Enhanced Fuzzy Assessment Methodology to Find Overlapping in Membership Function Using K Ratio to Find the Yield of Rice

Abstract

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Introduction

Fuzzy Expert System is developed with the concept of fuzzy logic and fuzzy set. The fuzziness of the fuzzy set is given by the membership function. Membership function is designed for input variable with the labels. Membership function helps to make out the numerical range of the input values with respect to the label. The different shapes of membership function are triangle, trapezoidal and bell as show in Figure 1.

Figure 1.

Membership function shapes

Membership function always exists in universe of discourse. To design the fuzzy expert system the membership function are to be constructed. In many cases there occurs some problem in membership function. They are

• 1.

  In many applications few membership functions will make the response of the developed system very slow. In some cases membership function makes the system fail to provide sufficient output in time, if some changes are made in input. Because of this change there is an oscillation in the system.

• 2.

  Membership function also causes rapid firing of many rule consequents for a little modification in input, but the outcome of the system which makes large change in output. This causes the system to be more instable. So while constructing membership function it should be carefully designed.

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Fuzzy Sets

Fuzzy logic is initiated with the concept of a fuzzy set. Classical sets are with crisp boundaries, usually with ordinary set is called a collection of objects with some properties distinguishing from other objects. A fuzzy set is a set without a crisp, clearly defined boundary. It can contain elements with only a partial degree of membership.

Key Terms in this Chapter

Knowledge Base: A collection of facts, rules, and procedures organized into schemas. A knowledge base is the assembly of all the information and knowledge about a specific field of interest.

Expert: Human being who has developed a high proficiency in making judgments in a specific, usually narrow and domain.

Membership Function: A membership function (MF) is a curve that defines how each point in the input space is mapped to a membership value (or degree of membership) between 0 and 1.

Artificial Intelligence: The branch of computer science that deals primarily with symbolic, non-algorithmic methods of problem solving.

Fuzzy Variable: In fuzzy logic, a quantity that can take on linguistic rather than precise numerical values. For example, a fuzzy variable, yield might have values such as “high,” “medium,” and “low.”

Fuzzy Set: A fuzzy set is a set without a crisp, clearly defined boundary. It can contain elements with only a partial degree of membership.

Inference Rules: In expert systems, a collection of if-then rules that govern the processing of knowledge rules acting as a critical part of the inference mechanism.

Knowledge Rules: A collection of if-then rules that represents the deep knowledge about a specific problem.

K Ratio: K ratio finds whether the membership function is correctly overlapped or not. K ratio lies between 0 to 1.

Inference Engine: The part of an expert system that actually performs the reasoning function.

Correlation Fuzzy Logic: Correlation fuzzy logic helps to find the relationship between the fuzzy numbers and membership function.

Certainty Factors (CF): Technique to represent uncertainty in expert systems where the belief in an event (or a fact or hypothesis) is expressed using the expert's unique assessment.

Expert system (ES): Computer system that applies to reasoning methodologies to knowledge in a specific domain to render advice or recommendations, much like a human expert.

Fuzzy Logic: A logically consistent way of reasoning that can cope with uncertain or partial information. Fuzzy logic is characteristic of human thinking and expert systems.