Selection method by fuzzy set theory and preference matrix

In fuzzy decision making problems, fuzzy ranking is one of the most preferred aeras. The aim of this paper to develop a new ranking method which is reliable and doesnot need tremendous arithmetic calculations. Also it can be used for all type of fuzzy numbers which are represented as crisp form or in linguistic form. Fuzzy multi criteria decision making commonly employs methods such as ordering method,Fuzzy Analytic Hierarchy Process [FAHP], Fuzzy Technique for Order Preference by Similarity to Ideal Solution [FTOPSIS]and hybrid method. The FAHP commonly uses triangular fuzzy numbers and trapezoidal fuzzy numbers while the FTOPSIS method identifies the best alternative as the one that is nearest to the positive ideal solution and farthest to the negative ideal solution. Although both these methods have been widely used, they have their drawbacks. The accuracy of these methods decreases as the number of alternative increases i.e. the more complex the problem, less the accuracy and all the methods have many computations. In order to overcome this problem, we propose a method which is a combination of method of Blin and Whinston(1973) and method of Shimura(1973). This way the advantages of both the methods may be utilized to arrive at a decision that involves vague data. In this  paper, we use the concept of preference matrix to find the membership grades and calculate the ranking. Keywords: Fuzzy set, preference matrix, multi person decision making, multi criteria decision making(MCDM), relativity function matrix

Fuzzy Risk Analysis for a Production System Based on the Nagel Point of a Triangle

Ordering and ranking fuzzy numbers and their comparisons play a significant role in decision-making problems such as social and economic systems, forecasting, optimization, and risk analysis problems. In this paper, a new method for ordering triangular fuzzy numbers using the Nagel point of a triangle is presented. With the aid of the proposed method, reasonable properties of ordering fuzzy numbers are verified. Certain comparative examples are given to illustrate the advantages of the new method. Many papers have been devoted to studies on fuzzy ranking methods, but some of these studies have certain shortcomings. The proposed method overcomes the drawbacks of the existing methods in the literature. The suggested method can order triangular fuzzy numbers as well as crisp numbers and fuzzy numbers with the same centroid point. An application to the fuzzy risk analysis problem is given, based on the suggested ordering approach

Density aggregation operators based on the intuitionistic trapezoidal fuzzy numbers for multiple attribute decision making

With respect to the multiple attribute decision making problems in which the attribute values take the form of the intuitionistic trapezoidal fuzzy numbers, some methods based on density aggregation operators are proposed. Firstly, the definition, expected value and the ranking method of intuitionistic trapezoidal fuzzy numbers are introduced, and the method of calculating density weighted vector is proposed. Then some density aggregation operators based on interval numbers and intuitionistic trapezoidal fuzzy numbers are developed, and a multiple attribute decision making method is presented. Finally an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness

Defuzzification of intuitionistic Z-Numbers for fuzzy multi criteria decision making

Z-numbers and intuitionistic fuzzy numbers are both important as they consider the reliability of the judgement, membership and non-membership functions of the numbers. The combination of these two numbers produce intuitionistic Z-numbers which need to be defuzzified before aggregation of multiple experts’ opinions could be done in the decision making problems. This paper presents the generalised intuitionistic Z-numbers and proposes a centroid-based defuzzification of such numbers, namely intuitive multiple centroid. The proposed defuzzification is used in the decision making model and applied to the supplier selection problem. The ranking of supplier alternatives is evaluated using the ranking function based on centroid. In the present paper, the ranking is improved since the intuitionistic fuzzy numbers (IFN) are integrated within the evaluations which were initially in form of Z-numbers, considering their membership and non-membership grades. The ranking of the proposed model gives almost similar ranking to the existing model, with simplified but detailed defuzzification method

Simulation-based evaluation of defuzzification-based approaches to fuzzy multi-attribute decision making

This paper presents a simulation-based study to evaluate the performance of 12 defuzzification-based approaches for solving the general fuzzy multiattribute decision-making (MADM) problem requiring cardinal ranking of decision alternatives. These approaches are generated based on six defuzzification methods in conjunction with the simple additive weighting (SAW) method and the technique for order preference by similarity to the ideal solution method. The consistency and effectiveness of these approaches are examined in terms of four new objective performance measures, which are based on five evaluation indexes. The Simulation result shows that the approaches, which are capable of using all the available information on fuzzy numbers, effectively in the defuzzification process, produce more consistent ranking outcomes. In particular, the SAW method with the degree of dominance defuzzification is proved to be the overall best performed approach, which is, followed by the SAW method with the area center defuzzification. These findings are of practical significance in real-world settings where the selection of the defuzzification-based approaches is required in solving the general fuzzy MADM problems under specific decision contexts

An integrated fuzzy approach to solving multi-criteria decision making problems / Nor Hanimah Kamis

Multi-criteria decision making (MCDM). Method is a technique where alternatives or options are assessed based on a set of criteria. Criteria weights determination and ranking of alternatives are two important aspects in solving MCDM problems. The evaluation of criteria importance by decision makers and performance rating towards alternatives often involve subjective preferences, which are normally vague and imprecise. This study proposed an improvised algorithm in criteria weights determination based on consistent fuzzy preference relations (CFPR). CFPR requires only (n-l) pair-wise comparisons from a given n criteria as compared to other some existing pairwise-based comparison approaches. We improvised Herrera-Viedma's et. al (2004) algorithm by introducing fuzzy numbers to represent input values for the entries of decision matrix. However, application of fuzzy numbers in representing importance of criteria requires tedious calculation. Therefore, centroid-index formula (Chen & Chen, 2000, 2003) was utilized in order to transform fuzzy numbers into crisp values, which indirectly gives lesser computation. The generalized Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method by Wang and Lee (2007) with some modification on criteria weights determination procedure using our proposed algorithm was employed in ranking the alternatives. An example problem on new staff selection in the Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM) Malaysia is given to demonstrate the computational parts of this proposed model. This model can be used as an alternative tool in solving MCDM problems

