Vector valued similarity measures for Atanassov's intuitionistic fuzzy sets

We present a new approach for defining similarity measures for Atanassov's intuitionistic fuzzy sets (AIFS), in which a similarity measure has two components indicating the similarity and hesitancy aspects. We justify that there are at least two facets of uncertainty of an AIFS, one of which is related to fuzziness while other is related to lack of knowledge or non-specificity. We propose a set of axioms and build families of similarity measures that avoid counterintuitive examples that are used to justify one similarity measure over another. We also investigate a relation to entropies of AIFS, and outline possible application of our method in decision making and image segmentation. © 2014 Elsevier Inc. All rights reserved.

Building fuzzy inference systems with similarity reasoning : NSGAII-based fuzzy rule selection and evidential functions

In our previous investigations, two Similarity Reasoning (SR)-based frameworks for tackling real-world problems have been proposed. In both frameworks, SR is used to deduce unknown fuzzy rules based on similarity of the given and unknown fuzzy rules for building a Fuzzy Inference System (FIS). In this paper, we further extend our previous findings by developing (1) a multi-objective evolutionary model for fuzzy rule selection; and (2) an evidential function to facilitate the use of both frameworks. The Non-Dominated Sorting Genetic Algorithms-p (NSGA-p) is adopted for fuzzy rule selection, in accordance with the Pareto optimal criterion. Besides that, two new evidential functions are developed, whereby given fuzzy rules are considered as evidence. Simulated and benchmark examples are included to demonstrate the applicability of these suggestions. Positive results were obtained.

A new similarity function for generalized trapezoidal fuzzy numbers

Numerous authors have proposed functions to quantify the degree of similarity between two fuzzy numbers using various descriptive parameters, such as the geometric distance, the distance between the centers of gravity or the perimeter. However, these similarity functions have drawback for specific situations. We propose a new similarity measure for generalized trapezoidal fuzzy numbers aimed at overcoming such drawbacks. This new measure accounts for the distance between the centers of gravity and the geometric distance but also incorporates a new term based on the shared area between the fuzzy numbers. The proposed measure is compared against other measures in the literature.

Searching for a consensus similarity function for generalized trapezoidal fuzzy numbers

There is controversy regarding the use of the similarity functions proposed in the literature to compare generalized trapezoidal fuzzy numbers since conflicting similarity values are sometimes output for the same pair of fuzzy numbers. In this paper we propose a similarity function aimed at establishing a consensus. It accounts for the different approaches of all the similarity functions. It also has better properties and can easily incorporate new parameters for future improvements. The analysis is carried out on the basis of a large and representative set of pairs of trapezoidal fuzzy numbers.

A fuzzy TOPSIS based multi criteria performance measurement model for lean supply chain

Increasing global competition, rapid technological changes, advances in manufacturing and information technology and discerning customers are forcing supply chains to adopt improvement practices that enable them to deliver high quality products at a lower cost and in a shorter period of time. A lean initiative is one of the most effective approaches toward achieving this goal. In the lean improvement process, it is critical to measure current and desired performance level in order to clearly evaluate the lean implementation efforts. Many attempts have tried to measure supply chain performance incorporating both quantitative and qualitative measures but failed to provide an effective method of measuring improvements in performances for dynamic lean supply chain situations. Therefore, the necessity of appropriate measurement of lean supply chain performance has become imperative. There are many lean tools available for supply chains; however, effectiveness of a lean tool depends on the type of the product and supply chain. One tool may be highly effective for a supply chain involved in high volume products but may not be effective for low volume products. There is currently no systematic methodology available for selecting appropriate lean strategies based on the type of supply chain and market strategy This thesis develops an effective method to measure the performance of supply chain consisting of both quantitative and qualitative metrics and investigates the effects of product types and lean tool selection on the supply chain performance Supply chain performance matrices and the effects of various lean tools over performance metrics mentioned in the SCOR framework have been investigated. A lean supply chain model based on the SCOR metric framework is then developed where non- lean and lean as well as quantitative and qualitative metrics are incorporated in appropriate metrics. The values of appropriate metrics are converted into triangular fuzzy numbers using similarity rules and heuristic methods. Data have been collected from an apparel manufacturing company for multiple supply chain products and then a fuzzy based method is applied to measure the performance improvements in supply chains. Using the fuzzy TOPSIS method, which chooses an optimum alternative to maximise similarities with positive ideal solutions and to minimise similarities with negative ideal solutions, the performances of lean and non- lean supply chain situations for three different apparel products have been evaluated. To address the research questions related to effective performance evaluation method and the effects of lean tools over different types of supply chains; a conceptual framework and two hypotheses are investigated. Empirical results show that implementation of lean tools have significant effects over performance improvements in terms of time, quality and flexibility. Fuzzy TOPSIS based method developed is able to integrate multiple supply chain matrices onto a single performance measure while lean supply chain model incorporates qualitative and quantitative metrics. It can therefore effectively measure the improvements for supply chain after implementing lean tools. It is demonstrated that product types involved in the supply chain and ability to select right lean tools have significant effect on lean supply chain performance. Future study can conduct multiple case studies in different contexts.

