In paper the fuzzy linear system d x C x A ~ ~ ~   where A and C are crisp matrices and n m  d~ is a LR fuzzy numbers vector, is investigated in detail. We generalize the definition and arithmetic operations of LR fuzzy numbers and convert the dual fuzzy linear system to two crisp systems of linear equations. Then the minimal fuzzy solution of the original fuzzy system is obtained by solving...

Strict lower sections, strict upper sections and open order intervals (strict order intervals) are classical 9 notions associated to crisp orderings (crisp total preorders). In this paper, we extend these notions to fuzzy orderings. We determine all the fuzzy orderings (they contain all the crisp orderings) which make it possible 11 to compare two fuzzy strict lower sections and two fuzzy stric...

AX B In the paper, a class of fuzzy matrix equations    B where A is an m × n crisp matrix and is an m × p arbitrary LR fuzzy numbers matrix, is investigated. We convert the fuzzy matrix equation into two crisp matrix equations. Then the fuzzy approximate solution of the fuzzy matrix equation is obtained by solving two crisp matrix equations. The existence condition of the strong LR fuzzy s...

this paper proposes a new mathematical model for the integrated procurement-production-distribution problem of a fuzzy mixed integer linear programming (fmilp) type. considering the uncertainty in real problems, a number of parameters such as demand, capacity, and cost where their values are not available or known precisely, have been considered as trapezoidal fuzzy numbers. to solve fuzzy mixe...

in this current study a generalized super-efficiency model is first proposed for ranking extreme efficient decision making units (dmus) in stochastic data envelopment analysis (dea) and then, a deterministic (crisp) equivalent form of the stochastic generalized super-efficiency model is presented. it is shown that this deterministic model can be converted to a quadratic programming model. so fa...

Fuzzy logic and fuzzy set theory enable us to use experts’ uncertain (“fuzzy”) knowledge in decision making. The corresponding methods usually generalize known methods of decision making which are based on the crisp (non-fuzzy) knowledge about the environment. These crisp methods enable us to come up with a crisp decision: e.g., whether we should build a plant or not. When we generalize these m...

The backing of the fuzzy ideal is normal ideal in some ring and in same time there fuzzy set whose is not fuzzy ideal and it backing set is ideal, i.e., it crisp is normal ideal. Consequently, in this paper we constructing a fuzziness function which defined on fuzzy sets and assigns membership grade for every fuzzy set whose it backing set are crisp ideal. Now, Let  be collection of all fuzzy s...

Fuzzy Description Logics generalize crisp ones by providing membership degree semantics for concepts and roles by fuzzy sets. Recently, answering of conjunctive queries has been investigated and implemented in optimized reasoner systems based on the rewriting approach for crisp DLs. In this paper we investigate how to employ such existing implementations for crisp query answering in DL-LiteR ov...

In this paper, we first define the notion of a complete general fuzzyautomaton with threshold c and construct an $H_{nu}$- group, as well as commutativehypergroups, on the set of states of a complete general fuzzy automatonwith threshold c. We then define invertible general fuzzy automata, discussthe notions of “homogeneity, “separation, “thresholdness connected, “thresholdnessinner irreducible...

We propose an extension of the Conn-Index to evaluate fuzzy cluster solutions obtained from fuzzy prototype vector quantization, whereas the original Conn-Index was designed for crisp vector quantization models. The fuzzy index explicitly takes the fuzzy assignments resulting from fuzzy vector quantization into account. This avoids the information loss which would occur if the original crisp in...