A new lexicographical approach for ranking fuzzy numbers

In the literature many ranking methods have been proposed for comparing the fuzzy numbers, most of them suffer from plenty of shortcomings such as complex calculations, inconsistency with human intuition. To overcome such shortcomings, a new ranking method is proposed for L-R flat fuzzy numbers which is based on the lexicographical ordering approach. It is shown that proposed ranking method satisfies all the reasonable properties of the ordering fuzzy quantities proposed by Wang & Kerre (Fuzzy Sets and Systems 118(2001) 375-385). Finally a comprehensive comparison is done between the existing ranking methods with the proposed one to demonstrate the effectiveness of the proposed ranking method. Keywords: Ranking method, L-R flat fuzzy number

Investors’ preference order of fuzzy numbers

AbstractNowadays greater and greater realistic financial problems are modeled by using the stochastic programming in the fuzzy environment. Hence, ranking a set of fuzzy numbers that is consistent with the investors’ preference becomes important for modelling a realistic problem. In this paper, we will provide a new ranking procedure that is consistent with the preference of the conservative investors. Our ranking procedure satisfies the axioms of three order relations for the separable fuzzy numbers or the triangle fuzzy numbers. We found that our ranking procedure has a better capability of discriminating the order of two fuzzy numbers. For the LR-type fuzzy numbers, our ranking procedure reduces the computational time substantially

A New Sign Distance-Based Ranking Method for Fuzzy Numbers

In this paper, a new sign distance-based ranking method for fuzzy numbers is proposed. It is a synthesis of geometric centroid and sign distance. The use of centroid and sign distance in fuzzy ranking is not new. Most existing methods (e.g., distance-based method [9]) adopt the Euclidean distance from the origin to the centroid of a fuzzy number. In this paper, a fuzzy number is treated as a polygon, in which a new geometric centroid for the fuzzy number is proposed. Since a fuzzy number can be represented in different shapes with different spreads, a new dispersion coefficient pertaining to a fuzzy number is formulated. The dispersion coefficient is used to fine-tune the geometric centroid, and subsequently sign distance from the origin to the tuned geometric centroid is considered. As discussed in [5-9], an ideal fuzzy ranking method needs to satisfy seven reasonable fuzzy ordering properties. As a result, the capability of the proposed method in fulfilling these properties is analyzed and discussed. Positive experimental results are obtained

A Fuzzy Modelling of a Hybrid MCDM Method for Supplier Selection = Egy hibrid MCDM-módszer fuzzy modellezése a beszállítók kiválasztásához

This article examines the significance of supplier selection in the procurement process, which has grown in prominence as a result of globalization and outsourcing. When selecting the best suppliers, supply chain managers must consider a variety of quantitative and qualitative aspects, as these have a substantial impact on supply chain performance. Multi-criteria decision-making (MCDM) approaches can help in this process by taking into account many competing considerations. However, due to uncertainties and ambiguity, supplier selection is a complex process, and fuzzy multi-criteria decision-making approaches can be used to determine the best supplier for the company's key operations. This research suggests a hybrid MCDM strategy that makes use of fuzzy modeling to help with complex decision-making processes. Organizations can improve their supply chain performance by selecting the best supplier based on numerous parameters such as cost, quality, delivery time, and supplier reputation. Jelen tanulmány a beszállítók kiválasztásának jelentőségét vizsgálja a beszerzési folyamatban, amely a globalizáció és a kiszervezés következtében egyre nagyobb jelentőségre tett szert. A legjobb beszállítók kiválasztásakor az ellátási lánc vezetőinek számos mennyiségi és minőségi szempontot kell figyelembe venniük, mivel ezek jelentős hatással vannak az ellátási lánc teljesítményére. A többkritériumos döntéshozatal (MCDM) megközelítések számos egymással versengő szempont figyelembevételével segíthetnek ebben a folyamatban. A bizonytalanságok és a többértelműség miatt azonban a beszállító kiválasztása összetett folyamat, és a fuzzy többkritériumú döntéshozatali megközelítések segítségével meghatározható a vállalat kulcsfontosságú műveleteihez legmegfelelőbb beszállító. Ez a kutatás egy hibrid MCDM stratégiát javasol, amely a fuzzy modellezést használja fel a komplex döntéshozatali folyamatok segítésére. A szervezetek számos paraméter, például a költségek, a minőség, a szállítási idő és a beszállító hírneve alapján a legjobb beszállító kiválasztásával javíthatják ellátási láncuk teljesítményét

Defuzzification of groups of fuzzy numbers using data envelopment analysis

Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships

Adjustable Security Proportions in the Fuzzy Portfolio Selection under Guaranteed Return Rates

[[abstract]]Based on the concept of high returns as the preference to low returns, this study discusses the adjustable security proportion for excess investment and shortage investment based on the selected guaranteed return rates in a fuzzy environment, in which the return rates for selected securities are characterized by fuzzy variables. We suppose some securities are for excess investment because their return rates are higher than the guaranteed return rates, and the other securities whose return rates are lower than the guaranteed return rates are considered for shortage investment. Then, we solve the proposed expected fuzzy returns by the concept of possibility theory, where fuzzy returns are quantified by possibilistic mean and risks are measured by possibilistic variance, and then we use linear programming model to maximize the expected value of a portfolio’s return under investment risk constraints. Finally, we illustrate two numerical examples to show that the expected return rate under a lower guaranteed return rate is better than a higher guaranteed return rates in different levels of investment risks. In shortage investments, the investment proportion for the selected securities are almost zero under higher investment risks, whereas the portfolio is constructed from those securities in excess investments.[[notice]]補正完