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

On the Choice of Similarity Measures for Type-2 Fuzzy Sets

Similarity measures are among the most common methods of comparing type-2 fuzzy sets and have been used in numerous applications. However, deciding how to measure similarity and choosing which existing measure to use can be difficult. Whilst some measures give results that highly correlate with each other, others give considerably different results. We evaluate all of the current similarity measures on type-2 fuzzy sets to discover which measures have common properties of similarity and, for those that do not, we discuss why the properties are different, demonstrate whether and what effect this has in applications, and discuss how a measure can avoid missing a property that is required. We analyse existing measures in the context of computing with words using a comprehensive collection of data-driven fuzzy sets. Specifically, we highlight and demonstrate how each method performs at clustering words of similar meaning

A Linear General Type-2 Fuzzy Logic Based Computing With Words Approach for Realising an Ambient Intelligent Platform for Cooking Recipes Recommendation

This paper addresses the need to enhance transparency in ambient intelligent environments by developing more natural ways of interaction, which allow the users to communicate easily with the hidden networked devices rather than embedding obtrusive tablets and computing equipment throughout their surroundings. Ambient intelligence vision aims to realize digital environments that adapt to users in a responsive, transparent, and context-aware manner in order to enhance users' comfort. It is, therefore, appropriate to employ the paradigm of “computing with words” (CWWs), which aims to mimic the ability of humans to communicate transparently and manipulate perceptions via words. One of the daily activities that would increase the comfort levels of the users (especially people with disabilities) is cooking and performing tasks in the kitchen. Existing approaches on food preparation, cooking, and recipe recommendation stress on healthy eating and balanced meal choices while providing limited personalization features through the use of intrusive user interfaces. Herein, we present an application, which transparently interacts with users based on a novel CWWs approach in order to predict the recipe's difficulty level and to recommend an appropriate recipe depending on the user's mood, appetite, and spare time. The proposed CWWs framework is based on linear general type-2 (LGT2) fuzzy sets, which linearly quantify the linguistic modifiers in the third dimension in order to better represent the user perceptions while avoiding the drawbacks of type-1 and interval type-2 fuzzy sets. The LGT2-based CWWs framework can learn from user experiences and adapt to them in order to establish more natural human-machine interaction. We have carried numerous real-world experiments with various users in the University of Essex intelligent flat. The comparison analysis between interval type-2 fuzzy sets and LGT2 fuzzy sets demonstrates up to 55.43% improvement when general type-2 fuzzy sets are used than when interval type-2 fuzzy sets are used instead. The quantitative and qualitative analysis both show the success of the system in providing a natural interaction with the users for recommending food recipes where the quantitative analysis shows the high statistical correlation between the system output and the users' feedback; the qualitative analysis presents social scienc

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

Information Security Risk Assessment Model Based on Computing with Words

The basis for company IT infrastructure security is information security risks assessment of IT services. The increased complexity, connectivity and rapid changes occurring in IT services make it impossible to apply traditional models of quantitative/qualitative risk assessment. Existing quantitative assessment models are time-consuming, at the same time, qualitative assessment models do not take into account the subjective expert assessments and the uncertainty of risk factors. This paper presents the new information security risk assessment model for IT services based on computing with words. The model methodology is based on OWASP risk rating methodology for web applications. To evaluate risk factors, it is proposed to use dictionary consisting of 16/32 granular terms (words). Problems of uncertainty in perceptual assessments of risk factors are taken into account using methods of the theory of discrete interval type-2 fuzzy sets and systems