Search results for: fuzzy measures

Authors: Seyed Habib A. Rahmati, Mohsen Sadegh Amalnick

Abstract:

Different terms of the statistical process control (SPC) has sketch in the fuzzy environment. However, measurement system analysis (MSA), as a main branch of the SPC, is rarely investigated in fuzzy area. This procedure assesses the suitability of the data to be used in later stages or decisions of the SPC. Therefore, this research focuses on some important measures of MSA and through a new method introduces the measures in fuzzy environment. In this method, which works based on Buckley approach, imprecision and vagueness nature of the real world measurement are considered simultaneously. To do so, fuzzy version of the gauge capability (Cg and Cgk) are introduced. The method is also explained through example clearly.

Keywords: measurement, SPC, MSA, gauge capability (Cg and Cgk)

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Authors: G. S. Thakur

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This paper presents a Fuzzy Soft Recruitment Model (FSRM) for faculty selection of MHRD technical institutions. The selection criteria are based on 4-tier flexible structure in the institutions. The Advisory Committee on Faculty Recruitment (ACoFAR) suggested nine criteria for faculty in the proposed FSRM. The model Fuzzy Soft is proposed with consultation of ACoFAR based on selection criteria. The Fuzzy Soft distance similarity measures are applied for finding best faculty from the applicant pool.

Keywords: fuzzy soft set, fuzzy sets, fuzzy soft distance, fuzzy soft similarity measures, ACoFAR

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Authors: Ali Koam, Ismail Ibedou, S. E. Abbas

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In this paper, it is introduced the notion of r-fuzzy ideal separation axioms Tᵢi = 0; 1; 2 based on a fuzzy ideal I on a fuzzy topological space (X; τ). An r-fuzzy ideal connectedness related to the fuzzy ideal I is introduced which has relations with a previous r-fuzzy fuzzy connectedness. An r-fuzzy ideal compactness related to Ι is introduced which has also relations with many other types of fuzzy compactness.

Keywords: fuzzy ideal, fuzzy separation axioms, fuzzy compactness, fuzzy connectedness

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Authors: Palash Dutta

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More frequently uncertainties are encountered in medical diagnosis and therefore it is the most important and interesting area of applications of fuzzy set theory. In this present study, an attempt has been made to extend Sanchez’s approach for medical diagnosis via interval valued picture fuzzy sets and exhibit the technique with suitable case studies. In this article, it is observed that a refusal can be expressed in the databases concerning the examined objects. The technique is performing diagnosis on the basis of distance measures and as a result, this approach makes it possible to introduce weights of all symptoms and consequently patient can be diagnosed directly.

Keywords: medical diagnosis, uncertainty, fuzzy set, picture fuzzy set, interval valued picture fuzzy set

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Authors: Marija Paunović, Nebojša Ralević, Dejan Ćebić

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Actuarial assessments in insurance are inherently subjective due to various factors, including data limitations and the complexity of problems. Fuzzy mathematics and credibility theory provide robust frameworks to manage this subjectivity and uncertainty. Uncertain future events are closely linked with the credibility theory. This paper extends the properties of c−credibility measure. We generalized the c−credibility measure in fuzzy environment and proved some properties of this measure. Those properties will provide more practical applications of the c−credibility measure of fuzzy events, especially in the context of insurance.

Keywords: uncertainty, fuzzy measures, c-credibility measure, c-credibility in fuzzy environment

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Authors: S. H. Nasseri, A. Ebrahimnejad

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Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.

Keywords: fuzzy linear programming, fuzzy numbers, duality, sensitivity analysis

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Authors: G. S. Thakur

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In this paper, four new operators (O1, O2, O3, O4) are proposed, defined and considered to study the new properties and identities on hesitant fuzzy sets. These operators are useful for different operation on hesitant fuzzy sets. The various theorems are proved using the new operators. The study of the proposed new operators has opened a new area of research and applications.

Keywords: vague sets, hesitant fuzzy sets, intuitionistic fuzzy set, fuzzy sets, fuzzy multisets

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Authors: Joseph Siani

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Over the last decades, dissatisfaction with global indicators of economic performance, such as GDP (Gross Domestic Product) per capita, has shifted the attention to what is now referred to as multidimensional poverty. In this framework, poverty goes beyond income to incorporate aspects of well-being not captured by income measures alone. This paper applies the totally fuzzy approach to estimate the fuzzy index of poverty (FIP) in fourteen Sub-Saharan African (SSA) countries using Demographic and Health Survey (DHS) data and explores whether pictures created by the standard headcount ratio at $1.90 a day and the fuzzy index of poverty tell a similar story. The results suggest that there is indeed considerable mismatch between poverty headcount and the fuzzy index of multidimensional poverty, meaning that the majority of the most deprived people (as identified by the fuzzy index of multidimensional poverty) would not be identified by the poverty headcount ratio. Moreover, we find that poverty is distributed differently by colonial heritage (language). In particular, the most deprived countries in SSA are French-speaking.

