Review of Fuzzy Decision-Making Methods

Introduction

MCDM has been an important field of study since the 1960s and has generated many conceptual and applied papers and books. To define the desired alternative, assign alternatives in a limited number of categories, or rate alternatives in a specific order of choice, MCDM methods have been developed. In the case of two or more opposing criteria, MCDM is a general term for all approaches that exist to help individuals make choices according to their interests. It can be assumed that using MCDM is a way of coping with complicated issues by splitting the issues into smaller bits. The fragments are reconstructed to show an overall image of decision-making after considering certain factors and making choices about smaller elements. Many MCDM approaches deal with distinct alternatives, which are defined by a collection of parameters. The values of the criteria may be specified as cardinal or ordinal data. Data could be precisely calculated or could be fuzzy, predefined at intervals. Modern MCDM approaches allow decision-makers to work with all the data types listed above.

The concept of decision-making

Different decision-making parameters were used as a dynamic decision-making mechanism that incorporates both quantitive and qualitative variables. Quite a few MCDM methods strategies and methods have been proposed in the past years to pick optimal likely options. In this work, I reviewed a bunch of articles that are published from 2000 to 2014.

As part of organizational analysis, several decision-making standards have evolved in terms of developing mathematical and computational methods to enable the subjective assessment by decision-makers of success criteria. Several experiments have been performed to establish the MCDM. MCDM methods and technologies have been used in many recent studies in the last years to address field challenges such as energy, climate, and productivity, supply chain integration, materials, quality management, GIS building, and project management, protection, and risk management, production processes, technology, and information management, operational analysis, and computer engineering, strategic management and so on.

The concept of fuzzy logic

Lotfi Zadeh invented Fuzzy logic in 1965, which allows for the clarification of intermediate values between traditional conceptions in terms of True and False. Its worth is reflected in its ability to discover information and control variable structures that aid in evaluating massive solutions to issues that cannot be solved using traditional logic. This would be accomplished by affiliating the vector set with the real field [0,1] rather than with the real field {0, 1}. Fuzzy logic is simple to comprehend, and it has powerful modes for interpreting mathematics and subjective features in the real world of computation. In contrast to writing out any possible scenario, it is easier and faster to answer.

Fuzzy logic’s area of expertise include:

• It may help to arrange our thoughts into simple, coherent sentences. As a result, fuzzy logic is a simplification of logic that describes the individual proclivity for objective reasoning.
• It is known as a kind of fuzzy set theory-derived multi-value logic.
• To overcome the types of primary challenges, it relies on conclusions obtained by infinite statements and dialectal dissonances.

It is determined by relative grades of interaction and is driven by vague, misleading, party real, or boundary-requiring human comprehension and cognitive techniques.

Fuzzy decision-making methods

Fuzzy Analytic Hierarchy Process. Fuzzification of Analytic Hierarchy Mechanism, simply Fuzzy AHP, is seen in traditional consumer surveys. Multiple items and alternatives are calculated by way of pairwise comparisons, the weight of each item calculation, and the calculation values for each item and alternative, but the consequence of this comparison is not 0.1, but instead, the amount is given by a numerical value [1].

TOPSIS. The TOPSIS approach suggests that each criterion has a propensity to increase or decrease utility asymptotically, resulting in the results which either positive ideal or negative ideal solutions being readily described. The method of Euclidian distance is recommended to determine the relative closeness of the options to the optimal solution. The priority order of the choices will include a sequence of measurements of these relative distances [2]. The TOPSIS approach transforms the different dimensions of criteria into the non-dimensional one, equivalent to the method called ELECTRE. The best alternative as a result of the TOPSIS method is the closest one to the positive ideal solution and of course, the farthest one to the negative ideal solution. This approach is used for ranking and to achieve the highest results in decision-making on several factors. To determine the criteria in each field, the Fuzzy TOPSIS method can be applied, and then all of the criteria are ranked depending on the region.

ELECTRE. ELECTRE stands for Elimination EtChoix Traduisant la REalite. It is another technique of MCDM technique, and this approach helps decision-makers to choose the right solution based on multiple parameters for the greatest benefit and least dispute. From a defined set of decisions, the ELECTRE method can be applied to choose the right one. There are various versions of ELECTRE, for example, ELECTRE I, II, III, IV, and TRI [3]. The base concepts of all these versions are the same. The difference among them is the functionality and the form of decision challenge. For instance, ELECTRE I is designed for selection problems, ELECTRE TRI is intended for the problems of assignment, and other versions such as I, II, III, IV are for problems of classification. The core concept is the appropriate use of “outranking relations”. Using teamwork indexes, the ELECTRE approach provides the capability to design decision-making. These indexes are matrices of congruence and incongruence. The indexes of congruence and incongruence are used to evaluate the outranking relationships among various choices by the decision-maker. And the decision-maker also uses these indexes to use crisp data which helps to choose the best option.

Grey Theory. Grey Theory is characterized as “incomplete information” or “poor information” and has a high statistical analysis of systems that are partially known and partially unknown. When the process of decision-making isn’t clear, Grey Theory looks at contextual analysis and there’s a lot of evidence, but it’s all new and inadequate [4]. In many decision-making problems, the Grey Theory has been successfully applied in recent years.

When there are a lot of options and requirements, the MCDM approaches mentioned above have been used a lot to find the right one. These approaches were chosen depending on the essence of the decision-making process. The ELECTRE method was used to choose the best, the TOPSIS method was used to rate the best, and Grey Theory was used to choose the best when full data was not available.

Conclusion

The real aim of an automated decision-making system is to allow the decision-maker the opportunity to see through the potential and make the right feasible choice based on historical and current evidence and future estimates. To estimate the threat or risk, and vulnerability of communities and resources to natural and man-made threats in the case of environmental sustainability. The necessitates the translation of evidence into expertise, as well as a detailed analysis of the implications of information usage, and also decision-making and stakeholder engagement. The inference taken from the site investigation is that using fuzzy would only have an indirect solution to the issue. Fuzzy logic is used to evaluate theoretical and practical data in several applications. The various techniques underneath FMCDM assist us in performing a variety of tasks in which common techniques are used for assessment and rating. Each approach is distinct in its way. This is how the analysis of an application can be done with fuzzy theory [5]. In early studies, information modeling is done to determine what information is required for which consumers.