Modern general system theory proposed a holistic integrative approach based on input-state-output dynamics as opposed to the traditional reductionist detail based approach. Information complexity and uncertainty required a fuzzy system theory, based on fuzzy sets and fuzzy logic. While successful in dealing with analysis, synthesis and control of technical engineering systems, general system th...

controller design remains an elusive and challenging problem foruncertain nonlinear dynamics. interval type-2 fuzzy logic systems (it2fls) incomparison with type-1 fuzzy logic systems claim to effectively handle systemuncertainties especially in the presence of disturbances and noises, but lack aformal mechanism to guarantee performance. in contrast, adaptive sliding modecontrol (asmc) provides...

Type-2 fuzzy sets have come to play an increasingly important role in both applications and in the general theory of fuzzy sets. The basis of type-2 fuzzy sets is a certain algebra of truth values, as set forth by Zadeh. This paper is a survey of results about this algebra, along with some new material.

The paper introduces a simple, yet powerful axiomatization of Zadeh’s notion of fuzzy set, based on formal fuzzy logic. The presented formalism is strong enough to serve as foundations of a large part of fuzzy mathematics. Its essence is elementary fuzzy set theory, cast as two-sorted first-order theory over fuzzy logic, which is generalized to simple type theory. We show a reduction of the ele...

Abstract: This paper presents a new general type-2 fuzzy logic method for edge detection applied to color format images. The proposed algorithm combines the methodology based on the image gradients and general type-2 fuzzy logic theory to provide a powerful edge detection method. General type-2 fuzzy inference systems are approximated using the α-planes approach. The edge detection method is te...

Using Multi-Criteria Decision-Making (MCDM) to solve complicated decisions often includes uncertainty, which could be tackled by utilizing the fuzzy sets theory. Type-2 fuzzy sets consider more uncertainty than type-1 fuzzy sets. These fuzzy sets provide more degrees of freedom to illustrate the uncertainty and fuzziness in real-world production projects. In this paper, a new multi-criteria ana...

considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. this paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong hausdorff topology.we study interrelationships between this theory and other fuzzy theories suchas intuitionis...

In this paper, the concept of fuzzy intensional logic is elaborated based on fuzzy type theory recently presented by the author.

Today, one of the most fundamental issues within the field of industrial and nonindustrial activities is evaluate the costs performance of the units which are associated with industrial and nonindustrial activities. Data envelopment analysis (DEA) is a nonparametric method for evaluating performance. Fuzzy sets theory is a powerful tool for mentioning ambiguous situations. Traditional DEA model...

Fuzzy languages and fuzzy automata are considered using techniques from algebraic theory of automata. Syntactic monoids of fuzzy languages play a crucial role in the study. Varieties of fuzzy languages are introduced and an Eilenberg-type correspondence between varieties of fuzzy languages, varieties of ordinary languages and varieties of monoids is established.