Crisp Environments Research Articles

Study of MHD nanofluid flow with fuzzy volume fraction in thermal field-flow fractionation

This paper discusses the magnetohydrodynamic Jeffery–Hamel nanofluid flow (MHD-JHNF) between two rigid non-parallel plane walls. It enhances the study of simple Jeffery–Hamel flow problems to the MHD nanofluid flow problems with uncertain volume fractions. It examines the impact of various parameters, such as channel angles and Reynolds number with magnetic field and nanoparticles, on the fuzzy velocity profiles. The nanoparticle volume fraction is considered an uncertain parameter by using a triangular fuzzy number ranging from 0.0 to 0.2. A novel double parametric form-based homotopy analysis approach with its convergence analysis is introduced to examine the fuzzy velocity profiles at distinct convergent and divergent channel positions and fuzzy velocity boundaries at other channels and illustrates the efficiency of the process. Finally, Maple software is used to make the numerical simulations, and the results are checked with the available results for specific cases in crisp environments.

Detection of the Type of Left and Right Returns-to-Scales Using Envelopment DEA Models in Crisp and Fuzzy Environments: An Application for Predicting Changes in the Stock Market

This paper aims to analyze left and right returns-to-scales in crisp and fuzzy data envelopment analysis (DEA). Since all previous envelopment DEA models for assessing left and right returns-to-scales are parametric, they are prone to encountering infeasibility problems, producing incorrect or different solutions for determining the type of returns-to-scale because of the different choices of parameter values. This misdiagnosis will lead to poor management decisions. Due to the mentioned problems, the issue of one-sided returns-to-scale has also not been studied in inaccurate environments. The present paper first proposes an alternative method of left and right returns-to-scales determination with crisp data to address this problem. This approach develops two non-parametric envelopment DEA models for analyzing left and right returns-to-scales. Then, the proposed method is extended to the fuzzy environment where data are considered more realistic. Due to its major advantages, credibility measure is used for solving fuzzy DEA models built to determine left and right returns-to-scales. As an application of the proposed method, data of companies in the Iran stock market are collected for 2014–2019 as fuzzy data and frontier units are analyzed by one-sided returns-to-scale.

Two-echelon imperfect production fuzzy supply chain model for reliability dependent demand with probabilistic deterioration and rework

This paper develops a fuzzy two-layer supply chain for manufacturer and retailer with defective and non-defective types of products. The manufacturer produces up to a specific time, including faulty and non-defective items, and after the screening, the non-defective item sends to the retailer. The retailer’s strategy is to do the screening of items received from the manufacturer; subsequently, the perfect quality items are used to fulfill the customer’s demand, and the defective items are reworked. The retailer considers that customer demand is time and reliability dependent. The supply chain considers probabilistic deterioration for the manufacturer and retailers along with the strategies such as production rate, unit production cost, cost of idle time of manufacturer, screening, rework, etc. The optimum average profit of the integrated model is evaluated for both the cases crisp and fuzzy environments. Managerial insights and the effect of changes in the parameters’ values on the optimal inventory policy under fuzziness are presented.

Solidarity Value and Solidarity Share Functions for TU Fuzzy Games

TU games under both crisp and fuzzy environments describe situations where players make full (crisp) or partial (fuzzy) binding agreements and generate worth in return. The challenge is then to decide how to distribute the profit among them in a rational manner: we call this a solution. In this paper, we introduce the notion of solidarity value and the solidarity share function as a suitable solution to TU fuzzy games. Two special classes of TU fuzzy games, namely, TU fuzzy games in Choquet integral form and in multilinear extension form, are studied and the corresponding solidarity value and the solidarity share functions are characterized.

Bi-cooperative games in bipolar fuzzy settings

In this paper, we introduce the notion of a bi-cooperative game with Bipolar Fuzzy Bi-coalitions and discuss the related properties. In many decision-making situations, players show bipolar motives while cooperating among themselves. This is modelled in both crisp and fuzzy environments. Bi-cooperative games with fuzzy bi-coalitions have already been proposed under the product order of bi-coalitions where one had memberships in [0, 1]. In the present paper, we adopt the alternative ordering: ordering by monotonicity and account for players’ memberships in , a break from the previous formulation. This simplifies the model to a great extent. The corresponding Shapley axioms are proposed. An explicit form of the Shapley value to a particular class of such games is also obtained. Our study is supplemented with an illustrative example.

A green supply chain production inventory model with uncertain holding cost

A green supply chain (GrSC) model with two plants facilities is formulated under uncertain environment. At first suppliers receive the deteriorating items in a lot and supplies the fresh units to manufacturer for production. Manufacturer has two plants: plant-1 and plant-2. Manufacturer purchases these fresh raw materials at a constant rate from supplier to manufacture the main product in plant-1. Retailer-I has purchased this product from manufacturer of plant-1 to sale it to the customers. The residue units of plant-1 has transferred to plant-2 with constant rate to manufacture another usable by-product. Retailer-II then purchases usable by-product and sales to the customers. Ideal costs of suppliers, manufacturer and retailers have been taken into account. Due to complexity of market situation, all inventory holding costs are considered as uncertain variables and these are reduced to crisp ones using uncertain theory. Supply rate, production rate and by-production rates are assumed as decision variables. Integrated model has been developed and solved analytically in crisp and uncertain environments to find the optimum value of the decision variables. Finally corresponding individual profits are calculated through numerical and graphical methods.

