Zadeh proposed and developed the theory of approximate reasoning in a long series of papers in the 1970’s (see e.g. [28, 29, 30, 31, 32, 34, 35]), at the same time when he introduced possibility theory [33] as a new approach to uncertainty modeling. His original approach is based on a fuzzy set-based representation of the contents of factual statements (expressing elastic restrictions on the po...

This paper adopts the spread of fuzzy variable as a new criteria in practical risk management problems, and develops a novel fuzzy expectation-spread (E-S) model for portfolio optimization problem. Since the spread is defined by Lebesgue-Stieltjes (L-S) integral, its computation for general fuzzy variables is a challenge issue for research, and usually depends on approximation scheme and soft c...

Since its introduction in the mid-sixties (Zadeh, L. A., (1965)), fuzzy set theory has gained recognition in a number of fields in the cases of uncertain, or qualitative or linguistically described system parameters or processes based on approximate reasoning, and has proven suitable and applicable with system describing rules of similar characteristics. It can be successfully applied with nume...

in this paper, we investigate the l-fuzzy proximities and the relationships betweenl-fuzzy topologies, l-fuzzy topogenous order and l-fuzzy uniformity. first, we show that the category of-fuzzy topological spaces can be embedded in the category of l-fuzzy quasi-proximity spaces as a coreective full subcategory. second, we show that the category of l -fuzzy proximity spaces is isomorphic to the ...

In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserv...

The existing Data Envelopment Analysis models for evaluating the relative eciency of a set of decision making units by using various inputs to produce various outputs are limited to crisp data in crisp production possibility set. In this paper, rst of all the production possibility set is extended to the fuzzy production possibility set by extension principle in constant return to scale, and th...

α-recursion lifts classical recursion theory from the first transfinite ordinal ω to an arbitrary admissible ordinal α [13]. Turing machine models for α-recursion and other types of transfinite computation have been proposed and studied [5] and [7] and are applicable in computational approaches to the foundations of logic and mathematics [11]. They also provide a natural setting for modeling ex...