Fuzzy Subsethood Measures Research Articles

An interval type-2 fuzzy axiomatic design method: A case study for evaluating blockchain deployment projects in supply chain

This study is concerned with the development of the axiomatic design (AD) method under an interval type-2 fuzzy (IT2F) environment and its application in evaluating blockchain deployment projects in supply chains. Blockchain is a transformative technology that has received significant attention recently. Blockchain technology can process various business transactions by offering a reliable and decentralized infrastructure. Supply chain management is an important application area of blockchains due to its desirable properties, including data security, extended visibility, product traceability, digitalization, and disintermediation. Since blockchain technologies are in their infancy, adopting them to supply chains requires proper design methodologies. Fuzzy AD offers valuable computational mechanisms to evaluate design options in the presence of functional requirements. However, extending AD to different fuzzy extensions is not an easy task, and area-based calculations hinder its widespread applicability. In this study, an IT2F-AD method is developed based on the concept of fuzzy subsethood. The potential of the fuzzy subsethood measure as the main computation engine within type-1 and IT2F-AD is demonstrated. Finally, an integrated multiple criteria decision-making (MCDM) model is proposed by using IT2F Best-Worst Method (IT2F-BWM) and IT2F-AD. The proposed model is used to prioritize blockchain deployment projects in a real-life case study.

A method of constructing fuzzy implications from the FIφ-construction

In the recent years, several new construction methods of fuzzy implications have been proposed. However, these construction methods actually care about that the new implication could preserve more properties. In this paper, we introduce a new method for constructing fuzzy implications based on an aggregation function with F (1, 0) =1, a fuzzy implication I and a non-decreasing function φ, called FIφ-construction. Specifically, some logical properties of fuzzy implications preserved by this construction are studied. Moreover, it is studied how to use the FIφ-construction to produce a new implication satisfying a specific property. Furthermore, we produce two new subclasses of fuzzy implications such as UIφ-implications and GpIφ-implications by this method and discuss some additional properties. Finally, we provide a way to generate fuzzy subsethood measures by means of FIφ-implications.

Similarity measures, penalty functions, and fuzzy entropy from new fuzzy subsethood measures

In this study, we discuss a new class of fuzzy subsethood measures between fuzzy sets. We propose a new definition of fuzzy subsethood measure as an intersection of other axiomatizations and provide two construction methods to obtain them. The advantage of this new approach is that we can construct fuzzy subsethood measures by aggregating fuzzy implication operators which may satisfy some properties widely studied in literature. We also obtain some of the classical measures such as the one defined by Goguen. The relationships with fuzzy distances, penalty functions, and similarity measures are also investigated. Finally, we provide an illustrative example which makes use of a fuzzy entropy defined by means of our fuzzy subsethood measures for choosing the best fuzzy technique for a specific problem.

A study of (T,N)-implications and its use to construct a new class of fuzzy subsethood measure

It is not hard to see that implications can be obtained by means of other operators. To name a few, we can mention (S,N)-, R- and QL-implications, which has been widely investigated. The aim of this work is to study a fuzzy implication called (T,N)-implication, obtained from the composition of a fuzzy negation and a t-norm. It is also discussed the conditions under which such functions preserve the main properties of fuzzy implications, such that some are related to the laws of contraposition. We also prove under what conditions our implication satisfies the following iterated boolean-like law in fuzzy logic: I(x,I(x,y))=I(x,y) for all x and y in the unit interval. Finally, we provide a way to construct fuzzy subsethood measures by means of (T,N)-implications.

Subsethood measures for interval-valued fuzzy sets based on the aggregation of interval fuzzy implications

The connection between fuzzy subsethood measures and fuzzy implications straightforwardly follows from the definition of inclusion for (crisp) sets. In accordance with this connection we introduce a new constructive method for (weak) fuzzy subsethood measures for interval-valued fuzzy sets based on the aggregation of fuzzy interval implications. For this purpose we generalize aggregation functions and propose a technique for aggregation of intervals. The benefit of our approach lies in the wide range of obtained fuzzy subsethood measures for interval-valued fuzzy sets. Moreover, the method gives the possibility to construct new fuzzy subsethood measures with properties that are appropriate to the situation under investigation. Another advantage of the method is its clear semantic interpretation.

