Toward Monotonicity Analysis between Two Vague Concepts Based on Fuzzy Rough Sets
نویسنده
چکیده
A fuzzy rough set approach has been proposed without using any fuzzy logical connectives. By this approach, gradual decision rules are induced from a given decision table. Fuzzy-rough modus ponens and fuzzy-rough modus tollens have been formulated based on the gradual decision rules. The equivalence condition between fuzzy-rough modus ponens and fuzzy-rough modus tollens is discussed. The condition is related to the monotonicity between membership degrees of fuzzy sets. Monotonicity indices are proposed to measure the degree of monotonicity between fuzzy sets.
منابع مشابه
A hybrid filter-based feature selection method via hesitant fuzzy and rough sets concepts
High dimensional microarray datasets are difficult to classify since they have many features with small number ofinstances and imbalanced distribution of classes. This paper proposes a filter-based feature selection method to improvethe classification performance of microarray datasets by selecting the significant features. Combining the concepts ofrough sets, weighted rough set, fuzzy rough se...
متن کاملA New Approach for Knowledge Based Systems Reduction using Rough Sets Theory (RESEARCH NOTE)
Problem of knowledge analysis for decision support system is the most difficult task of information systems. This paper presents a new approach based on notions of mathematical theory of Rough Sets to solve this problem. Using these concepts a systematic approach has been developed to reduce the size of decision database and extract reduced rules set from vague and uncertain data. The method ha...
متن کاملEmpirical Distribution of Non-Precise Data: Roughness and Fuzziness
In many fields, especially in environmetrics and social sciences, it is impossible to obtain exact quantitative data about a variable of interest. Many researchers have suggested that vague, non-precise observations should be described by fuzzy sets. Fuzzy set theory originated by Zadeh (1965) relies on ordering relations that express intensity (degree) of membership of an object in a set. Appl...
متن کاملA comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets: Definitions, properties and robustness analysis
Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuz...
متن کاملFuzzy Set Extensions of the Dominance-Based Rough Set Approach
Rough set theory has been proposed by Pawlak in the early 80s to deal with inconsistency problems following from information granulation. It operates on an information table composed of a set U of objects described by a set Q of condition and decision attributes. Decision attributes make a partition of U into decision classes. Basic concepts of rough set theory are: indiscernibility relation on...
متن کامل