Fuzzy Set Values Research Articles

A Novel Entropy of Interval Valued Fuzzy Set

The main attribution of this paper is to propose two methods to construct entropy of interval valued fuzzy sets (IVFSs). First, we use an IVFS to construct two FSs and define entropy by similarity measure of the two FSs; then we use an IVFS to construct two IVFSs and also define entropy by similarity measure of the two IVFSs. At the same time, we give two examples to show that our methods are effective.

Weighted fuzzy interpolative reasoning for sparse fuzzy rule-based systems based on piecewise fuzzy entropies of fuzzy sets

In this paper, we propose a new method for weighted fuzzy interpolative reasoning in sparse fuzzy rule-based systems based on piecewise fuzzy entropies of fuzzy sets. First, the proposed method uses the representative values of antecedent fuzzy sets, the representative values of observation fuzzy sets, and the representative values of consequence fuzzy sets of fuzzy rules to get the characteristic points of the fuzzy interpolative result represented by a fuzzy set. Then, it calculates the piecewise fuzzy entropies between any two characteristic points of the antecedent fuzzy sets, the piecewise fuzzy entropies between any two characteristic points of the observation fuzzy sets, and the piecewise fuzzy entropies between any two characteristic points of the consequence fuzzy sets of the fuzzy rules, respectively. Then, it calculates the weights of the antecedent fuzzy sets of each fuzzy rule, respectively, and calculates the weight of each fuzzy rule. Then, it calculates the piecewise fuzzy entropies between any two characteristic points of the fuzzy interpolative result. Finally, it uses the secant method to calculate the degree of membership of each obtained characteristic point of the fuzzy interpolative result. The experimental results show that the proposed method outperforms the existing methods for dealing with the multivariate regression problems, the Mackey–Glass chaotic time series prediction problem, and the time series prediction problems.

Overview of Lattices of Convex Normal Functions

The algebra of truth values of type-2 fuzzy sets is the set of maps from the unit interval to itself with convolution ordering. In applications of type-2 fuzzy sets, the full algebra is seldom used, but rather certain subalgebras that satisfy useful algebraic properties. The algebra of truth values of type-2 fuzzy sets is not itself a lattice, but the subalgebras considered here are lattices and, in fact, are complete distributive lattices. The subalgebras of special interest are the lattice of convex normal maps, the lattice of convex strongly normal maps, and the lattice of upper semicontinuous convex normal maps. We review and summarize some interesting properties of these subalgebras. A special feature of our treatment is a representation of these algebras as sets of monotone functions with pointwise order, making the operations more intuitive.

Fuzzy interpolative reasoning based on ranking values of polygonal fuzzy sets and automatically generated weights of fuzzy rules

In this paper, we propose a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on ranking values of polygonal fuzzy sets and automatically generated weights of fuzzy rules. First, the proposed method gets the characteristic points of the observation polygonal fuzzy sets and the characteristic points of the antecedent polygonal fuzzy sets of the fuzzy rules, respectively, by using the α-cut operations, respectively, where α ∈ [0, 1]. Then, it calculates the ranking value of each observation polygonal fuzzy set and the ranking value of each antecedent polygonal fuzzy set, respectively. Then, it calculates the difference between the ranking value of each observation polygonal fuzzy set and the ranking value of each antecedent polygonal fuzzy set. Then, it calculates the weight of each fuzzy rule based on the obtained differences between the ranking values of the observation polygonal fuzzy sets and the ranking values of the antecedent polygonal fuzzy sets. Then, based on the obtained characteristic points of the observation polygonal fuzzy sets, the obtained characteristic points of the antecedent polygonal fuzzy sets, and the obtained weights of the fuzzy rules, it gets the characteristic points of the fuzzy interpolative reasoning result represented by a polygonal fuzzy set. The experimental results show that the proposed method can overcome the drawbacks of the existing methods for fuzzy interpolative reasoning in sparse fuzzy rule-based systems.

Một mô hình cơ sở dữ liệu quan hệ mờ

This paper introduces a fuzzy relational data base model (FRDB) that extends the conventional relational data base model with two key features: (1) the relations represent the set of data tuples to be the fuzzy relations; (2) selection conditions are associated with fuzzy set values to be able to query the fuzzy, imprecise information of objects in relations. An interpretation of the membership degree of tuples for fuzzy relations is proposed on the basis of the fuzzy set theory to develop the data model and data manipulating model of FRDB that consist of schemas, fuzzy relations and algebraic operations. Some properties of the fuzzy relational algebraic operations are also formulated and proven as extensions of the properties of relational algebraic operations in the conventional relational data base model.

