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This paper proposes a personal tour planning problem with uncertain traveling times and satisfaction values of sightseeing places dependent on sightseeing. Since traveling times are dependent on the time of day, it is difficult to represent this uncertain model using the general static network model. In this paper, Time-Expanded Network (TEN), which contains a copy to the set of nodes in the underlying...
Petri nets serve as a graphical and mathematical modelling tool applicable to many systems. They can be represented in many ways. One of the most known and applicable representation of Petri nets is the linear-algebraic one. The aim of this paper is to present an original linear-algebraic representation of generalised fuzzy Petri nets. Such representation enables us an easy implementation, also parallel,...
This study applied relationship life cycle concept and separated two stages including relationship development and relationship maintenance to derivate influence factors in each stage based on relative literature for relationship development. This study proposed a model which called “Relationship Hierarchy Structural Fuzzy ANP Model”, and apply this model to investigate and compare interaction, influence,...
A value-at-risk portfolio selection model to maximize not only the expected daily geometric return but also value-at-risk is discussed. The analytical solutions of the value-at-risk portfolio problem are derived. From the analytical results, this paper gives formulae to show the explicit relations among the following important parameters in portfolio: Value-at-risk, the expected daily geometric return,...
Face recognition is a topic of great interest in different areas, especially those related to security. The identification of a person by the image of her face is a difficult task because of changes experienced by the face due to various factors, such as facial expression, aging and even the lighting. This paper presents a new face recognition technique based on the combination of a competitive fuzzy...
In this paper, we synthesize interval type-2 fuzzy set models of linguistic probability words and linguistic quantifiers by applying the Enhanced Interval Approach to data collected from subjects about those words. We establish some user friendly sub-vocabularies of linguistic probabilities and linguistic modifiers, so that they can be used in advanced computing with words applications. The user friendly...
This paper investigates the problem of solving sup-conjunctor composite finite interval-valued fuzzy relational equations over complete Brouwerian lattices. First, we introduce the notions of tolerable solution set, united solution set and controllable solution set, respectively and discuss their properties. Secondly, we obtain some necessary and sufficient conditions that these solution sets are...
Certain advantages of midpoint/radius notation for boxes are well known. Box notation, a concise midpoint/radius scheme employing a ‘box operator’, ϖ, significantly simplifies box calculations. The box math approach to interval analysis, emphasizing ‘image-centered’ representations and assessment of quality of approximation, demonstrates the power of mid-point/ radius methods. A prime example is the...
The mathematical foundations of fuzzy morphological associative memories (FMAMs) can be found in mathematical morphology on complete lattices that include the class of fuzzy sets over a certain universe as a special case. The advent of type-2 fuzzy systems suggests the development of type-2 FMAMs and in particular interval-valued (type-2) FMAMs since the classes of general type-2 fuzzy sets and interval-valued...
Fuzzy models offer a convenient way to describe complex and nonlinear systems. Fuzzy relational equations, viewed as a certain class of fuzzy models, play a pivotal role in fuzzy modeling. Their theory supports ways in which these equations could be solved and offers a characterization of the resulting families of solutions. Assuming that the corresponding relational equation or a system of relational...
In this paper the problem of the minimization of active power losses in a real Smart Grid located in the area of Rome is faced by defining and solving a suited multi-objective optimization problem. It is considered a portion of the Italian electric distribution network managed by the ACEA Distribuzione S.p.A. which presents backflow of active power for 20% of the annual operative time. The network...
In this paper we face the problem of the joint optimization of both topology and network parameters in order to minimize the total active power losses in a real Smart Grid. It is considered a portion of the Italian electric distribution network managed by the ACEA Distribuzione S.p.A. located in Rome which presents back-flows of active power for 20% of the annual operative time. It includes about...
This paper just deals with the starting point in the twenty years old paper [1] by Charles Elkan, with which he tried to puzzle fuzzy logic: That the formula 1-min (a,1−b) = max (b, min (1−a, 1−a)) holds in the unit interval.
In this paper, we propose a procedure for computing the dissimilarity measure of finite general type-2 fuzzy sets, represented as sequences of vertical slices. Through representing general type-2 fuzzy sets as a sequence of objects, we compute their overall dissimilarity value using suited matching algorithms for generalized sequences. The evaluation of the proposed matching algorithm is performed...
We focused on a new direction of fuzzy control that, we believe, has received little, if any, attention. We explored how the look-up table (LUT) controllers and one special type of Mamdani fuzzy controllers were mathematically related and how to represent the former by the latter. A LUT controller is one of the most widely used tools in industry, especially in automotive engineering. The reasons for...
We introduce two new classes of single-parameter aggregation functions based upon the Tsallis q-exponential function of non-extensive statistical mechanics. These aggregation functions facilitate simple modeling of two different common human reasoning traits of “threshold” inference, where either: 1) at least one input must exceed a threshold in order to achieve a non-zero aggregation output, or 2)...
In this paper a comparison of the use of Type-1 and Type-2 fuzzy logic in the benchmark problem known as the problem of the water tank is presented. Fuzzy logic allows managing uncertainty, which is very common in linguistic fuzzy systems. It has been shown that Type-2 fuzzy systems manage better the uncertainty in real world problems but, evidence exists also to show that using Type-2 technology...
In this paper a metaheuristic for Particle Swarm Optimization (PSO) and two of its variants (inertia weight and constriction coefficient) are used as optimization strategies for designing the membership functions of Fuzzy Control Systems for the water tank and inverted pendulum. Each variant has its own advantages in the algorithm, allowing the exploration and exploitation in different ways and this...
The proposed learning methodology based on a hybrid mechanism for training interval A2-C1 type-2 non-singleton type-2 Takagi-Sugeno-Kang fuzzy logic systems uses a recursive square-root filter to tune the type-1 consequent parameters and the steepest descent method to tune the interval type-2 antecedent parameters. This hybrid-learning algorithm changes the interval type-2 model parameters adaptively...
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