Keywords: fuzzy set approach, multidimensional poverty, poverty headcount, overlap, Sub-Saharan Africa

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Authors: T. Pathinathan, M. Peter

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Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

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Authors: Liang-Hsuan Chen, Chia-Jung Chang

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Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

Keywords: fuzzy random variables, distance measure, expected value, descriptive parameters

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Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

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In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: Jolly Puri, Shiv Prasad Yadav

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Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.

Keywords: multi-component DEA, fuzzy multi-component DEA, fuzzy resources, decision making units (DMUs)

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Authors: O. Poleshchuk, E. Komarov

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This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: interval type-2 fuzzy sets, fuzzy regression, weighted interval

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Authors: E. Koyuncu

Abstract:

The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Keywords: fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Hamid Reza Behnood, Esmaeel Ayati, Tom Brijs, Mohammadali Pirayesh Neghab

Abstract:

Investment projects in road safety planning can benefit from an effectiveness evaluation regarding their expected safety outcomes. The objective of this study is to develop a decision support system (DSS) to support policymakers in taking the right choice in road safety planning based on the efficiency of previously implemented safety measures in a set of regions in Iran. The measures considered for each region in the study include performance indicators about (1) police operations, (2) treated black spots, (3) freeway and highway facility supplies, (4) speed control cameras, (5) emergency medical services, and (6) road lighting projects. To this end, inefficiency measure is calculated, defined by the proportion of fatality rates in relation to the combined measure of road safety performance indicators (i.e., road safety measures) which should be minimized. The relative inefficiency for each region is modeled by the Data Envelopment Analysis (DEA) technique. In a next step, a fuzzy decision-making system is constructed to convert the information obtained from the DEA analysis into a rule-based system that can be used by policy makers to evaluate the expected outcomes of certain alternative investment strategies in road safety.

Keywords: performance indicators, road safety, decision support system, data envelopment analysis, fuzzy reasoning

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Authors: K. M. Alsager, N. O. Alshehri

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In this paper, we proposed the notion of single valued neutrosophic hesitant fuzzy rough set, by combining single valued neutrosophic hesitant fuzzy set and rough set. The combination of single valued neutrosophic hesitant fuzzy set and rough set is a powerful tool for dealing with uncertainty, granularity and incompleteness of knowledge in information systems. We presented both definition and some basic properties of the proposed model. Finally, we gave a general approach which is applied to a decision making problem in disease diagnoses, and demonstrated the effectiveness of the approach by a numerical example.

Keywords: single valued neutrosophic fuzzy set, single valued neutrosophic fuzzy hesitant set, rough set, single valued neutrosophic hesitant fuzzy rough set

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Authors: Shih-Pin Chen, Shih-Syuan You

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This study proposes a regression model with flexible spreads for fuzzy input-output data to cope with the situation that the existing measures cannot reflect the actual estimation error. The main idea is that a dissemblance index (DI) is carefully identified and defined for precisely measuring the actual estimation error. Moreover, the graded mean integration (GMI) representation is adopted for determining more representative numeric regression coefficients. Notably, to comprehensively compare the performance of the proposed model with other ones, three different criteria are adopted. The results from commonly used test numerical examples and an application to Taiwan's business monitoring indicator illustrate that the proposed dissemblance index method not only produces valid fuzzy regression models for fuzzy input-output data, but also has satisfactory and stable performance in terms of the total estimation error based on these three criteria.

Keywords: dissemblance index, forecasting, fuzzy sets, linear regression

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Authors: Luiz F. J. Maia

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This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

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Authors: Behnam Tavakkol

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Uncertain data mining algorithms use different ways to consider uncertainty in data such as by representing a data object as a sample of points or a probability distribution. Fuzzy methods have long been used for clustering traditional (certain) data objects. They are used to produce non-crisp cluster labels. For uncertain data, however, besides some uncertain fuzzy k-medoids algorithms, not many other fuzzy clustering methods have been developed. In this work, we develop a fuzzy kernel k-medoids algorithm for clustering uncertain data objects. The developed fuzzy kernel k-medoids algorithm is superior to existing fuzzy k-medoids algorithms in clustering data sets with non-linearly separable clusters.

Keywords: clustering algorithm, fuzzy methods, kernel k-medoids, uncertain data

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Authors: Tumadhir Fahim M Alsulami