Mathematical model of glucose-insulin regulatory system on diabetes mellitus in fuzzy and crisp environment

In this paper we study the mathematical model for glucose insulin regulatory system of diabetes mellitus in fuzzy and crisp environment. To how the behavior of the model is changes in fuzzy environment is discussed briefly. The stability analyses on fuzzy and crisp environments are illustrated. The numerical solutions are found in both cases.

The robust linear programming technique for multi-dimensional analysis of preferences

The linear programming technique for multi–dimensional analysis of preferences (LINMAP) is one of the noted multi–attributes decision making (MADM) techniques and has been implemented in crisp and fuzzy environments. Robust optimisation attempts to obtain a solution which is feasible in all circumstances arising due to the uncertainty of parameters. The purpose of this study is to extend the LINMAP method for addressing robustness in MADM problems. In this methodology, robust optimisation concepts are used to describe robustness in decision information and decision making processes. Each alternative is evaluated based on its weighted distance to a robust positive ideal solution (RPIS). The RPIS and the robust weights of attributes are estimated using a new robust linear programming technique. Finally, Monte Carlo simulation is applied to test the robustness of the solution. A numerical example is provided to illustrate the effectiveness of the methodology.

Genetic Algorithm Based Hybrid Fuzzy System for Assessing Morningness

This paper describes a real life case example on the assessment process of morningness of individuals using genetic algorithm based hybrid fuzzy system. It is observed that physical and mental performance of human beings in different time slots of a day are majorly influenced by morningness orientation of those individuals. To measure the morningness of people various self-reported questionnaires were developed by different researchers in the past. Among them reduced version of Morningness-Eveningness Questionnaire is mostly accepted. Almost all of the linguistic terms used in questionnaires are fuzzily defined. So, assessing them in crisp environments with their responses does not seem to be justifiable. Fuzzy approach based research works for assessing morningness of people are very few in the literature. In this paper, genetic algorithm is used to tune the parameters of a Mamdani fuzzy inference model to minimize error with their predicted outputs for assessing morningness of people.

A fuzzy based decision model for nontraditional machining process selection

Manufacturing systems are processes in which inputs obtained from interior and exterior sources are transformed into an output by gathering inputs in an optimal way to guide the enterprises. Machining process plays a critical role in industry, and thus, directly affects the efficiency of the manufacturing systems. Due to different importance of the conflicting criterions, the multi-criteria decision-making methods are extremely useful in the selection process of the proper machining type. This study provides distinct systematic approaches in fuzzy and crisp environments to deal with the selection problem of proper machining process and proposes a decision support model for the guidance of decision makers to assess potentials of seven distinct nontraditional machining processes, namely laser beam machining, plasma arc machining, water jet machining, abrasive water jet machining, electrochemical machining, electrical discharge machining (EDM), and wire–EDM in the cutting process of carbon structural steel with the width of plate of 10 mm. The required data for decision and weight matrices are obtained via a questionnaire to specialists, as well as by deep discussions with experts and making use of past studies. Finally, an application of the proposed model is also performed via the SETED 1.0 software to show the applicability of the model.

An intelligent algorithm for optimum forecasting of manufacturing lead times in fuzzy and crisp environments

The manufacturing lead time (MLT) prediction is a vital activity in any manufacturing organisation. This study presents a comprehensive procedure for comparing fuzzy regressions (FR) and conventional regressions (CR), artificial neural network (ANN), adaptive network fuzzy inference system (ANFIS) and genetic algorithm (GA) for manufacturing lead time estimation in both crisp and ambiguous environments. According to a proper sensitivity analysis, the best model is selected based on the lowest mean absolute percentage error (MAPE). Weekly lead times for a large complex electric-motor assembly line are chosen as the actual case of this study. The results of the models implemented on the data for 70 weeks in the assembly line illustrate the applicability and superiority of the proposed algorithm.

Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment

The aim of this article is further extending the linear programming techniques for multidimensional analysis of preference (LINMAP) to develop a new methodology for solving multiattribute decision making (MADM) problems under Atanassov's intuitionistic fuzzy (IF) environments. The LINMAP only can deal with MADM problems in crisp environments. However, fuzziness is inherent in decision data and decision making processes. In this methodology, Atanassov's IF sets are used to describe fuzziness in decision information and decision making processes by means of an Atanassov's IF decision matrix. A Euclidean distance is proposed to measure the difference between Atanassov's IF sets. Consistency and inconsistency indices are defined on the basis of preferences between alternatives given by the decision maker. Each alternative is assessed on the basis of its distance to an Atanassov's IF positive ideal solution (IFPIS) which is unknown a prior. The Atanassov's IFPIS and the weights of attributes are then estimated using a new linear programming model based upon the consistency and inconsistency indices defined. Finally, the distance of each alternative to the Atanassov's IFPIS can be calculated to determine the ranking order of all alternatives. A numerical example is examined to demonstrate the implementation process of this methodology. Also it has been proved that the methodology proposed in this article can deal with MADM problems under not only Atanassov's IF environments but also both fuzzy and crisp environments.