Ranking trapezoidal fuzzy numbers based on set theoretic indices with Hurwicz criterion / Nazirah Ramli

Ranking of fuzzy numbers (FNs) is an important procedure for many applications in fuzzy theory, in particular, decision-making. Various methods of ranking fuzzy numbers (RFNs) have been developed but no method can rank overlapped trapezoidal fuzzy numbers (TrFNs) satisfactorily in all cases and situations. Some methods produce non-discriminate and non-intuitive results, limited to normal TrFNs and only consider neutral decision makers’ perspective. Some methods also have complex computation and cannot discriminate the ranking of TrFNs having the same mode and symmetric spread. The objective of this thesis is to develop new ranking indices (NRI) based on Sokal & Sneath, Dice and Ochiai set theoretic similarity measure (STSM) indices, and formulate the procedures for ranking overlapped TrFNs where the overlapped TrFNs are classified into seven main types. Eight phases are involved in the development of the NRI which consist of determining the fuzzy maximum (FMax), fuzzy minimum (FMin), evidences, total evidences, pair wise ranking, transitivity of relation and ranking of n TrFNs. The TrFNs involved are taken from the benchmark cases in the literature. The usage of second function principle in determining the FMax and FMin enables the NRI to rank non-normal TrFNs and this has overcome the limitations in some of the previous ranking indices which can only rank normal TrFNs. This study investigates on the development of the NRI and based on that, two observations and three algorithms are created. The determination of ranking results of the NRI involved three stages which are by comparing the values of total evidences in the development phase, by using the observations and by using the algorithms. The observations had rendered the NRI as advantageous method in RFNs since the ranking results can be obtained for all with , and represent pessimistic, neutral and optimistic decision makers’ perspective respectively. Based on the algorithms, the ranking of each type of overlapped TrFNs can be determined merely by the point wise operations. This study evaluates the performance of NRI in terms of rationality, consistency and robustness criteria. The NRI satisfies five axioms on the rationality properties which is similar with some of the previous ranking indices. Most of the ranking results for NRI which are independent with decision makers’ perspective have consistent ranking with the previous methods. The ranking results for some TrFNs with included TrFNs having the same mode and symmetric spread (which cannot be discriminated by a number of the previous methods) are affected by the decision makers’ perspective and this shows that the NRI has strong discrimination ability. For the robustness criterion of the NRI, type of changes of the TrFNs and conditions for robustness are proposed, and these have been applied to the Anugerah Kualiti Naib Canselor (AKNC) case study. The findings show that the NRI is robust for solving AKNC case study with the Dice and Ochiai ranking indices have less computing time compared with some of the previous methods. As the NRI can rank all types of FNs and all types of decision makers’ perspective, and the ranking can be determined merely by the point wise operations, NRI becomes an advantageous ranking method for solving multi-criteria decision-making (MCDM) problems in fuzzy environment. 1 ,05 .0,05 .01 ,5.

Ranking fuzzy numbers by volume of solid of revolution of membership function about axis of support

It is admissible that fuzzy numbers (FNs) are apt for representing imprecise or vague data in real-world problems. While using FNs in decision-making problems, selecting the best alternative among available alternatives is challenging, and therefore, ranking FNs is essential. We can find different studies in the literature, but to our knowledge, no one attempted to rank FNs using the concept of volume. This paper proposes a new method for ranking generalized fuzzy numbers (GFNs) using the volume of the solid obtained by revolving its membership function (MF) about the x-axis. We calculate the volumes of positive and negative sides along with the centroid of a generalized fuzzy number(GFN) to define the fuzzy number(FN) score. This score represents the defuzzified value of FN, is used to select the best alternative, and overcomes the limitations in some existing methods like ranking FNs having the same centroid, crisp numbers, symmetric fuzzy numbers, and FNs with the same core

Dominance intensity measure within fuzzy weight oriented MAUT: an application

We introduce a dominance intensity measuring method to derive a ranking of alternatives to deal with incomplete information in multi-criteria decision-making problems on the basis of multi-attribute utility theory (MAUT) and fuzzy sets theory. We consider the situation where there is imprecision concerning decision-makers’ preferences, and imprecise weights are represented by trapezoidal fuzzy weights.The proposed method is based on the dominance values between pairs of alternatives. These values can be computed by linear programming, as an additive multi-attribute utility model is used to rate the alternatives. Dominance values are then transformed into dominance intensity measures, used to rank the alternatives under consideration. Distances between fuzzy numbers based on the generalization of the left and right fuzzy numbers are utilized to account for fuzzy weights. An example concerning the selection of intervention strategies to restore an aquatic ecosystem contaminated by radionuclides illustrates the approach. Monte Carlo simulation techniques have been used to show that the proposed method performs well for different imprecision levels in terms of a hit ratio and a rank-order correlation measure