67,758 research outputs found

    A New Penta-valued Logic Based Knowledge Representation

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    In this paper a knowledge representation model are proposed, FP5, which combine the ideas from fuzzy sets and penta-valued logic. FP5 represents imprecise properties whose accomplished degree is undefined, contradictory or indeterminate for some objects. Basic operations of conjunction, disjunction and negation are introduced. Relations to other representation models like fuzzy sets, intuitionistic, paraconsistent and bipolar fuzzy sets are discussed.Comment: The 12th International Conference Information Processing and Management of Uncertainty in Knowledge-Based Systems, June 22-27, 2008, Malaga, Spai

    Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets

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    Similarity measures provide one of the core tools that enable reasoning about fuzzy sets. While many types of similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we introduce a general method for extending existing interval type-2 similarity measures to similarity measures for general type-2 fuzzy sets. Specifically, we show how similarity measures for interval type-2 fuzzy sets can be employed in conjunction with the zSlices based general type-2 representation for fuzzy sets to provide measures of similarity which preserve all the common properties (i.e. reflexivity, symmetry, transitivity and overlapping) of the original interval type-2 similarity measure. We demonstrate examples of such extended fuzzy measures and provide comparisons between (different types of) interval and general type-2 fuzzy measures.Comment: International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013

    New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh\u27s Logical Operators

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    In this paper , we have defined First Zadeh’s implication , First Zadeh’s intuitionistic fuzzy conjunction and intuitionistic fuzzy disjunction of two intuitionistic fuzzy soft sets and some their basic properties are studied with proofs and examples

    Lukasiewicz Fuzzy Implication Operator on Pythagorean Fuzzy Tautological Matrices

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    In this paper, introduced Pythagorean fuzzy tautologial matrices and Pythagorean fuzzy cotautological matrices and some properties of Lukasiwicz implication operator over Pythagorean fuzzy tautologial matrices and Pythagorean fuzzy cotautological matrices are discussed. Also discussed the relation between implication with Lukasiewicz disjunction and conjunction operations of PFCMs and PFCTMs

    INITIAL APPLICATIONS OF FUZZY SET PROCEDURES FOR ESTIMATION OF EXPORT BASE EMPLOYMENT

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    Current export base methods that calculate basic and non-basic employment are too restrictive because they fail to account for uncertainty involved in the process. This paper shows the assignment of industries as either basic or non-basic by the location quotient procedure does not consistently represent the data for Nevada counties. Using fuzzy set procedures and membership functions in conjunction with the location quotient allow more flexibility in terms of matching the data for each industry in the region of interest. Using fuzzy set procedures we determine the proportion of employment that is basic and non-basic in nine non-governmental industries.Labor and Human Capital,

    Fuzzy logic: An analysis of logical connectives and their characterizations

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    The focus of this thesis is to determine exactly which functions serve as appropriate fuzzy negation, conjunction and disjunction functions. To this end, the first chapter serves as motivation for why fuzzy logic is needed, and includes an original demonstration of the inadequacy of many valued logics to resolve the sorites paradox. Chapter 2 serves as an introduction to fuzzy sets and logic. The canonical fuzzy set of tall men is examined as a motivating example, and the chapter concludes with a discussion of membership functions. Four desirable conditions of the negation function are given in Chapter 3, but it is shown that they are not independent. It suffices to take two of these conditions, monotonicity and involutiveness, as negation axioms. Two characterization proofs are given, one with an increasing generator and the other with a decreasing generator. An example of a general class of negation functions is studied, along with their corresponding increasing and decreasing generators. Chapters 4 and 5 provide an analysis of fuzzy conjunction and disjunction functions, respectively. Five axioms for each are given: boundary conditions, commutativity, associativity, monotone non-decreasing, and continuity. Yager\u27s class of conjunction and disjunction functions are each shown to satisfy all five of these axioms. The additional assumption of strict monotonicity is added to obtain pseudo-characterizations analogous to the characterizations of the negation function. Finally, it is shown that although the min function is a conjunction function, it does not have a decreasing or an increasing generator. Similar results are obtained in Chapter 5 for disjunction functions, with a concluding theorem that the max function has no generators. The interactions of these three connectives is the content of Chapter 6. In this chapter, negation, conjunction, and disjunction triples are considered that satisfy both of DeMorgan\u27s laws. Distributivity of conjunction and disjunction over each other is examined. It is then shown that the only conjunction and disjunction pair that satisfies the distributivity axiom is the min, max pair. In conclusion, Chapter 7 discusses why having unique functions serve as conjunction and disjunction is desirable. It also contains a brief discussion of the implication connective and some areas for further investigation

    Learning and tuning fuzzy logic controllers through reinforcements

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    A new method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system is presented. In particular, our Generalized Approximate Reasoning-based Intelligent Control (GARIC) architecture: (1) learns and tunes a fuzzy logic controller even when only weak reinforcements, such as a binary failure signal, is available; (2) introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; (3) introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and (4) learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward network, which can then adaptively improve performance by using gradient descent methods. We extend the AHC algorithm of Barto, Sutton, and Anderson to include the prior control knowledge of human operators. The GARIC architecture is applied to a cart-pole balancing system and has demonstrated significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing

    Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

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    Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing
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