36,138 research outputs found
Employing an Enhanced Interval Approach to encode words into Linear General Type-2 fuzzy sets for Computing With Words applications
In 1996, Zadeh coined Computing With Words (CWWs) to be a methodology in which words are used instead of numbers for computing and reasoning. One of the main challenges which faced the CWWs paradigm has been modelling words adequately. Mendel has pointed out that the CWWs paradigm should employ type-2 fuzzy logic to model words. This paper proposes employing an Enhanced Interval Approach (EIA) to create Linear General Type-2 (LGT2) fuzzy sets from Interval Type-2 (IT2) fuzzy sets to encode words for CWWs applications. We have performed experiments on 18 words belonging to 3 different linguistic variables (having 6 linguistic terms each). Interval data has been collected from 17 subjects and 18 linguistic terms have been modeled with IT2 fuzzy sets using EIA. The proposed conversion approach uses several key points within the parameters of IT2 fuzzy sets to redesign the linguistic variable using LGT2 fuzzy sets. Both IT2 and LGT2 fuzzy sets have been evaluated within a CWWs Framework, which aims to mimic the ability of humans to communicate and manipulate perceptions via words. The comparison results show that LGT2 fuzzy sets can be better than IT2 fuzzy sets in mimicking human reasoning as well as learning and adaptation since the progressive Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE) values for LGT2 based CWWs Framework converge faster and are lower than those for IT2 based CWWs Framework
Interval type-2 Atanassov-intuitionistic fuzzy logic for uncertainty modelling
This thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark a shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzzy set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess this thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1.
In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzz set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess the viability and efficacy of the developed framework, the possibilities of the optimisation of the parameters of this class of fuzzy systems are rigorously examined.
First, the parameters of the developed model are optimised using one of the most popular fuzzy logic optimisation algorithms such as gradient descent (first-order derivative) algorithm and evaluated on publicly available benchmark datasets from diverse domains and characteristics. It is shown that the new interval type-2 Atanassov intuitionistic fuzzy logic system is able to handle uncertainty well through the minimisation of the error of the system compared with other approaches on the same problem instances and performance criteria.
Secondly, the parameters of the proposed framework are optimised using a decoupledextended Kalman filter (second-order derivative) algorithm in order to address the shortcomings of the first-order gradient descent method. It is shown statistically that the performance of this new framework with fuzzy membership and non-membership functions is significantly better than the classical interval type-2 fuzzy logic systems which have only the fuzzy membership functions, and its type-1 counterpart which are specified by single membership and non-membership functions.
The model is also assessed using a hybrid learning of decoupled extended Kalman filter and gradient descent methods. The proposed framework with hybrid learning algorithm is evaluated by comparing it with existing approaches reported in the literature on the same problem instances and performance metrics. The simulation results have demonstrated the potential benefits of using the proposed framework in uncertainty modelling. In the overall, the fusion of these two concepts (interval type-2 fuzzy logic system and Atanassov intuitionistic fuzzy logic system) provides a synergistic capability in dealing with imprecise and vague information
Interval type-2 Atanassov-intuitionistic fuzzy logic for uncertainty modelling
This thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark a shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzzy set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess this thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1.
In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzz set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess the viability and efficacy of the developed framework, the possibilities of the optimisation of the parameters of this class of fuzzy systems are rigorously examined.
First, the parameters of the developed model are optimised using one of the most popular fuzzy logic optimisation algorithms such as gradient descent (first-order derivative) algorithm and evaluated on publicly available benchmark datasets from diverse domains and characteristics. It is shown that the new interval type-2 Atanassov intuitionistic fuzzy logic system is able to handle uncertainty well through the minimisation of the error of the system compared with other approaches on the same problem instances and performance criteria.
Secondly, the parameters of the proposed framework are optimised using a decoupledextended Kalman filter (second-order derivative) algorithm in order to address the shortcomings of the first-order gradient descent method. It is shown statistically that the performance of this new framework with fuzzy membership and non-membership functions is significantly better than the classical interval type-2 fuzzy logic systems which have only the fuzzy membership functions, and its type-1 counterpart which are specified by single membership and non-membership functions.
