# Fuzzy Ahp

Topics: Fuzzy logic, Multi-criteria decision analysis, Decision making Pages: 10 (3144 words) Published: April 1, 2013
Fuzzy Analytical Hierarchy Process (FAHP) Based Model for Multi Criteria Decision Making (MCDM) Parag A. Guruji, Chandan M. Bhattad
Department of Computer Science and Engineering, Walchand College of Engineering Sangli (An Autonomous Institute)

Vishrambag, Sangli, Maharashtra, India- 416415

Abstract: The application of fuzzy AHP to the multi criteria decision making has brought great improvement in the realistic decision making by providing means for quantifying the qualitative properties which are closer to reality. The considerable amount of context specific work has been done in the area of application of FAHP in MCDM. In this paper, we discuss a generic model for applying FAHP in MCDM systems whose purpose is to make the design of MCDM systems context independent to the maximum extent. The fundamental fuzzy operations and further functional steps in the working of the model are emphasized on in this paper. The application of this model to the network security evaluation problem is discussed as an illustration, which explains the use of the model under consideration as a basic skeleton structure for the designing of corresponding intelligent MCDM.

chair, (or say a car)she recognizes it to be a chair (or a car) by “the degree of closeness” of this new shape with a “predefined ideal value” which is a known chair’s shape present in her memory in this case. Thus, in fuzzy logic, the convention prescribing that a statement is either true or false is changed and is a matter of degree measured on an ordered scale S that is no longer {0, 1}, but usually the unit interval [0, 1]. This degree of fit is called degree of truth of the statement φ in the interpretation I. Fuzzy statements have the form φ ≥ l or φ ≤ u, where, l, u ∈ [0, 1] and φ is a fuzzy statement. Fuzzy statements encode that the degree of truth of φ is at least equal to l and at most equal to u. B. MCDM (Multi Criteria Decision Making) The name itself suggests that this process involves selecting the single alternative among many of them available. To make a logically justifiable decision, the driving criteria must be defined clearly and evaluated objectively relative to each other. The quest is to take situation context dependent decisions which demands the clear definition of required characteristics (i.e. most economic, most accurate, most optimal, etc.) of expected decision before it has been taken. These characteristics are determined by the criteria used and the extent of importance given to each of the criteria. C. FAHP Fuzzy Analytical Hierarchy Process is a structured technique for organizing and analysing complex decisions, based on mathematics and psychology. The hierarchical structure used herein naturally captures the notion of dependencies within the multiple criteria in MCDM. The accumulation of effects caused due to different values of stake holders at different levels of the hierarchy enables the decision makers to think of nodes at one level at a time without caring

I. INTRODUCTION A. Fuzzy Logic Logic is a science or methodology of defining certain rules that provide the reasoning for occurrence of certain events. Its correctness depends directly upon the degree of resemblance of its predictions with the real results. Fuzzy Logic is one such methodology which works on identification of some ideal value for a subject and defines deviation of real equivalents of that subject from it in different events. So, clearly it differs from Aristotelian logic which deals only with discrete values. In the quest of mimicking human brain’s behaviour in intelligent systems, studies have proven that human brain responds more comfortably in a fuzzy manner. For e.g. A human being perceiving a “new” (not seen before) model of a

for values of its descendants as they’ve been catered already. Clearly, it is achieved by adopting the bottom-up approach for determining the fuzzy values of each node in the...

References: [1] Multi Criteria Decision Making in Fuzzy Description Logics: A First Step by Umberto Straccia [2] A Fuzzy Decision Making Approach In Evaluating Ferry Service Quality by Abdullah Lazim, Nurhanadia Wahab (2010) [3] A Network Security Evaluation Method based on FUZZY and RST
[4] Fuzzy logic and the Decision Matrix by Christopher M. Barlow, 2001 [3] Fuzzy Logic Via Computing With Words by Ashok Deshpande [4] Redesigning Decision Matrix Method with indeterminacy- based inference process by Jose L. Salmerona and Florentin Smarandacheb [5] Fuzzy Systems for MultiCriteria Decision Making by Fábio J. J. Santos and Heloisa A. Camargo (Dec. 2010) [6] A Network Security Evaluation Method based on FUZZY and RST by Zhang Lijuan and Wang Qingxian (2nd ICETC, 2010)