Fuzzy Logic


Decision-making and Fuzzy Temporal Logic

arXiv.org Artificial Intelligence

This paper shows that the fuzzy temporal logic can model figures of thought to describe decision-making behaviors. In order to exemplify, some economic behaviors observed experimentally were modeled from problems of choice containing time, uncertainty and fuzziness. Related to time preference, it is noted that the subadditive discounting is mandatory in positive rewards situations and, consequently, results in the magnitude effect and time effect, where the last has a stronger discounting for earlier delay periods (as in, one hour, one day), but a weaker discounting for longer delay periods (for instance, six months, one year, ten years). In addition, it is possible to explain the preference reversal (change of preference when two rewards proposed on different dates are shifted in the time). Related to the Prospect Theory, it is shown that the risk seeking and the risk aversion are magnitude dependents, where the risk seeking may disappear when the values to be lost are very high.


Bounded Fuzzy Possibilistic Method

arXiv.org Machine Learning

This paper introduces Bounded Fuzzy Possibilistic Method (BFPM) by addressing several issues that previous clustering/classification methods have not considered. In fuzzy clustering, object's membership values should sum to 1. Hence, any object may obtain full membership in at most one cluster. Possibilistic clustering methods remove this restriction. However, BFPM differs from previous fuzzy and possibilistic clustering approaches by allowing the membership function to take larger values with respect to all clusters. Furthermore, in BFPM, a data object can have full membership in multiple clusters or even in all clusters. BFPM relaxes the boundary conditions (restrictions) in membership assignment. The proposed methodology satisfies the necessity of obtaining full memberships and overcomes the issues with conventional methods on dealing with overlapping. Analysing the objects' movements from their own cluster to another (mutation) is also proposed in this paper. BFPM has been applied in different domains in geometry, set theory, anomaly detection, risk management, diagnosis diseases, and other disciplines. Validity and comparison indexes have been also used to evaluate the accuracy of BFPM. BFPM has been evaluated in terms of accuracy, fuzzification constant (different norms), objects' movement analysis, and covering diversity. The promising results prove the importance of considering the proposed methodology in learning methods to track the behaviour of data objects, in addition to obtain accurate results.


Distributional reinforcement learning with linear function approximation

arXiv.org Machine Learning

Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited. One exception is Rowland et al. (2018)'s analysis of the C51 algorithm in terms of the Cram\'er distance, but their results only apply to the tabular setting and ignore C51's use of a softmax to produce normalized distributions. In this paper we adapt the Cram\'er distance to deal with arbitrary vectors. From it we derive a new distributional algorithm which is fully Cram\'er-based and can be combined to linear function approximation, with formal guarantees in the context of policy evaluation. In allowing the model's prediction to be any real vector, we lose the probabilistic interpretation behind the method, but otherwise maintain the appealing properties of distributional approaches. To the best of our knowledge, ours is the first proof of convergence of a distributional algorithm combined with function approximation. Perhaps surprisingly, our results provide evidence that Cram\'er-based distributional methods may perform worse than directly approximating the value function.


Finite-Sample Analysis for SARSA and Q-Learning with Linear Function Approximation

arXiv.org Machine Learning

Though the convergence of major reinforcement learning algorithms has been extensively studied, the finite-sample analysis to further characterize the convergence rate in terms of the sample complexity for problems with continuous state space is still very limited. Such a type of analysis is especially challenging for algorithms with dynamically changing learning policies and under non-i.i.d.\ sampled data. In this paper, we present the first finite-sample analysis for the SARSA algorithm and its minimax variant (for zero-sum Markov games), with a single sample path and linear function approximation. To establish our results, we develop a novel technique to bound the gradient bias for dynamically changing learning policies, which can be of independent interest. We further provide finite-sample bounds for Q-learning and its minimax variant. Comparison of our result with the existing finite-sample bound indicates that linear function approximation achieves order-level lower sample complexity than the nearest neighbor approach.


The FA Quantifier Fuzzification Mechanism: analysis of convergence and efficient implementations

arXiv.org Artificial Intelligence

The fuzzy quantification model FA has been identified as one of the best behaved quantification models in several revisions of the field of fuzzy quantification. This model is, to our knowledge, the unique one fulfilling the strict Determiner Fuzzification Scheme axiomatic framework that does not induce the standard min and max operators. The main contribution of this paper is the proof of a convergence result that links this quantification model with the Zadeh's model when the size of the input sets tends to infinite. The convergence proof is, in any case, more general than the convergence to the Zadeh's model, being applicable to any quantitative quantifier. In addition, recent revisions papers have presented some doubts about the existence of suitable computational implementations to evaluate the FA model in practical applications. In order to prove that this model is not only a theoretical approach, we show exact algorithmic solutions for the most common linguistic quantifiers as well as an approximate implementation by means of Monte Carlo. Additionally, we will also give a general overview of the main properties fulfilled by the FA model, as a single compendium integrating the whole set of properties fulfilled by it has not been previously published.