FUZZY LINEAR PROGRAMMING APPROACH TO MULTI-ATTRIBUTE DECISION-MAKING WITH LINGUISTIC VARIABLES AND INCOMPLETE INFORMATION

The aim of this paper is to develop a new fuzzy linear programming technique for solving multi-attribute decision-making (MADM) problems with incomplete weight preference information under fuzzy environments. In this methodology, linguistic variables are used to capture fuzziness in decision information and decision-making processes by means of a fuzzy decision matrix. Consistency and inconsistency indices are defined on the basis of preference relations between alternatives given by the decision maker under uncertain environments. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) which is unknown a priori. Then the FIS and the weights of attributes are estimated using a new linear programming model based upon the consistency and inconsistency indices defined. The fuzzy distance of each alternative to the FIS can be calculated to determine the ranking order of all alternatives. An extended illustrative example on the selection of air-fighters is presented to demonstrate the implementation process of this methodology. The methodology proposed in this paper can deal with MADM problems under not only fuzzy environments but also crisp environments. Also it has been proven that different weight information structures may result in different final decision results.

Fuzzy LINMAP method for multiattribute decision making under fuzzy environments

The Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) developed by Srinivasan and Shocker [V. Srinivasan, A.D. Shocker, Linear programming techniques for multidimensional analysis of preference, Psychometrika 38 (1973) 337–342] is one of the existing well-known methods for multiattribute decision making (MADM) problems. However, the LINMAP only can deal with MADM problems in crisp environments. Fuzziness is inherent in decision data and decision making processes, and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy ratings. The aim of this paper is further extending the LINMAP method to develop a new methodology for solving MADM problems under fuzzy environments. In this methodology, linguistic variables are used to capture fuzziness in decision information and decision making processes by means of a fuzzy decision matrix. A new vertex method is proposed to calculate the distance between trapezium fuzzy number scores. Consistency and inconsistency indices are defined on the basis of preferences between alternatives given by the decision maker. Each alternative is assessed on the basis of its distance to a fuzzy positive ideal solution (FPIS) which is unknown. The FPIS and the weights of attributes are then estimated using a new linear programming model based upon the consistency and inconsistency indices defined. Finally, the distance of each alternative to the FPIS can be calculated to determine the ranking order of all alternatives. A numerical example is examined to demonstrate the implementation process of this methodology. Also it has been proved that the methodology proposed in this paper can deal with MADM problems under not only fuzzy environments but also crisp environments.

Buyer–seller fuzzy inventory model for a deteriorating item with discount

Multi-objective economic lot size models of deteriorating items for both the buyer and the seller are developed in crisp and fuzzy environments. A buyer tries to minimize total average cost and at the same time the seller maximizes the total average revenue allowing discount on bulk purchase with the restricted material cost of the buyer. Here, the total average expenditure for the buyer, the estimated total average revenue for the seller and the resource for the material purchase are assumed to be crisp (Model 1) and fuzzy (Model 2) in nature. The impreciseness in the above objectives and constraint have been expressed by fuzzy linear membership functions. It has been solved by the additive goal and fuzzy additive goal programming methods with different weights. Also, to ensure the achievement level, thresholds are considered in crisp and fuzzy models. All the models are illustrated with numerical examples and the results are compared.

Multi-Objective Fuzzy Inventory Model For Deteriorating Items With Shortages Over A Finite Time Horizon

We consider here the inventory problems with infinite rate of replenishment in crisp and fuzzy environments over a finite time horizon for deteriorating multi-items taking time dependent demand and allowing shortages and equal replenishment cycles. Here, the objectives of maximizing the profit and minimizing the replenishment cost are imprecise in nature. Total shortage cost is assumed to be limited but vague and imprecise in non-stochastic sense. The impreciseness in the above objectives’ and constraint’ goals have been expressed by fuzzy linear Membership Functions (MFs). Under these assumptions, a Decision Maker (DM) is confronted with four possibilities depending upon the nature of the first and last cycles and he/she has to choose the best one for maximum profit-ratio (i.e. the ratio of total profit to total cost). Hence, both crisp and fuzzy models with different shortage criteria are developed and solved by the weighted fuzzy non-linear programming (WFNLP) and goal attainment methods (GAM). Fuzzy models have also been solved by an integrated goal attainment and fuzzy non-linear programming technique (GAFNLP). Models are illustrated with numerical examples and the results are compared.

Determining the feature relevance for non-classically described objects and a new algorithm to compute typical fuzzy testors

In this paper we introduce an algorithm for computing all the typical fuzzy testors of a training matrix with non-classically described objects in Goldman's approach. We also introduce a new expression for determining the feature relevance in crisp and fuzzy environments.