Fuzzy Logic: Overviews

A literature review on current approaches and applications of fuzzy expert systems

arXiv.org Artificial Intelligence

The main purposes of this study are to distinguish the trends of research in publication exits for the utilisations of the fuzzy expert and knowledge-based systems that is done based on the classification of studies in the last decade. The present investigation covers 60 articles from related scholastic journals, International conference proceedings and some major literature review papers. Our outcomes reveal an upward trend in the up-to-date publications number, that is evidence of growing notoriety on the various applications of fuzzy expert systems. This raise in the reports is mainly in the medical neuro-fuzzy and fuzzy expert systems. Moreover, another most critical observation is that many modern industrial applications are extended, employing knowledge-based systems by extracting the experts' knowledge.

Kernels on fuzzy sets: an overview

arXiv.org Artificial Intelligence

This paper introduces the concept of kernels on fuzzy sets as a similarity measure for $[0,1]$-valued functions, a.k.a. \emph{membership functions of fuzzy sets}. We defined the following classes of kernels: the cross product, the intersection, the non-singleton and the distance-based kernels on fuzzy sets. Applicability of those kernels are on machine learning and data science tasks where uncertainty in data has an ontic or epistemistic interpretation.

Sensitivity study of ANFIS model parameters to predict the pressure gradient with combined input and outputs hydrodynamics parameters in the bubble column reactor

arXiv.org Artificial Intelligence

Intelligent algorithms are recently used in the optimization process in chemical engineering and application of multiphase flows such as bubbling flow. This overview of modeling can be a great replacement with complex numerical methods or very time-consuming and disruptive measurement experimental process. In this study, we develop the adaptive network-based fuzzy inference system (ANFIS) method for mapping inputs and outputs together and understand the behavior of the fluid flow from other output parameters of the bubble column reactor. Neural cells can fully learn the process in their memory and after the training stage, the fuzzy structure predicts the multiphase flow data. Four inputs such as x coordinate, y coordinate, z coordinate, and air superficial velocity and one output such as pressure gradient are considered in the learning process of the ANFIS method. During the learning process, the different number of the membership function, type of membership functions and the number of inputs are examined to achieve the intelligent algorithm with high accuracy. The results show that as the number of inputs increases the accuracy of the ANFIS method rises up to R^2>0.99 almost for all cases, while the increment in the number of rules has a effect on the intelligence of artificial algorithm. This finding shows that the density of neural objects or higher input parameters enables the moded for better understanding. We also proposed a new evaluation of data in the bubble column reactor by mapping inputs and outputs and shuffle all parameters together to understand the behaviour of the multiphase flow as a function of either inputs or outputs. This new process of mapping inputs and outputs data provides a framework to fully understand the flow in the fluid domain in a short time of fuzzy structure calculation.

Resilient Supplier Selection in Logistic 4.0: An integrated approach of Fuzzy Multi-Attribute Decision Making (F-MADM) and Multi-choice Goal Programming (MCGP) with Heterogeneous

arXiv.org Artificial Intelligence

Supplier selection problem has gained extensive attention in the prior studies. However, research based on Fuzzy Multi-Attribute Decision Making (F-MADM) approach in ranking resilient suppliers in logistic 4.0 is still in its infancy. Traditional MADM approach fails to address the resilient supplier selection problem in logistic 4.0 primarily because of the large amount of data concerning some attributes that are quantitative, yet difficult to process while making decisions. Besides, some qualitative attributes prevalent in logistic 4.0 entail imprecise perceptual or judgmental decision relevant information, and are substantially different than those considered in traditional suppler selection problems. This study, for the first time, develops a Decision Support System (DSS) that will help the decision maker to incorporate and process such imprecise heterogeneous data in a unified framework to rank a set of resilient suppliers in the logistic 4.0 environment. The proposed framework induces a triangular fuzzy number from large-scale temporal data using probability-possibility consistency principle. Large number of non-temporal data presented graphically are computed by extracting granular information that are imprecise in nature. Fuzzy linguistic variables are used to map the qualitative attributes. Finally, fuzzy based TOPSIS method is adopted to generate the ranking score of alternative suppliers. These ranking scores are used as input in a Multi-Choice Goal Programming (MCGP) model to determine optimal order allocation for respective suppliers. Finally, a sensitivity analysis assesses how the Cost versus Resilience Index (SCRI) changes when differential priorities are set for respective cost and resilience attributes.

On the Functional Equivalence of TSK Fuzzy Systems to Neural Networks, Mixture of Experts, CART, and Stacking Ensemble Regression

arXiv.org Artificial Intelligence

Fuzzy systems have achieved great success in numerous applications. However, there are still many challenges in designing an optimal fuzzy system, e.g., how to efficiently train its parameters, how to improve its performance without adding too many parameters, how to balance the trade-off between cooperations and competitions among the rules, how to overcome the curse of dimensionality, etc. Literature has shown that by making appropriate connections between fuzzy systems and other machine learning approaches, good practices from other domains may be used to improve the fuzzy systems, and vice versa. This paper gives an overview on the functional equivalence between Takagi-Sugeno-Kang fuzzy systems and four classic machine learning approaches -- neural networks, mixture of experts, classification and regression trees, and stacking ensemble regression -- for regression problems. We also point out some promising new research directions, inspired by the functional equivalence, that could lead to solutions to the aforementioned problems. To our knowledge, this is so far the most comprehensive overview on the connections between fuzzy systems and other popular machine learning approaches, and hopefully will stimulate more hybridization between different machine learning algorithms.

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.

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.

Toward Human-Understandable, Explainable AI

IEEE Computer

Recent increases in computing power, coupled with rapid growth in the availability and quantity of data have rekindled our interest in the theory and applications of artificial intelligence (AI). However, for AI to be confidently rolled out by industries and governments, users want greater transparency through explainable AI (XAI) systems. The author introduces XAI concepts, and gives an overview of areas in need of further exploration--such as type-2 fuzzy logic systems--to ensure such systems can be fully understood and analyzed by the lay user.

Elliptical Distributions-Based Weights-Determining Method for OWA Operators

arXiv.org Artificial Intelligence

The ordered weighted averaging (OWA) operators play a crucial role in aggregating multiple criteria evaluations into an overall assessment supporting the decision makers' choice. One key point steps is to determine the associated weights. In this paper, we first briefly review some main methods for determining the weights by using distribution functions. Then we propose a new approach for determining OWA weights by using the RIM quantifier. Motivated by the idea of normal distribution-based method to determine the OWA weights, we develop a method based on elliptical distributions for determining the OWA weights, and some of its desirable properties have been investigated.