In this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...

Each noun in natural languages can have attribute values, which are in general adjectives, and action values, which are in general verbs. In the computational verb theory, a computational verb collapse can transform an action value into an attribute value while computational verb extension principles can transform an attribute value into action values. The transformations between attribute valu...

During the past several years fuzzy logic control has swell from one of the major active and profitable areas for research in the application of fuzzy set, especially in the zone of industrial process which do not lead themselves to control conventional methods because of lack of quantitative data regarding the input-output relations. Fuzzy control is based on fuzzy logica logical system which ...

We study direct limits and reduced products of algebras with fuzzy equalities. On the one hand, algebras with fuzzy equalities are natural fuzzy structures that disallow to map similar arguments to dissimilar ones. On the other hand, they are exactly the semantic structures of the equational fragment of first-order fuzzy logic. In this paper we propose generalizations of direct limits and reduc...

In classical (two-valued) logic, CNF and DNF forms of each propositional formula are equivalent to each other. In fuzzy logic, CNF and DNF forms are not equivalent, they form an interval that contains the fuzzy values of all classically equivalent propositional formulas. If we want to select a single value from this interval, then it is natural to select a linear combination of the interval's e...

nowadays, by the expansion of information technology in human life and dependence of business upon it, data protection, as one the most valuable and critical assets of the organization, has become the vital tool of modern industry and prerequisite for sustaining business process. in order to face the challenges and to take advantage of new opportunities brought forth by it advances we suggest o...

in this article, a speed control of dc motor is designed and illustrated using fuzzy logic-based programmable logic controller (plc). the dc motor is an attractive part of electrical equipment in many industrial applications requiring variable speed and load specifications due to its ease of controllability. the designed system is consisted of three main parts including programmable logic contr...

This paper marks the 50th anniversary of the publication of my first paper on fuzzy sets, “Fuzzy sets,” Information and Control, 1965. What is of historical interest is that initially—and for some time thereafter—my paper was an object of indifference, skepticism and derision. A prominent school of thought claimed that fuzzy set theory is probability theory in disguise. Positive comments were f...