A Neuro-Fuzzy Classifier-Cum-Quantifier for Analysis of Alcohols and Alcoholic Beverages Using Responses of Thick-Film Tin Oxide Gas Sensor Array

A novel neuro-fuzzy classifier-cum-quantifier is presented. The proposed classifier retrieves both qualitative and quantitative information simultaneously from the steady-state responses of thick-film tin oxide gas sensor array when it was exposed to seven different kinds of alcohols and alcoholic beverages. The individual concentration bands were represented in the output feature space by fuzzy subsethood measure. The qualitative and quantitative classifications were done by training an artificial neural network (ANN) with backpropagation algorithm. Each output neuron of the network represented one out of the seven alcohols and alcoholic beverage classes and was trained to fire at the fuzzy subsethood value of the particular concentration band of a particular alcohol or alcoholic beverage whose sample was presented to the network. The proposed network gave satisfactory performance and simultaneous qualitative and quantitative classification of the alcohols and alcoholic beverages was obtained using a single neural network.

Fuzzy Subsethood for Fuzzy Sets of Type-2 and Generalized Type-<formula formulatype="inline"><tex Notation="TeX"> ${n}$</tex></formula>

In this paper, we use Zadeh's extension principle to extend Kosko's definition of the fuzzy subsethood measure S(G, H) to type-2 fuzzy sets defined on any set X equipped with a measure. Subsethood is itself a fuzzy set that is a crisp interval when G and H are interval type-2 sets. We show how to compute this interval and then use the result to compute subsethood for general type-2 fuzzy sets. A definition of subsethood for arbitrary fuzzy sets of type-n > 2 is then developed. This subsethood is a type-(n - 1) fuzzy set, and we provide a procedure to compute subsethood of interval type-3 fuzzy sets.

WEAK FUZZY S-SUBSETHOOD MEASURES: OVERLAP INDEX

Starting from the definitions of the weak fuzzy subsethood measure (V.R. Young, Fuzzy subsethood. Fuzzy Sets and Systems, 77 (1996) 371–384) and of strong fuzzy inclusion, (D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, New York, Academic Press, 1980) we define weak fuzzy S-subsethood measures. We analyze their axiomatization and present various constructions obtained by aggregating implication operators with special properties. We conclude by presenting the conditions under which we can construct fuzzy entropies and overlap indices from these measures.

Definition and construction of fuzzy DI-subsethood measures

In this paper we study a method of construction of the fuzzy subsethood measures of V.R. Young [V.R. Young, Fuzzy subsethood, Fuzzy Sets and Systems 77 (1996) 371–384] and the fuzzy subsethood measures of J. Fan, X. Xie, and J. Pei [J. Fan, X. Xie, J. Pei, Subsethood measures: new definitions, Fuzzy Sets and Systems 106 (1999) 201–209]. We establish the conditions under which our constructions satisfy the axioms of Sinha and Dougherty’s inclusion measures and we present different methods for obtaining fuzzy entropies from said measures. Next we present a particular case of Young’s subsethood measures, DI-subsethood measures. For these we also analyze their construction and the conditions under which they satisfy different axioms.

Subsethood based adaptive linguistic networks for pattern classification

This paper presents a fuzzy-neural network that admits both numeric as well as linguistic inputs. Numeric inputs are fuzzified by input nodes upon presentation to the network. Fuzzy rule-based knowledge is translated directly into a network architecture. Connections in the network are represented by fuzzy sets: Input to hidden connections represent rule antecedents; hidden to output connections represent rule consequents. The novelty of the model lies in the method of activation spread in the network which is based on a fuzzy mutual subsethood measure. Rule (hidden) node activations are computed as a fuzzy inner product. For a given numeric or fuzzy input, numeric outputs are computed using volume based defuzzification. A supervised learning procedure based on gradient descent is employed to train the network. The model has a natural capability for inference, function approximation, and classification and is versatile in that it can handle numeric and fuzzy inputs simultaneously. In this paper, we focus on the classification ability of the model and demonstrate its performance on three benchmark classification problems: the Iris data set, Ripley's synthetic two class problem, and Pal and Mitra's Telegu vowel data. Results show that the classifier performs at par or better than various other techniques.