The Goldilocks principle: applying the exclusive disjunction to fuzzy sets

Qualitative Comparative Analysis (QCA), a technique by which the tools of Boolean algebra are applied to equifinal causal conditions, is gaining popularity amongst scholars. This paper draws upon a distinction largely overlooked by the QCA literature: the difference between inclusive- and exclusive-or (OR and XOR). I argue that XOR should be included amongst the tools of QCA, explain why XOR is more easily applied to crisp- than fuzzy-set QCA, and provide two original techniques for applying XOR to fuzzy sets: mechanical and calibrated. With the calibrated technique, the application of the exclusive-or is related to substantive knowledge of the cases with two threshold values: (1) how large two fuzzy set values need to be in order to violate a prior commitment or overshoot a target outcome, and (2) how similar two values need to be in order to violate the rule: ‘A or B, but not both’. This paper improves the capacity of QCA expressions to mirror natural language closely, formalize conversational implicature, and deal with mutually exclusive clusters of sufficiency conditions. It includes a helpful step-by-step guide for QCA practitioners.

Fuzzy Multiple Attributes Group Decision-Making Based on Ranking Interval Type-2 Fuzzy Sets and the TOPSIS Method

In this paper, we present a new method for fuzzy multiple attributes group decision-making based on the proposed ranking method of trapezoidal interval type-2 fuzzy sets and the TOPSIS method. Firstly, we present a new method for ranking trapezoidal interval type-2 fuzzy sets. Secondly, we construct the decision matrix and the average decision matrix, respectively. Thirdly, we construct the weighting decision matrix and average weighting decision matrix, respectively. Fourthly, we construct the ranking decision matrix by calculating the ranking values of trapezoidal interval type-2 fuzzy sets in the average decision matrix. Then, we get the absolute positive ideal solution and the absolute negative ideal solution with respect to the attributes based on the ranking decision matrix. Then, we calculate the distance between each alternative and the absolute positive ideal solution and calculate the distance between each alternative and the negative ideal solution, respectively. Finally, we calculate the relative degree of closeness of each alternative. The larger the value of the relative degree of closeness of an alternative, the better the preference order of the alternative. The proposed fuzzy multiple attributes group decision-making method can overcome the drawbacks of the existing method.

Gujarati character recognition using adaptive neuro fuzzy classifier with fuzzy hedges

Recognition of Indian scripts is a challenging problem and work towards development of an OCR for handwritten Gujarati, an Indian script is still in infancy. This paper implements an Adaptive Neuro Fuzzy Classifier (ANFC) for Gujarati character recognition using fuzzy hedges (FHs). FHs are trained with other network parameters by scaled conjugate gradient training algorithm. The tuned fuzzy hedge values of fuzzy sets improve the flexibility of fuzzy sets; this property of FH improves the distinguishability rates of overlapped classes. This work is further extended for feature selection based on FHs. The values of fuzzy hedges can be used to show the importance of degree of fuzzy sets. According to the FH value, the redundant, noisily features can be eliminated, and significant features can be selected. An FH-based feature selection algorithm is implemented using ANFC. This paper aims to demonstrate recognition of ANFC-FH and improved results of the same with feature selection.

Cross-sectoral comparison of concessions in transport

Purpose – The purpose of this paper is to present a methodology of comparing concession projects developed in different transport sub-sectors. The methodology is tested in the comparison of three different cases, each of which represent a particular mode of transport: a road development project, a city tramway project and a port lock construction initiative. Design/methodology/approach – A fuzzy logic approach methodology is applied in carrying out the comparison between cases. Granulation is achieved by employing a Contextual (Ws) Risk Analysis Framework, as risks constitute the basis to public private partnership (PPP) structure. Linguistic variables are then used to describe the comparative findings. Findings – The methodology presented allows for the comparison of three cases from different transport sub-sectors. Identification of similarities provides the potential to transfer experience from one sector to the other. With respect to the three cases studied, it was identified that traffic risk seems to be passed on to the private operators in relation to the level of exclusivity. Finally, PPP projects initiated by central government (as opposed to those initiated by local governments) seem to be more finance-driven than service-driven. Research limitations/implications – As the number of cases to be compared increases, quantitative comparative analysis fuzzy set values can be included in order to carry out a full analysis. The present approach should be considered introductory, as fuzzy sets are not generated due to the limited number of surveys (cases) compared (hence the term “pre-fuzzy”). Practical implications – The methodology presented and the cases tested indicate the possibility for knowledge/experience transfer and the transferability of best practices. Originality/value – Cross-sub-sectoral comparisons for transport PPP projects have not been identified in literature.

