximum common substructure search based on the complete spectra.

From Intervals to Fuzzy Truth-Values: Adding Flexibility to Reasoning Under Uncertainty

In dealing with representing knowledge under uncertainty there is a sustained tendency to increase flexibility in order to avoid problems of inconsistency in the knowledge. Early uncertainty management systems dealt with single real values within a predefined range, soon interval valued approaches were proposed and more recently we have witnessed the introduction of fuzzy-interval valued approaches, i.e., possibility distributions and fuzzy truth-values. In this paper we describe these fuzzy set based approaches with an emphasis on the concept of fuzzy truth-value.

A generic ATMS

The main aim of this paper is to create a general truth maintenance system based on the De Kleer algorithm. This system (the ATMS) is to be designed so that it can be used in different propositional monotonic logic models of reasoning systems. The knowledge base system that will interact with it is described. Furthermore, we study the efficiency that transferring the ATMS to a logic with several truth values presupposes. Definitions and properties of the generic ATMS are particularized to interact both with a reasoning system based on multivalued logic specifically for the case of [0, 1 ]-valued logic and with a reasoning system based on fuzzy logic. The latter will be designed to reason with fuzzy truth values, although a parallel project might be followed using linguistic labels directly.

A fuzzy reasoning approach for rule-based systems based on fuzzy logics

This paper presents a weighted fuzzy reasoning algorithm for rule-based systems based on weighted fuzzy logics. The proposed algorithm allows the truth values of the conditions appearing in the antecedent portions of the rules, the certainty factors of the rules, and the weights of the conditions appearing in the antecedent portions of the rules to be represented by trapezoidal fuzzy numbers. Given the fuzzy truth values of some conditions, the algorithm can perform weighted fuzzy reasoning to evaluate the fuzzy truth values of other conditions automatically.

A measurement-theoretic analysis of the fuzzy logic model of perception.

The fuzzy logic model of perception (FLMP) is analyzed from a measurement-theoretic perspective. FLMP has an impressive history of fitting factorial data, suggesting that its probabilistic form is valid. The authors raise questions about the underlying processing assumptions of FLMP. Although FLMP parameters are interpreted as fuzzy logic truth values, the authors demonstrate that for several factorial designs widely used in choice experiments, most desirable fuzzy truth value properties fail to hold under permissible rescalings, suggesting that the fuzzy logic interpretation may be unwarranted. The authors show that FLMP's choice rule is equivalent to a version of G. Rasch's (1960) item response theory model, and the nature of FLMP measurement scales is transparent when stated in this form. Statistical inference theory exists for the Rasch model and its equivalent forms. In fact, FLMP can be reparameterized as a simple 2-category logit model, thereby facilitating interpretation of its measurement scales and allowing access to commercially available software for performing statistical inference.

A new approach to inference in approximate reasoning

Abstract We introduce a new approach to inference in approximate reasoning based on truth value restriction. The degree to which the actual given value A of a variable X agrees with the antecedent value B in a production “If X is B then Y is C ” is represented as a fuzzy subset of a truth space. We introduce a new form of implication based on the exponential operation. A new compatibility relation based on the input value A and the antecedent value B is defined. A fuzzy truth value true derived from the antecedent value B is also defined. It is shown that by mapping this compatibility relation into the truth space, a fuzzy truth value is generated which produces an exponential family of the fuzzy truth value true . We show that the inferred consequent can be generated from this truth value. Theoretical results showing the validity of this method to (1) chain rules consisting of several single fuzzy conditional propositions, and (2) conjunctive fuzzy conditional propositions, are also presented. Theoretical and simulation results demonstrate that our method is superior to the existing methods when intuitively correct responses are required.

Fuzzy values in fuzzy logic

One of the main features of Fuzzy Logic is its capability to deal with the concept of compatibility between two propositions, in such a way that the inference process modeled through the Compositional Rule of Inference is independent from the particular possibility distributions involved. It is in this context that the compatibility functions can be considered as fuzzy truth values, labels or qualifications, playing the same role as the values true and false play in the Classical Logic, where the meaning of propositions is nothing but its truth value. In this article we consider a restricted family of labels having the following desirable properties: (a) easy parametric representation, (b) easy semantic interpretation, (c) to allow a gradation in the family according to the modifications performed by each label, and (d) to be closed under inference processes (FR-functions), and also under some suitable and meaningful operations between them.

Verification, Testing and Validation of Rule-Based Expert Systems

Expert systems (ES) are used for applications in automatic control requiring high reliability. A failure in such systems can cause a great disaster. We give an overview of validation, verification, and testing methods that can be used to improve ES reliability. The test data generation for rule-based ES is investigated in detail. The statement and contribution adequacy criteria for analysing and testing ES are introduced. These criteria may be applied to different types of rule-based expert systems. The problems offinding test sets for ES without uncertainties, for ES using one uncertainty measure, and for ES allowing fuzzy truth values are considered. Several classes of ES with polynomial static analysis and test data generation complexity are characterized.