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The concept of this paper builds on connecting between two important notions, fuzzy ideals of BCK-algebras and derivation of BCI-algebras. The result we got is a new concept called derivation fuzzy ideals of BCI-algebras. Followed by various results and important theorems on different types of ideals. In chapter 1: We presented the basic and fundamental concepts of BCK\ BCI- algebras as follows: BCK/BCI-algebras, BCK sub-algebras, bounded BCK-algebras, positive implicative BCK-algebras, commutative BCK-algebras, implicative BCK- algebras. Moreover, we discussed ideals of BCK-algebras, positive implicative ideals, implicative ideals and commutative ideals. In the last section of chapter 1 we proposed the notion of derivation of BCI-algebras, regular derivation of BCI-algebras and basic definitions and properties. In chapter 2: It includes 3 sections as follows: Section 1 contains elementary concepts of fuzzy sets and fuzzy set operations. Section 2 shows O. G. Xi idea, where he applies fuzzy sets concept to BCK-algebras and we studied fuzzy sub-algebras as well. Section 3 contains fuzzy ideals of BCK-algebras basic definitions, closed fuzzy ideals, fuzzy commutative ideals, fuzzy positive implicative ideals, fuzzy implicative ideals, fuzzy H-ideals and fuzzy p-ideals. Moreover, we investigated their concepts in diverse theorems and propositions. In chapter 3: The main concept of our thesis on derivation fuzzy ideals of BCI- algebras is introduced. Chapter 3 splits into 4 sections. We start with General definitions and important theorems on derivation fuzzy ideal theory in section 1. Section 2 and 3 contain derivations fuzzy p-ideals and derivations fuzzy H-ideals of BCI- algebras, several important theorems and propositions were introduced. The last section studied derivations fuzzy implicative ideals of BCI-algebras and it includes new theorems and results. Furthermore, we presented a new theorem that associate derivations fuzzy implicative ideals, derivations fuzzy positive implicative ideals and derivations fuzzy commutative ideals. These concepts and the new results were obtained and introduced in chapter 3 were submitted in two separated articles and accepted for publication.

Keywords: BCK, BCI, algebras, derivation

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Authors: Oktay Nusratov, Ramin Rzaev, Aydin Goyushov

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Fuzzy inference method based approach to the forming of modular intellectual system of assessment the quality of communication services is proposed. Developed under this approach the basic fuzzy estimation model takes into account the recommendations of the International Telecommunication Union in respect of the operation of packet switching networks based on IP-protocol. To implement the main features and functions of the fuzzy control system of quality telecommunication services it is used multilayer feedforward neural network.

Keywords: quality of communication, IP-telephony, fuzzy set, fuzzy implication, neural network

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Authors: Jun-Ho Chung, Sung-Hyun Yoo, In-Hwan Choi, Hyun-Kook Lee, Moon-Kyu Song, Choon-Ki Ahn

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The extended finite impulse response (EFIR) filter is addressed to optimize membership functions (MFs) of the fuzzy model that has strong nonlinearity. MFs are important parts of the fuzzy logic system (FLS) and, thus optimizing MFs of FLS is one of approaches to improve the performance of output. We employ the EFIR as an alternative optimization option to nonlinear fuzzy model. The performance of EFIR is demonstrated on a fuzzy cruise control via a numerical example.

Keywords: fuzzy logic system, optimization, membership function, extended FIR filter

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Authors: Walied Hanora

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This paper presents the problem of robust state feedback H∞ for discrete time nonlinear system represented by Takagi-Sugeno fuzzy systems. Based on fuzzy lyapunov function, the condition ,which is represented in the form of Liner Matrix Inequalities (LMI), guarantees the H∞ performance of the T-S fuzzy system with uncertainties. By comparison with recent literature, this approach will be more relaxed condition. Finally, an example is given to illustrate the proposed result.

Keywords: fuzzy lyapunov function, H∞ control , linear matrix inequalities, state feedback, T-S fuzzy systems

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Authors: Purnima Pandit

Abstract:

Malaria remains one of the world’s most deadly infectious disease and arguably, the greatest menace to modern society in terms of morbidity and mortality. To choose the right treatment and to ensure a quality of life suitable for a specific patient condition, early and accurate diagnosis of malaria is essential. It reduces transmission of disease and prevents deaths. Our work focuses on designing an efficient, accurate fuzzy inference system for malaria diagnosis.

Keywords: fuzzy inference system, fuzzy logic, malaria disease, triangular fuzzy number

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Authors: Negin Binesh, Mohammad Hossein Niksokhan, Amin Sarang

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Best Management Practices (BMPs) are considered as one of the most important structural adaptive measures to climate change and urban development challenges in recent decades. However, not every location is appropriate for applying BMPs in the watersheds. In this paper, location prioritization of two kinds of BMPs was done: Pourous pavement and Detention pond. West Flood-Diversion (WFD) catchment in northern parts of Tehran, Iran, was considered as the case study. The methodology includes integrating the results of Storm Water Management Model (SWMM) into Fuzzy Analytic Hierarchy Process (FAHP) method using Geographic Information System (GIS). The results indicate that mostly suburban areas of the watershed in northern parts are appropriate for applying detention basin, and downstream high-density urban areas are more suitable for using permeable pavement.

Keywords: adaptive measures, BMPs, location prioritization, urban flooding

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Authors: Trilok Mathur, Shivi Agarwal

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This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods.

Keywords: Caputo-type fuzzy fractional derivative, Fractional Riccati differential equations, Laplace-Adomian-Pade method, Mittag Leffler function

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Authors: B. Güney, Ç. Teke

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In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit.

Keywords: food industry, fuzzy linear programming, fuzzy logic, linear programming

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Authors: Yurii Bloshko, Oksana Olar

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This paper presents the analysis of 6 different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms

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