Erratum to A Characterisation of Weak Integer Additive Set-Indexers of Graphs [Journal of Fuzzy Set Valued Analysis 2014 (2014) 1-7

In the recently published article titled A Characterisation of Weak Integer Additive Set-Indexers of Graphs (article id:jfsva-00189) an inadvertent error in the final simplification has been occured.

Inclusion and exclusion hypothesis tests for the fuzzy mean

A hypothesis test for the inclusion of the expected value of a fuzzy-valued random element in a given fuzzy set is provided. The exclusion, or the empty intersection of the expected value of a random fuzzy set and a fuzzy set, is also tested, that allows us to define one-sided tests for this expected value without the need of considering any restrictive ordering. Both tests are developed by using a measure of the intersection between fuzzy sets. Asymptotic and bootstrap techniques are established. Some simulations are included to show the performance of the bootstrap approaches. Finally, the methodology proposed is applied on a real-life situation related to the field of sensorial analysis.

Multicriteria Decision-Making Method Using Expected Values in Trapezoidal Hesitant Fuzzy Setting

Abstract This paper extends hesitant fuzzy sets to trapezoidal hesitant fuzzy sets based on the combination of the concepts of trapezoidal fuzzy numbers and hesitant fuzzy sets and defines some operations on trapezoidal hesitant fuzzy sets. Then, a decision-making method with linguistic assessments is proposed based on expected values of trapezoidal hesitant fuzzy sets to solve the multicriteria decision-making problem in which the criteria weights are completely unknown and the criteria values for an alternative can be given by the linguistic values of trapezoidal fuzzy numbers provided by a group of decision makers to transform them into trapezoidal hesitant fuzzy sets. The criteria weights can be obtained by establishing a weight model based on the standard deviation of expected values from the trapezoidal hesitant fuzzy decision matrix. Then by an approach of weighted expected values for alternatives, the ranking order of all the alternatives can be determined and the best one can be easily identified as well. Finally, a practical example for the flexible manufacturing system is given to demonstrate the application of the proposed decision-making method. The numerical example shows that the proposed method is reasonable and applicable.

Special Issue on Modeling and Simulation

Special Issue on Modeling and Simulation

A new time invariant fuzzy time series forecasting method based on particle swarm optimization

In the analysis of time invariant fuzzy time series, fuzzy logic group relationships tables have been generally preferred for determination of fuzzy logic relationships. The reason of this is that it is not need to perform complex matrix operations when these tables are used. On the other hand, when fuzzy logic group relationships tables are exploited, membership values of fuzzy sets are ignored. Thus, in defiance of fuzzy set theory, fuzzy sets’ elements with the highest membership value are only considered. This situation causes information loss and decrease in the explanation power of the model. To deal with these problems, a novel time invariant fuzzy time series forecasting approach is proposed in this study. In the proposed method, membership values in the fuzzy relationship matrix are computed by using particle swarm optimization technique. The method suggested in this study is the first method proposed in the literature in which particle swarm optimization algorithm is used to determine fuzzy relations. In addition, in order to increase forecasting accuracy and make the proposed approach more systematic, the fuzzy c-means clustering method is used for fuzzification of time series in the proposed method. The proposed method is applied to well-known time series to show the forecasting performance of the method. These time series are also analyzed by using some other forecasting methods available in the literature. Then, the results obtained from the proposed method are compared to those produced by the other methods. It is observed that the proposed method gives the most accurate forecasts.

Based on the Fuzzy Set-valued Statistics and the Fuzzy Mathematics Theory in Air Traffic Control System Safety Appraisal Application

Abstract Elaborated carries on the safety evaluation to the air traffic control system the important meaning .First, the person-equipment- environment- management system management model takes the instruction based on the systems engineering theory, establishes the air traffic management system safety evaluating indicator system. Next, based on the fuzzy set value statistical theory, calculates various targets the weight, and has carried on the fail-safe analysis to its weight; Based on the fuzzy mathematics theory, the use fuzzy comprehensive judgment carries on the safety evaluation to the air traffic management system. Finally, through the example analysis computation, confirmed has proposed the method the validity and the feasibility.