OWA aggregation of multi-criteria with mixed uncertain fuzzy satisfactions

arXiv.org Artificial Intelligence

We apply the Ordered Weighted Averaging (OWA) operator in multi-criteria decision-making. To satisfy different kinds of uncertainty, measure based dominance has been presented to gain the order of different criterion. However, this idea has not been applied in fuzzy system until now. In this paper, we focus on the situation where the linguistic satisfactions are fuzzy measures instead of the exact values. We review the concept of OWA operator and discuss the order mechanism of fuzzy number. Then we combine with measure-based dominance to give an overall score of each alternatives. An example is illustrated to show the whole procedure.


An Evolutionary Hierarchical Interval Type-2 Fuzzy Knowledge Representation System (EHIT2FKRS) for Travel Route Assignment

arXiv.org Artificial Intelligence

Urban Traffic Networks are characterized by high dynamics of traffic flow and increased travel time, including waiting times. This leads to more complex road traffic management. The present research paper suggests an innovative advanced traffic management system based on Hierarchical Interval Type-2 Fuzzy Logic model optimized by the Particle Swarm Optimization (PSO) method. The aim of designing this system is to perform dynamic route assignment to relieve traffic congestion and limit the unexpected fluctuation effects on traffic flow. The suggested system is executed and simulated using SUMO, a well-known microscopic traffic simulator. For the present study, we have tested four large and heterogeneous metropolitan areas located in the cities of Sfax, Luxembourg, Bologna and Cologne. The experimental results proved the effectiveness of learning the Hierarchical Interval type-2 Fuzzy logic using real time particle swarm optimization technique PSO to accomplish multiobjective optimality regarding two criteria: number of vehicles that reach their destination and average travel time. The obtained results are encouraging, confirming the efficiency of the proposed system.


Regularized Fuzzy Neural Networks to Aid Effort Forecasting in the Construction and Software Development

arXiv.org Artificial Intelligence

Predicting the time to build software is a very complex task for software engineering managers. There are complex factors that can directly interfere with the productivity of the development team. Factors directly related to the complexity of the system to be developed drastically change the time necessary for the completion of the works with the software factories. This work proposes the use of a hybrid system based on artificial neural networks and fuzzy systems to assist in the construction of an expert system based on rules to support in the prediction of hours destined to the development of software according to the complexity of the elements present in the same. The set of fuzzy rules obtained by the system helps the management and control of software development by providing a base of interpretable estimates based on fuzzy rules. The model was submitted to tests on a real database, and its results were promissory in the construction of an aid mechanism in the predictability of the software construction.


Fuzzy expert system for prediction of prostate cancer

arXiv.org Artificial Intelligence

A fuzzy expert system (FES) for the prediction of prostate cancer (PC) is prescribed in this article. Age, prostate-specific antigen (PSA), prostate volume (PV) and $\%$ Free PSA ($\%$FPSA) are fed as inputs into the FES and prostate cancer risk (PCR) is obtained as the output. Using knowledge based rules in Mamdani type inference method the output is calculated. If PCR $\ge 50\%$, then the patient shall be advised to go for a biopsy test for confirmation. The efficacy of the designed FES is tested against a clinical data set. The true prediction for all the patients turns out to be $68.91\%$ whereas only for positive biopsy cases it rises to $73.77\%$. This simple yet effective FES can be used as supportive tool for decision making in medical diagnosis.


Dialectical Rough Sets, Parthood and Figures of Opposition-1

arXiv.org Artificial Intelligence

In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and variants were recently introduced by the present author as an optimal framework for anti-chain based algebraic semantics of general rough sets and the inverse problem. In the framework, various sub-types of crisp and non-crisp objects are identifiable that may be missed in more restrictive formalism. This is also because in the latter cases concepts of complementation and negation are taken for granted - while in reality they have a complicated dialectical basis. This motivates a general approach to dialectical rough sets building on previous work of the present author and figures of opposition. In this paper dialectical rough logics are invented from a semantic perspective, a concept of dialectical predicates is formalised, connection with dialetheias and glutty negation are established, parthood analyzed and studied from the viewpoint of classical and dialectical figures of opposition by the present author. Her methods become more geometrical and encompass parthood as a primary relation (as opposed to roughly equivalent objects) for algebraic semantics.