Development of fuzzy process accuracy index for decision making problems

Abstract

Several statistical decision making tools and methods are available to organize evidence, evaluate risks, and aid in decision making. Process capability indices are the summary statistics to point out the process performance. In this paper, these indices are analyzed to obtain a new decision making tool. Process accuracy index (C_a) measures the degree of process centering and gives alerts when the process mean departures from the target value. It focuses on the location of process mean and the distance between mean and target value. We modify the traditional process accuracy index to obtain a new tool under fuzziness. With the proposed tool, specification limits and process mean can be defined as triangular or trapezoidal fuzzy numbers. The proposed tool is illustrated to solve a supplier selection problem.

Introduction

Decision making can be defined as an outcome of evaluation processes leading to determine the most appropriate choice among several alternatives. Every decision making process produces a final choice. The output can be an action or an opinion of choice. Making a decision implies that there are alternative choices to be considered, and in such a case we want not only to identify as many of these alternatives as possible but to choose the one that (1) has the highest probability of success or effectiveness and (2) best fits with our goals, desires, lifestyle, values, and so on. Decision making is a complex problem because of conflicting constraints. An increase in the number of alternatives, goals, and criteria makes difficult to give a decision. Because of this difficulty, research on how to solve such problems has been enormous. It has been widely recognized that most decisions made in the real world take place in an environment in which the goals and constraints are not known precisely because of their complexity. Thus, the problem cannot be defined exactly or represented by a crisp value precisely. To deal with imprecise information or even ill-structured decision problems, Zadeh [34] developed the fuzzy set theory as a modeling tool. He [35] also outlined the generalized theory of uncertainty (GTU) which represents a significant change both in perspective and direction in dealing with uncertainty and information. Recently, Zadeh [36] has viewed fuzzy logic in a nonstandard perspective. In this perspective, the cornerstones of fuzzy logic which are graduation, granulation, precisiation, and the concept of a generalized constraint are discussed.

Fuzzy logic is a branch of mathematics that allows a computer to model the real world in the same way that people do. It provides a simple way to reason with vague, ambiguous, and imprecise input or knowledge. Human beings are involved in the decision analysis since decision making should take into account human subjectivity, rather than employing only objective probability measures. This makes fuzzy decision making indispensable [10].

In this paper, a new tool based on fuzzy process accuracy index is proposed to evaluate process performance. Process accuracy index (C_a) both measures the degree of process centering and gives alerts when the process mean departures from the target value. It is used to make a decision with fuzzy parameters for capturing vagueness under fuzzy environment. The proposed tool is illustrated to make a decision to select the most appropriate supplier in a supplier selection problem.

The rest of this paper is organized as follows: process capability indices are briefly explained in Section 2. New insights to the index C_a are given in Section 3. Then fuzzy process accuracy indices $({\stackrel{\sim }{C}}_a)$ are developed in Section 4. In Section 5, an application to a supplier selection problem using ${\stackrel{\sim }{C}}_a$ index is illustrated. The results and conclusions are summarized in Section 6.