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Approximate Reasoning in Fuzzy Resolution

International Journal of Intelligence Science 2013年第2期3卷 86-98页

作者： Banibrata Mondal swapan raha Department of Mathematics Visva-Bharati University Santiniketan West Bengal India

Resolution is an useful tool for mechanical theorem proving in modelling the refutation proof procedure, which is mostly used in constructing a “proof” of a “theorem”. An attempt is made to utilize approximate reasoning methodology in fuzzy resolution. Approximate reasoning is a methodology which can deduce a specific information from general knowledge and specific observation. It is dependent on the form of general knowledge and the corresponding deductive mechanism. In ordinary approximate reasoning, we derive from A→B and by some mechanism. In inverse approximate reasoning, we conclude from A→B and using an altogether different mechanism. An important observation is that similarity is inherent in fuzzy set theory. In approximate reasoning methodology-similarity relation is used in fuzzification while, similarity measure 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.

关键词： Approximate Reasoning Similarity Index Similarity Based Reasoning Resolution Principle

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Solving Intuitionistic Fuzzy Linear Programming Problem—II

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International Journal of Intelligence Science 2019年第4期9卷 93-110页

作者： Arpita Kabiraj Prasun Kumar Nayak swapan raha Department of Mathematics Siksha-Bhavana (Institute of Sciences) Visva-Bharati University Santiniketan India Department of Mathematics Midnapore College (Autonomous) Midnapore India.

Under non-random uncertainty, a new idea of finding a possibly optimal solution for linear programming problem is examined in this paper. It is an application of the intuitionistic fuzzy set concept within scope of the existing fuzzy optimization. Here, we solve a linear programming problem (LPP) in an intuitionistic fuzzy environment and compare the result with the solution obtained from other existing techniques. In the process, the result of associated fuzzy LPP is also considered for a better understanding.

关键词： Fuzzy Linear Programming Problem (FLPP) Intuitionistic Fuzzy Set (IFS) Intuitionistic Fuzzy Number (IFN) Intuitionistic Fuzzy Linear Programming Problem (IFLPP)

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Solving Intuitionistic Fuzzy Linear Programming Problem

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International Journal of Intelligence Science 2019年第1期9卷 44-58页

作者： Arpita Kabiraj Prasun Kumar Nayak swapan raha Department of Mathematics Siksha Bhavana (Institute of Sciences) Santiniketan India Department of Mathematics Midnapore College (Autonomous) Midnapore India

Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece of information in such a way that these degrees are not complement to each other. Accordingly, an attempt is made to solve intuitionistic fuzzy linear programming problems using a technique based on an earlier technique proposed by Zimmermann to solve fuzzy linear programming problem. Our proposed technique does not require the existing ranking of intuitionistic fuzzy numbers. This method is also different from the existing weight assignment method or the Angelov’s method. A comparative study is undertaken and interesting results have been presented.

关键词： Intuitionistic Fuzzy Set Intuitionistic Index Intuitionistic Fuzzy Number Intuitionistic Fuzzy Linear Programming Problem Fuzzy Linear Programming Problem

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International Journal of Intelligence Science 2018年第4期8卷 89-116页

作者： Asim Pal Injamam Ul Karim Banibrata Mondal swapan raha Department of Mathematics Institute of Sciences Visva-Bharati University Santiniketan India

In this paper, an attempt is made to prove that some similarity based fuzzy systems can be found to behave as function approximators. A typical similarity based fuzzy system is proposed and its behaviour is shown to have the said property. It elucidates the connection between similarity relation and similarity measure of fuzzy sets to fuzzy inference methodology. The concept of similarity relation is used in fuzzification of crisp input values. Similarity index is used in measuring approximate equality of fuzzy sets over a given universe of discourse of a linguistic variable. The similarity between the observation(s) and the antecedent of a rule is used in selecting rule(s) for possible firing and also in modifying the relation between the antecedent and consequent of the rule based on the specific observation. Inference is drawn through the usual composition and subsequently by projecting the modified fuzzy restriction acting on the variables of interest on the universe of the linguistic variable in the consequent of the rule. A specificity based defuzzification scheme is proposed for multiple-rule firing. It has been proved systematically that such a similarity based fuzzy system can uniformly approximate continuous functions to any desired degree of accuracy on a closed and bounded interval. Simulation results are presented for the well-known dc-motor problem. A comparative study is made to establish the validity and efficiency of the proposed similarity based fuzzy system.

关键词： Fuzzification Defuzzification Approximate Reasoning Similarity Relation Similarity Index Universal Approximator

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