Fuzzy Approach to Rank Global Climate Models

Eleven coupled model intercomparison project 3 based global climate models are evaluated for the case study of Upper Malaprabha catchment, India for precipitation rate. Correlation coefficient, normalised root mean square deviation, and skill score are considered as performance indicators for evaluation in fuzzy environment and assumed to have equal impact on the global climate models. Fuzzy technique for order preference by similarity to an ideal solution is used to rank global climate models. Top three positions are occupied by MIROC3, GFDL2.1 and GISS with relative closeness of 0.7867, 0.7070, and 0.7068. IPSL-CM4, NCAR-PCMI occupied the tenth and eleventh positions with relative closeness of 0.4959 and 0.4562.

Semi-Supervised OWA Aggregation for Link-Based Similarity Evaluation and Alias Detection

T.Boongoen and Q. Shen. Semi-Supervised OWA Aggregation for Link-Based Similarity Evaluation and Alias Detection. Proceedings of the 18th International Conference on Fuzzy Systems (FUZZ-IEEE'09), pp. 288-293, 2009. Sponsorship: EPSRC

Fuzzy ART

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP synthesize fuzzy logic and ART networks by exploiting the formal similarity between the computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic: intersection (∩) with the fuzzy intersection (∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric: theory in which the fuzzy inter:>ec:tion and the fuzzy union (∨), or component-wise maximum, play complementary roles. Complement coding preserves individual feature amplitudes while normalizing the input vector, and prevents a potential category proliferation problem. Adaptive weights :otart equal to one and can only decrease in time. A geometric interpretation of fuzzy AHT represents each category as a box that increases in size as weights decrease. A matching criterion controls search, determining how close an input and a learned representation must be for a category to accept the input as a new exemplar. A vigilance parameter (p) sets the matching criterion and determines how finely or coarsely an ART system will partition inputs. High vigilance creates fine categories, represented by small boxes. Learning stops when boxes cover the input space. With fast learning, fixed vigilance, and an arbitrary input set, learning stabilizes after just one presentation of each input. A fast-commit slow-recode option allows rapid learning of rare events yet buffers memories against recoding by noisy inputs. Fuzzy ARTMAP unites two fuzzy ART networks to solve supervised learning and prediction problems. A Minimax Learning Rule controls ARTMAP category structure, conjointly minimizing predictive error and maximizing code compression. Low vigilance maximizes compression but may therefore cause very different inputs to make the same prediction. When this coarse grouping strategy causes a predictive error, an internal match tracking control process increases vigilance just enough to correct the error. ARTMAP automatically constructs a minimal number of recognition categories, or "hidden units," to meet accuracy criteria. An ARTMAP voting strategy improves prediction by training the system several times using different orderings of the input set. Voting assigns confidence estimates to competing predictions given small, noisy, or incomplete training sets. ARPA benchmark simulations illustrate fuzzy ARTMAP dynamics. The chapter also compares fuzzy ARTMAP to Salzberg's Nested Generalized Exemplar (NGE) and to Simpson's Fuzzy Min-Max Classifier (FMMC); and concludes with a summary of ART and ARTMAP applications.