Design of an Interval Type-2 Fuzzy Logic Controller for Automatic Voltage Regulator System

A type-2 fuzzy logic controller is proposed in this article for an automatic voltage regulator system. For controller design, memberships of system variables are represented using interval value fuzzy sets. Fuzzy logic based on interval value sets is capable of modeling the uncertainty and imprecision in a better way. The proposed controller surpasses the best performance obtained by an optimized proportional-integral-derivative controller in improving the step response of an automatic voltage regulator system. Simulation results also reveal the robustness of the controller to system parameter changes.

Transforming Model from Vague Set to Fuzzy Set Based on the DWCO Operator

In the research on transforming vague set to fuzzy set, it is the key question to carry on the judgment to the vague-degree's tendentiousness. Vague set's vague-degree expresses one kind of indefinite degree, therefore the question transforming vague set to fuzzy set may regard as the venture decision under the definite condition. When the policy-maker carries on the venture decision, the policy-maker's risk preferences decided by the subjective and objective condition is a very essential policy-making parameter. In this paper, introduce the risk-income balancing weight into the transforming model, thus enable reflect the policy-maker's risk preferences well in the transforming result. In addition, decompose the value of fuzzy set's membership degree into the following two parts: the value of vague set's real membership degree, the weighting sum of the risk value and the tendency value.

UNCERTAIN AND FUZZY OBJECT BASES: A DATA MODEL AND ALGEBRAIC OPERATIONS

Fuzzy set theory and probability theory are complementary for soft computing, in particular object-oriented systems with imprecise and uncertain object properties. However, current fuzzy object-oriented data models are mainly based on fuzzy set theory or possibility theory, and lack of a rigorous algebra for querying and managing uncertain and fuzzy object bases. In this paper, we develop an object base model that incorporates both fuzzy set values and probability degrees to handle imprecision and uncertainty. A probabilistic interpretation of relations on fuzzy sets is introduced as a formal basis to coherently unify the two types of measures into a common framework. The model accommodates both class attributes, representing declarative object properties, and class methods, representing procedural object properties. Two levels of property uncertainty are taken into account, one of which is value uncertainty of a definite property and the other is applicability uncertainty of the property itself. The syntax and semantics of the selection and other main data operations on the proposed object base model are formally defined as a full-fledged algebra.

Development of an adaptive neuro-fuzzy classifier using linguistic hedges: Part 1

In this study, the development of an adaptive neuro-fuzzy classifier (ANFC) is proposed by using linguistic hedges (LHs). The LHs that are constituted by the power of fuzzy sets introduce the importance of the fuzzy sets for fuzzy rules. They can also change the primary meaning of fuzzy membership functions to secondary meaning. To improve the meaning of fuzzy rules and classification accuracy, a layer, which defines the adaptive linguistic hedges, is added into the proposed classifier network. The LHs are trained with other network parameters by scaled conjugate gradient (SCG) training algorithm. The tuned LH values of fuzzy sets improve the flexibility of fuzzy sets, this property of LH can improve the distinguishability rates of overlapped classes. The new classifier is compared with the other classifiers for different classification problems. The empirical results indicate that the recognition rates of the new classifier are better than the other fuzzy-based classification methods with less fuzzy rules.

Key Success and Failure Paths in Fashion Marketing Strategies

Abstract Both successful and unsuccessful design+marketing projects in high fashion products and services represent creating and implementing recipes or paths of key success factors (KSFs). While implementing any one KSF is not sufficient for success, creating and taking certain paths that includes partially-independent KSFs is sufficient for success; other paths lead to failure; some paths are never taken because they are never though of or designers consider them to be totally unrealistic options. Consequently, fashion marketing strategists need to look beyond research attempting to learn the net effects of independent influences of KSFs. Configurations (i.e., recipes) representing alternative combinations of design+marketing dimensions are indicators of sufficiency for success versus failure for fashion marketing projects. The study of alternative decision configurations is particularly useful for fashion marketing strategists and researchers. The objectives of this article include (1) describing keys ...