The model is also assessed using a hybrid learning of decoupled extended Kalman filter and gradient descent methods. The proposed framework with hybrid learning algorithm is evaluated by comparing it with existing approaches reported in the literature on the same problem instances and performance metrics. The simulation results have demonstrated the potential benefits of using the proposed framework in uncertainty modelling. In the overall, the fusion of these two concepts (interval type-2 fuzzy logic system and Atanassov intuitionistic fuzzy logic system) provides a synergistic capability in dealing with imprecise and vague information
Fuzzy natural language similarity measures through computing with words
A vibrant area of research is the understanding of human language by machines to engage in
conversation with humans to achieve set goals. Human language is naturally fuzzy by nature,
with words meaning different things to different people, depending on the context. Fuzzy
words are words with a subjective meaning, typically used in everyday human natural
language dialogue and often ambiguous and vague in meaning and dependent on an
individual’s perception. Fuzzy Sentence Similarity Measures (FSSM) are algorithms that can
compare two or more short texts which contain fuzzy words and return a numeric measure
of similarity of meaning between them.
The motivation for this research is to create a new FSSM called FUSE (FUzzy Similarity
mEasure). FUSE is an ontology-based similarity measure that uses Interval Type-2 Fuzzy Sets
to model relationships between categories of human perception-based words. Four versions
of FUSE (FUSE_1.0 – FUSE_4.0) have been developed, investigating the presence of linguistic
hedges, the expansion of fuzzy categories and their use in natural language, incorporating
logical operators such as ‘not’ and the introduction of the fuzzy influence factor.
FUSE has been compared to several state-of-the-art, traditional semantic similarity measures
(SSM’s) which do not consider the presence of fuzzy words. FUSE has also been compared to
the only published FSSM, FAST (Fuzzy Algorithm for Similarity Testing), which has a limited
dictionary of fuzzy words and uses Type-1 Fuzzy Sets to model relationships between
categories of human perception-based words. Results have shown FUSE is able to improve on
the limitations of traditional SSM’s and the FAST algorithm by achieving a higher correlation
with the average human rating (AHR) compared to traditional SSM’s and FAST using several
published and gold-standard datasets.
To validate FUSE, in the context of a real-world application, versions of the algorithm were
incorporated into a simple Question & Answer (Q&A) dialogue system (DS), referred to as
FUSION, to evaluate the improvement of natural language understanding. FUSION was tested
on two different scenarios using human participants and results compared to a traditional
SSM known as STASIS. Results of the DS experiments showed a True rating of 88.65%
compared to STASIS with an average True rating of 61.36%. Results showed that the FUSE
algorithm can be used within real world applications and evaluation of the DS showed an
improvement of natural language understanding, allowing semantic similarity to be
calculated more accurately from natural user responses.
The key contributions of this work can be summarised as follows: The development of a new
methodology to model fuzzy words using Interval Type-2 fuzzy sets; leading to the creation of
a fuzzy dictionary for nine fuzzy categories, a useful resource which can be used by other
researchers in the field of natural language processing and Computing with Words with other
fuzzy applications such as semantic clustering. The development of a FSSM known as FUSE,
which was expanded over four versions, investigating the incorporation of linguistic hedges,
the expansion of fuzzy categories and their use in natural language, inclusion of logical
operators such as ‘not’ and the introduction of the fuzzy influence factor. Integration of the
FUSE algorithm into a simple Q&A DS referred to as FUSION demonstrated that FSSM can be
used in a real-world practical implementation, therefore making FUSE and its fuzzy dictionary
generalisable to other applications
Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets
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
On the incorporation of interval-valued fuzzy sets into the Bousi-Prolog system: declarative semantics, implementation and applications
In this paper we analyse the benefits of incorporating interval-valued fuzzy
sets into the Bousi-Prolog system. A syntax, declarative semantics and im-
plementation for this extension is presented and formalised. We show, by using
potential applications, that fuzzy logic programming frameworks enhanced with
them can correctly work together with lexical resources and ontologies in order
to improve their capabilities for knowledge representation and reasoning
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