Fuzzy ART Choice Functions

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP networks synthesize fuzzy logic and ART by exploiting the formal similarity between tile computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic intersection (∩) with the fuzzy intersection(∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric theory in which the fuzzy intersection and the fuzzy union (∨), or component-wise maximum, play complementary roles. A geometric interpretation of fuzzy ART represents each category as a box that increases in size as weights decrease. This paper analyzes fuzzy ART models that employ various choice functions for category selection. One such function minimizes total weight change during learning. Benchmark simulations compare peformance of fuzzy ARTMAP systems that use different choice functions.

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.

A fuzzy logic based approach for software testing

How to provide cost-effective strategies for Software Testing has been one of the research focuses in Software Engineering for a long time. Many researchers in Software Engineering have addressed the effectiveness and quality metric of Software Testing, and many interesting results have been obtained. However, one issue of paramount importance in software testing — the intrinsic imprecise and uncertain relationships within testing metrics — is left unaddressed. To this end, a new quality and effectiveness measurement based on fuzzy logic is proposed. Related issues like the software quality features and fuzzy reasoning for test project similarity measurement are discussed, which can deal with quality and effectiveness consistency between different test projects. Experiments were conducted to verify the proposed measurement using real data from actual software testing projects. Experimental results show that the proposed fuzzy logic based metrics is effective and efficient to measure and evaluate the quality and effectiveness of test projects.

Representing images by means of interval-valued fuzzy sets. Application to stereo matching

Stereo matching tries to find correspondences between locations in a pair of displaced images of the same scene in order to extract the underlying depth information. Pixel correspondence estimation suffers from occlusions, noise or bias. In this work, we introduce a novel approach to represent images by means of interval-valued fuzzy sets to overcome the uncertainty due to the above mentioned problems. Our aim is to take advantage of this representation in the stereo matching algorithm. The image interval-valued fuzzification process that we propose is based on image segmentation in a different way to the common use of segmentation in stereo vision. We introduce interval-valued fuzzy similarities to compare windows whose pixels are represented by intervals. In the experimental analysis we show the goodness of this representation in the stereo matching problem. The new representation together with the new similarity measure that we introduce shows a better overall behavior with respect to other very well-known methods.

A new online updating framework for constructing monotonicity-preserving fuzzy inference systems

In this paper, a new online updating framework for constructing monotonicity-preserving Fuzzy Inference Systems (FISs) is proposed. The framework encompasses an optimization-based Similarity Reasoning (SR) scheme and a new monotone fuzzy rule relabeling technique. A complete and monotonically-ordered fuzzy rule base is necessary to maintain the monotonicity property of an FIS model. The proposed framework attempts to allow a monotonicity-preserving FIS model to be constructed when the fuzzy rules are incomplete and not monotonically-ordered. An online feature is introduced to allow the FIS model to be updated from time to time. We further investigate three useful measures, i.e., the belief, plausibility, and evidential mass measures, which are inspired from the Dempster- Shafer theory of evidence, to analyze the proposed framework and to give an insight for the inferred outcomes from the FIS model.

A new method for deriving priority weights by extracting consistent numerical-valued matrices from interval-valued fuzzy judgement matrix

It is important to derive priority weights from interval-valued fuzzy preferences when a pairwise comparative mechanism is used. By focusing on the significance of consistency in the pairwise comparison matrix, two numerical-valued consistent comparison matrices are extracted from an interval fuzzy judgement matrix. Both consistent matrices are derived by solving the linear or nonlinear programming models with the aid of assessments from Decision Makers (DMs). An interval priority weight vector from the extracted consistent matrices is generated. In order to retain more information hidden in the intervals, a new probability-based method for comparison of the interval priority weights is introduced. An algorithm for deriving the final priority interval weights for both consistent and inconsistent interval matrices is proposed. The algorithm is also generalized to handle the pairwise comparison matrix with fuzzy numbers. The comparative results from the five examples reveal that the proposed method, as compared with eight existing methods, exhibits a smaller degree of uncertainty pertaining to the priority weights, and is also more reliable based on the similarity measure. © 2014 Elsevier Inc. All rights reserved.