Swapan Raha

Similarity-based approximate reasoning: methodology and application

This correspondence elucidates the importance of similarity, as modeled by a measure of similarity, in approximate reasoning. A set of axioms is proposed to compute a reasonable measure of similarity between two imprecise concepts represented as fuzzy sets. For approximate reasoning, a similarity index between the fact and the antecedent of a rule is computed and is used in the reasoning mechanism. Accordingly, the existing reasoning mechanism is modified. A new similarity-based approximate reasoning methodology is proposed. As an illustration of its effectiveness, the proposed mechanism is used to develop a rule-based pattern classifier.

Reasoning with vague default

Abstract Motivated by the recognized inadequacy of conventional techniques for the representation and manipulation of defaults which allow vague concepts as well, in this paper we present a theoretical study of an approach to default reasoning with vague default based on fuzzy logic. Zadehs theory of possibility is used as a framework for modelling default rule incorporated with vagueness. In our approach we have attempted to represent a vague default value as a vague statement augmented with partial truth. Such a logical proposition may hold true to some degree. The truth values are qualitative and are possibly infinite in number. For reasoning with vague default we have considered a similarity based approach. A new concept of similarity index has been developed. Simple, yet concrete, examples have been considered to illustrate the proposed model.

Reasoning with vague truth

Abstract This paper presents a theoretical study of a formal technique for representing and manipulating partially true vague knowledge in computer. Our approach to the representation and manipulation of such truth-qualified vague knowledge is based on the theory of possibility due to Zadeh. We have introduced a concept of similarity index, a measure of likeness of fuzzy sets of the same type. Using the concept of similarity index, we have formulated a method for reasoning with partially truth-qualified vague knowledge. Examples have been considered to illustrate the usefulness of the proposed method.

Approximate reasoning with time

Abstract The need to make time-dependent assumptions is frequently encountered in many systems, especially in dynamical systems. This paper presents a theoretical study of the representation and manipulation of some vague concepts in the temporally changing world. Our approach to the modeling is based on Zadehs theory of possibility. We introduce a concept of similarity index in reasoning with time. We present two different types of widely used models — one rule-based and another resolution-based — for reasoning with time. We consider simply yet concrete examples to illustrate the usefulness of the proposed models.

Similarity based approximate reasoning: fuzzy control

This paper presents an approach to similarity based approximate reasoning that elucidates the connection between similarity and existing approaches to inference in approximate reasoning methodology. A set of axioms is proposed to get a reasonable measure of similarity between two fuzzy sets. The similarity between the fact(s) and the antecedent of a rule is used to modify the relation between the antecedent and the consequent of the rule. An inference is drawn using the well-known projection operation on the domain of the consequent. Zadehs compositional rule of inference and existing similarity based reasoning techniques are considered for a new similarity based approximate reasoning technique. The proposed mechanism is used to develop a modified fuzzy control system. A new defuzzification scheme is proposed. Simulation results are presented for the well-known inverted pendulum problem.

Matrix Game with Z-numbers

In this paper, a matrix game is considered in which the elements are represented as Z-numbers. The objective is to formalize the human capability for solving decision-making problems in uncertain situations. A ranking method of Z-numbers is proposed and used to define pure and mixed strategies. These strategies are then applied to find the optimal solution to the game problem with an induced pay off matrix using a min max, max min algorithm and the multi-section technique. Numerical examples are given in support of the proposed method.

Approximate reasoning based on generalized disjunctive syllogism

Abstract In this paper we present a purely semantic approach to approximate reasoning based on the extended concept of the law of disjunctive syllogism. The concept of generalized disjunctive syllogism is discussed. Deductive models of approximate reasoning are formulated based on that concept. Simple but concrete examples are cited to illustrate the models.

Analogy between approximate reasoning and the method of interpolation

Abstract In this paper we present an analogy between approximate reasoning and the method of interpolation for a large class of problems. We first describe the analogy and then illustrate it through several simple yet concrete examples. The new results obtained through the method of interpolation are compared with those obtained by the application of the existing method of approximate reasoning. Thus we show that approximate reasoning can also be realized effectively by the method of interpolation.

On extended fuzzy reasoning

Abstract In this paper, we discuss a consistent resolvent (conclusion) in extended fuzzy reasoning. The present work constitutes of a description of the problem together with a demonstration of the theoretical work. The tool for the construction of such a resolvent will include the logical procedures of ordinary and extended fuzzy reasoning.

Approximate reasoning in fuzzy resolution

Resolution is useful in modelling the refutation proof procedure for mechanical theorem proving. Resolution is used in constructing a ‘proof’ of a ‘theorem’. An attempt is made to utilize approximate reasoning methodology in fuzzy resolution. In approximate reasoning methodology — similarity is used in fuzzy inference mechanism. This research proposes that similarity based approximate reasoning — modelling generalised modus ponens/generalised modus tollens — can be used to derive a resolution-like inference pattern in fuzzy logic. The proposal is well-illustrated with artificial examples.